Managerial Economics, 6th Edition
By
Samuelson, Marks
File: Ch01; CHAPTER 1: Introduction to Economic Decision Making
Each question contains a code showing the section of the chapter text from which it was taken. The codes for this chapter are: Code 1 2 3 4
Section Introduction Seven Examples of Managerial Decisions Six Steps to Decision Making Private and Public Decisions
MULTIPLE CHOICE
1. A sensible decision should incorporate a a) List of alternative courses of action. b) Complete prediction of the future. c) Statement of goals and objectives. d) Summary list of pros and cons. e) Answers a and c are both correct. ANSWER: e. SECTION: 1
2. Managerial economics can best be defined as the a) Economic analysis of internal management functions. b) Study of economic incentives in organizations and markets. c) Impact of global economic factors on business. d) Analysis of major management decisions using economic tools. e) None of the above answers is correct. ANSWER: d SECTION: 2
3. Is profit maximization an unambiguous guide to decision making in the private sector? a) Yes. This is clear and results in sound decisions. b) Yes, although profit is of no concern at all to non-profit agencies. c) No, because of risk and uncertainty about future events. d) No, because managers may disagree as to the best means of maximizing profits. e) No, top management’s real financial incentives are usually at odds with profit maximization. ANSWER: c SECTION: 3
4. Are models helpful in predicting the outcomes of decisions?
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a) No, models are too theoretical to be applicable in real world decisions. b) No, because there is too much uncertainty to ever forecast outcomes accurately. c) Yes, even though they simplify the analysis and omit some features of the problem. d) Yes, models can describe situations in complete detail. e) Yes, but large-scale models tend to be prohibitively expensive. ANSWER: c SECTION: 3
5. The two main kinds of models are a) Short run and long run. b) Deterministic and probabilistic. c) Theoretical and pragmatic. d) Simple and complex. e) Mathematical and graphical. ANSWER: b SECTION: 3
6. Sensitivity analysis can best be defined as a) Being sensitive to the impact of the firm’s decisions on other variables. b) Analyzing tradeoffs among multiple objectives. c) Measuring results against objectives. d) Examining the reliability of key data used to make a decision. e) Examining how a decision would change if key economic facts were changed. ANSWER: e SECTION: 3
7. According to the theory of the firm, what is management's ultimate objective? a) Short-term profit, even if this sacrifices long-term profit. b) Maximizing the value of the firm. c) Long-term profit, even if this sacrifices short-term profit. d) Being responsive to all of the firm’s stakeholders. e) Maximizing market share. ANSWER: b SECTION: 4
8. The example of a multinational car maker a) Offers a good case for the use of risk management models. b) involves multiple pricing and production decisions. c) Shows how a firm might respond to trade restrictions. d) Provides a clear case for limited government regulation. e) None of the above answers is correct. ANSWER: b SECTION: 3
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9. Which of the following is NOT one of the suggested steps in decision making? a) Predicting the consequences b) Implementing the decision. c) Defining the problem. d) Negotiating a decision consensus. e) Neither answer b nor d is a decision step. ANSWER: e SECTION: 3
10. Which of the following might cause managers to fail to maximize the value of the firm? a) They have other objectives that conflict with value maximization. b) They may have incomplete information upon which to act. c) They may make mistakes in analysis. d) They may fail to implement decisions that lead to value maximization. e) All of the above. ANSWER: e SECTION: 4
11. According to the satisficing model of management behavior, firms seek a) Some satisfactory level of performance rather than maximization. b) To satisfy all stakeholders: customers, workers, shareholders, and local constituents. c) To satisfy corporate shareholders. d) To maximize sales revenue rather than maximizing the value of the firm. e) A satisfactory level of market share. ANSWER: a SECTION: 4
12. Which of the following is sometimes suggested as an alternative model of management behavior? a) Sales maximization. b) Satisfying multiple stakeholders. c) Maximizing net present value. d) Maximizing the personal wealth and compensation of top management. e) Minimizing the risk of firm bankruptcy. ANSWER: a SECTION: 4
13. In evaluating public programs, benefit-cost analysis a) Considers only measurable benefits and costs. b) Insists that public projects should be profitable, i.e., pay for themselves. c) States that a program should be undertaken if and only if its total benefits exceed its total costs. d) Attempts to impute monetary values to all benefits and costs.
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e) Answers c and d are both correct. ANSWER: e SECTION: 4
14. Making decisions based on overall judgment and experience a) Is especially suited for devising long-term corporate strategy. b) Is the overwhelming norm for top corporate executives. c) Is problematic because the logic of one’s judgment is uncheckable. d) Offers a sound alternative to analytical decision making. e) Answers a and c are both correct. ANSWER: c SECTION: 4
SHORT ANSWER
15. Carefully define managerial economics, and explain how it is useful in decision-making. ANSWER: Managerial economics is the analysis of major management decisions using the tools of economics. It applies familiar concepts such as demand, cost, market structure, resource allocation, and the like. Managerial economics emphasizes the theory of the firm and employs quantitative analysis in making decisions. Simple models are used to emphasize the most important features of the decision problem. SECTION: 1
16. Carefully define the term "model" and explain how models are used in managerial economics. ANSWER: A model is a simplified description of a process, relationship, or other phenomenon. The two main types of models are deterministic and probabilistic. Models are used primarily to explain and to predict economic events. They are useful in selecting key features for analysis (and, therefore, they deliberately ignore less important features). SECTION: 3
17. Carefully define probabilistic and deterministic models, and explain how they differ. ANSWER: Deterministic models are predictive models in which the outcome of a decision is certain (or close enough that it doesn’t matter). In probabilistic models, there is no one certain outcome but, rather, many possible outcomes with a probability attached to each. SECTION: 3
18. How does decision making in the private, for-profit sector differ from decision making in the public sector?
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ANSWER: In the private sector, managers seek maximum value for the firm. Managers focus primarily on the effects of a decision on the firm's profits. With an eye to profit, managers will not generally take into account the impacts (benefits and costs) on other parties. In the public sector, decisions are guided by benefit-cost analysis (not simply profit analysis). The benefits and costs to all affected parties (not just the program’s revenues and costs) must be evaluated and totaled in order to make a sound decision. SECTION: 4
19. What are the two difficulties that may make profit maximization an ambiguous guide to decision making? Explain why they complicate the analysis. ANSWER: The two difficulties are (1) the timing of benefits and costs and (2) the presence of risk and uncertainty. Generally speaking, many decisions involve making costly investments “up front” in return for benefits or profits in the future. This requires the decision-maker to develop comparable measures of present and future monetary values. Uncertainty underscores the fact that some outcomes are not known with complete confidence. Costs may be far larger than expected, benefits far smaller, and delays in completion may diminish profits. The manager’s task is to foresee the range of possible outcomes and to estimate the likelihood of different consequences. SECTION: 4
20. One of the major steps in decision-making is to explore the alternatives. Do most managerial decisions have a few, limited number of options? Explain. Illustrate your answer with an appropriate example. ANSWER: Most decisions have several (often many) competing options. Even when the choices are limited, there are often more alternatives than first meet the eye. For example, Disney had to decide whether to build a new theme park, and if so, where, and what at what scale. In addition, subsequent decisions involved advertising and pricing strategies. Many managerial decisions involve more than a once-for-all choice from a set of options. Instead, managers face a sequence of decisions. For instance, should a firm (1) attempt to develop a new product, (2) if all goes well, when and how should it launch and promote it, and (3) how should it price it (and gear up capacity to supply the expected sales at its chosen price)? SECTION: 3
21. Value maximization is the main objective of top management. Briefly describe alternative objectives. ANSWER: The three most important alternatives are: satisficing behavior, sales maximization, and pursuing the firm’s social responsibilities to all stakeholders. (See the discussion in the text.) SECTION: 4
ESSAY
22. A company is thinking about significantly expanding its production capacity. What variables would it consider in making this decision? What might be useful sources of information to use in estimating the potential profit impact of the expansion?
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ANSWER: The most important variables are increased sales revenues and increased costs. Information on sales revenue would include current price and quantity data and the past growth rate of sales, and the impact the firm’s advertising and promotional spending (and, of course anticipating the likely response of rival firms). Information on costs would include the capital cost of building new facilities or expanding old ones (including borrowing costs influenced by interest rates) and annual fixed and variable costs (for equipment, labor, energy costs) needed to produce the greater level of output. Note that the expansion might bring the firm some reductions in average costs due to the use of new technology. SECTION: 2
23. You head a new startup firm with a business plan calling for opening a number of clinics that perform laser eye surgery to correct common vision problems. You hope that over time your company can claim a substantial share of what you estimate to be a $8 billion per year market. Briefly describe the most important factors influencing your venture’s revenues and costs. Describe the most important risks. ANSWER: A complete answer should point out a number of obvious factors. On the demand side, the key question is the size of the total market willing and able to pay for the laser surgery (so as to dispense with glasses and contact lens). Because the procedure is not covered by insurance, demand will depend directly on the price (per eye) your company and others set for the procedure. Demand also depends upon the real and perceived risks of laser surgery. Demand issues raise a number of decision questions. How should your firm price and promote the clinics and procedures? Should it enlist elite physicians to oversee and endorse your firm’s services (as a means of differentiation). Given current competitors and future entrants, what share of the total market can your firm reasonably expect to claim? Costs are equally important. Medical equipment and office space represent significant capital costs. Besides other operating costs, your company will pay a significant licensing fee (royalty) for each procedure to the laser’s patent holder. Of course, the ultimate average cost per patient will depend on the number of patients you attract and on your scale of operation. Finally, there are significant risks – not only uncertainties on the revenue and cost sides already mentioned – but medical risks to patients and liability and regulatory risks to your company. SECTION 2
24. Carefully define sensitivity analysis, and provide three examples of how a manager might use it. ANSWER: Sensitivity analysis considers how an optimal decision would change if key economic facts or conditions were altered. Some examples of how to use it include: (1) predicting sales under different macro economic conditions (growth or recession), (2) the effects of escalating oil prices on energy costs, or (3) the effect of a close competitor cutting its price. In each case, the changing factor not only affects the firm’s profit, it also implies changes in the firm’s production and pricing decisions. SECTION: 3
25. You are the troubleshooter for a major manufacturing firm. It seems that a particular facility has experienced problems with quality for several years. In addition, there have been some major problems with the facility's labor union. A bitter strike, lasting six months, occurred prior to signing the current contract. Past management teams have visited and inspected the site but have been unable to achieve change, despite detailed study and recommendations. Recently, sales of the facility's product line have declined in the face of increased import competition from an East Asian country, and this is unlikely to change in the near future. Currently, the Board is considering two new courses of action. One is retooling the facility to manufacture a new line of products. This would involve capital costs of several millions of dollars. It would also mean that there would be no production from the facility while retooling and retraining takes place. The second
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option is closing down of the facility. This would involve costs in the form of termination benefits, as well as funding some pension benefits of senior employees. There appear to be no buyers for the plant, and it would likely remain idle for some time. Possibly, no buyer could be found for it, and the plant might be vacant for years, while continuing to be a tax drain on the company. How would you use the steps of decision-making and the concept of value maximization to recommend a course of action to the Board? Explain. ANSWER: Management finds itself on the horns of a dilemma since it appears that any course of action – continuing current production, retooling, or closing the plant – will involve losses. Nonetheless, the tools of managerial economics still apply. Here, the firm seeks the course of action that minimizes its losses (If losses are minimized, then the value of the firm is maintained as far as possible). Thus, management must carefully estimate and compare the relative costs of its options. SECTION: 3
26. In striving to make the best possible decisions, a firm’s CEO always relies on a highly analytical approach. However, the firm’s Chairman of the Board argues that in his experience, the analytical approach can only go so far. He advocates analysis as only one of several decision approaches. What is your view? Discuss and explain. ANSWER: The virtue of the analytical approach is that it considers and analyzes the most important factors involved in a given decision. However, it is not infallible for many of the reasons noted in the chapter. (Managers may have the wrong incentives and/or pursue the wrong objectives. They might lack the necessary information to formulate a sound decision. Or they may fail to implement the decision – no matter how right it is.) As the text notes, “The key is to use the analytical approach flexibly.” Different cases may require different degrees of analysis in each decision step. Certainly, the Chairman is right in insisting that there are other ways to make decisions, ranging from: company rules of thumb, gut checks, invoking one’s experience, judgment and intuition, to “I’ll sleep on it.” These other means might provide useful insights and ingredients. Or to take an extreme case, sometimes, “flashes of genius” may offer decision solutions that are surprising and highly creative (and by no means irrational). For instance, a marketing plan might include radical elements constituting major changes in how a product is offered for sale. This approach is inspired, but it is also risky. It might spectacularly succeed, or just as spectacularly fail. In short, it remains the case that a sound analysis is required to articulate the logic of the decision (indeed, to convince others of its merits). SECTION: 4
27. A small nation is considering upgrading its air force to incorporate new technology. It faces two main choices. The first is to acquire a fleet of the latest fighter aircraft, with the newest electronics and weapons. The cost of the acquisition (assuming that the U.S. President and Congress agree to the sale) is $45 million per plane, including a stock of spare parts that should last five years. The second choice is to buy an electronic upgrade for existing aircraft, with a complete overhaul of the airframes. The cost of such an upgrade is $8 million per plane, with about a 10% loss of fleet because of damage beyond repair and “cannibalization” to obtain the highest number of flyable planes. The upgrading of existing planes results in aircraft with about 90% of the capability of the new aircraft. Top pilots in the small country's air force are concerned that they may not be flying the best aircraft, and could face a disadvantage in combat against newer planes flown by a potential enemy. However, they acknowledge that if a numerical superiority against the enemy can be obtained, an overall victory is still likely. Their theory is that three of the upgraded planes should be able to win against one of the newer planes flown by an enemy (although the pilots expect higher losses in combat). As an economic consultant, how would you advise the defense ministry of the small country in deciding how best to spend its available budget for air defense? What objective(s) are important for this decision? What are the pros and cons of the available options?
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ANSWER: In this case, the objective is not maximum profit or operating revenue, but obtaining the best possible air force within the prescribed budget. The two main alternatives are to purchase new aircraft, or upgrade existing planes. Clearly, an important consideration is the difference in cost of the two possibilities. An upgrade is far cheaper, and results in 90% of the operational capability of the new plane. For $45 million spent on a single new plane, the country can upgrade between five and six existing aircraft. Assuming that the air force pilots are correct that three of the older, upgraded planes can defeat a single, newer plane, upgrading provides a greater effective amount of firepower in a future air conflict. However, an additional issue should be taken into account: higher pilot losses can be expected with the upgrade. The cost of lives lost can be important for a country that places a high value on human life. A sound decision should indicate at least a third possible choice, that is, to order a small number of new planes in addition to upgrading most of the old planes. The new planes could accompany the older planes on missions and stand by to combat enemy fighters. While expensive, it is cheaper than buying an entirely new fleet, and could reduce overall pilot loss. SECTION: 4
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File: Ch02; CHAPTER 2: Optimal Decisions Using Marginal Analysis
Each question contains a code showing the section of the chapter text from which it was taken. The codes for this chapter are: Code 1 2 3 4 5
Section A Simple Model of the Firm Marginal Analysis Marginal Revenue and Marginal Cost Sensitivity Analysis Appendix
MULTIPLE CHOICE
1. In the simple model of the firm, management's main tasks are to a) Set the quantity of output and estimate costs. b) Set output quantity and price. c) Set price and estimate revenue. d) Determine the scale of operation and estimate profit. e) Set advertising spending and price. ANSWER: b SECTION: 1
2. According to the model of the firm, management’s main goal is to a) Satisfy its shareholders. b) Maximize profit. c) Maximize its market share. d) Achieve efficiency – that is, minimize its average cost per unit. e) Maintain steady and predictable earnings growth. ANSWER: b SECTION: 1
3. According to the law of demand, if a firm reduces the price of its good a) Consumers in aggregate will demand more units. b) Consumers will demand roughly the same number of units. c) Consumers will demand more units only if they have the income to pay for them. d) The effect is uncertain; it depends on the behavior of rival firms. e) Competing firms are sure to match the price cut. ANSWER: a SECTION: 1
4. According to the simple model of the firm, management can predict 2-1
Optimal Decisions Using Marginal Analysis
a) The market price only within a wide margin of error. b) The behavior of its main competitors with certainty. c) Costs with certainty, but revenues imprecisely. d) Nether revenues nor costs very precisely. e) Both revenues and costs with certainty. ANSWER: e SECTION: 1
5. Demand is given by Q = 600 - 30P. At price P = $15, the firm’s unit sales are a) 100. b) 150. c) 300. d) 450. e) 600. ANSWER: b SECTION: 1
6. Demand is given by: P = 1,750 - 25Q. If the firm wishes to sell 50 units, the requisite price is a) $500. b) $400. c) $300. d) $200. e) $100. ANSWER: a SECTION: 1
7. The firm’s demand curve is given by Q = 800 - 2P. Therefore, its inverse demand curve is a) MR = 800 – 4P. b) P = 800 – 2Q. c) P = 400 - .5Q. d) P = 800 - .5Q.. e) There is insufficient information to determine the inverse demand curve. ANSWER: c SECTION: 1
8. A firm’s total cost function is given by: C = 100 + 10Q + 2Q 2. At Q = 10, a) Total cost is 400 and marginal cost is 10. b) Marginal cost is constant. c) Average cost is 50. d) Fixed cost is 100 and marginal cost is 50. e) None of the above answers is correct. ANSWER: d SECTION: 3
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9. Marginal analysis measures the effect of a) Changing the firm’s objectives. b) Changes in demand on profit. c) Small changes in one or more decision variables. d) Small changes in revenues and costs. e) Small changes in external economic factors. ANSWER: c SECTION: 2
10. At its current output level, a firm’s marginal profit is positive. Therefore, it should a) Decrease output until marginal profit is zero. b) Increase output because MR < MC. c) Increase both its output and its price. d) Increase output because MR > MC. e) Increase output until it is producing at full capacity. ANSWER: d SECTION: 2
11. A firm’s profit equation is given by: = -200 + 80Q - .2Q2. Therefore, a) Marginal profit = 80 - .2Q. b) The firm’s profit-maximizing output is Q = 400. c) The firm’s profit-maximizing output is Q = 200. d) Answers a and b are both correct. e) None of the answers above is correct. ANSWER: c SECTION: 2
12. Marginal revenue is the a) Price the firm obtains for the last unit sold. b) Change in revenue from a unit increase in price. c) Change in revenue from producing and selling an additional unit of output. d) Amount of additional revenue from an increase in demand. e) Answers a and c are both correct. ANSWER: c SECTION: 3
13. Marginal cost is the a) Additional cost of increased overhead. b) Additional cost of producing an extra unit of output. c) Additional cost of increasing the scale of production. d) Additional cost of increasing use of an input such as labor. e) Variable cost of production.
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ANSWER: b SECTION: 3
14. Starting from the firm’s cost function, marginal cost can be determined by a) Dividing total cost by total output. b) Computing the derivative of the cost function. c) Dividing total variable cost by total output. d) Computing the difference in cost between two vastly different scales of operation. e) Answers b and c are both correct. ANSWER: b SECTION: 3
15. For a downward sloping demand curve, the associated marginal revenue curve a) Coincides with the demand curve. b) Lies below and parallel to the demand curve. c) Has the same price intercept but a steeper slope than the demand curve. d) Is positive for all levels of sales. e) None of the above answers is correct. ANSWER: c SECTION: 3
16. To maximize profit, management should a) Set output to minimize its average cost per unit. b) Set output so that average revenue just equals average cost. c) Set price to maximize profit margin per unit. d) Set output so that marginal revenue equals marginal cost. e) Set output so that marginal revenue is zero. ANSWER: d SECTION: 3
17. A decrease in fixed costs implies that a) Marginal revenue will increase; marginal cost will decrease. b) Marginal revenue will not change; marginal cost will decrease. c) Neither average total cost nor marginal cost will change. d) Neither marginal revenue nor marginal cost will change. e) Both marginal revenue and marginal cost will decrease. ANSWER: d SECTION: 4
18. Suppose that the cost of a raw material decreases. The most likely effect is that a) Price will be unchanged, and quantity will increase. b) Price will decrease, and quantity will increase. c) Both price and quantity will decrease. 2-4
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d) Price will decrease, and quantity will be unchanged. e) Both price and quantity will be unchanged. ANSWER: b SECTION: 4
19. A firm negotiates a new labor contract, raising the average hourly wage. What is the most likely effect on the firm's price and output? a) No effect. Both price and quantity will be unchanged. b) Price will increase, and quantity will be unchanged. c) Both price and quantity will increase. d) Price will be unchanged, and quantity will decrease. e) Price will increase, and quantity will decrease. ANSWER: e SECTION: 4
20. The demand for a firm’s product dramatically increases. What are the most likely effects on the marginal revenue and marginal cost curves? a) Marginal revenue will increase, and marginal cost will decrease. b) No effect. Neither will change. c) Both marginal revenue and marginal cost will increase. d) Marginal revenue will be unchanged; marginal cost will increase. e) Marginal revenue will increase; marginal cost will not change. ANSWER: e SECTION: 4
21. In franchising, conflicts between parent and storeowners arise because a) The parent seeks higher sales than store owners want. b) The parent cannot trust the store owners. c) The two sides have to negotiate how advertising costs are split. d) The parent seeks higher prices; store owners prefer lower prices. e) The parent make nearby store owners compete against one another. ANSWER: a SECTION: 4
22. If a firm’s profit is given by: = -2Q3 + 36Q2 - 120Q -150, then its optimal output is a) Q = 12 b) Q = 10 c) Q = 2 d) A maximum does not exist. Profit is unbounded. e) None of these answers is correct. ANSWER: b SECTION: 4
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SHORT ANSWER
23. What is the "law of demand"? How do managers use it in decision-making? ANSWER: The law of demand states that all other factors held constant, the higher the unit price of a good, the fewer the number of units demanded by consumers and, consequently, sold by the firm. Managers use the demand curve as the basis for predicting the revenue consequences of alternative output and pricing policies. SECTION: 1
24. Carefully define marginal analysis, and explain how it is useful in managerial economics. ANSWER: Marginal analysis is the process of considering small changes in a decision and determining whether such a change will improve the ultimate objective. The manager can follow a clear rule: Make a small move to a nearby alternative if and only if the move will improve one's objective. Keep moving until no further move will help. SECTION: 2
25. Suppose that the inverse demand curve is given by P = 2,500 – 10Q. Compute total revenue and marginal revenue, and determine the quantity that maximizes total revenue. ANSWER: R = P•Q = 2,500Q -10Q2. In turn, MR = dR/dQ = 2,500 - 20Q. We maximize revenue by setting MR equal to 0. Therefore, 2,500 – 20Q = 0 implies Q = 125. SECTION: 3
26. Suppose that a firm sells in a highly competitive market, in which the going price is $15 per unit. The firm’s cost equation is C = $25 + .25Q2. a) Find the profit-maximizing level of output for the firm. Determine its level of profit. b) Suppose that fixed costs increase to $75. Verify that this change in fixed costs does not affect the firm's optimal output. ANSWER: a) In a competitive market, R = P•Q = 15Q implying MR = dR/dQ = 15. In turn, MC = dC/dQ = .5Q. Setting MR = MC, we find that 15 = .5Q, or Q = 30. At Q = 30, we find that R = $450, C = 250, and = $200. b) The increase in fixed cost has no effect on MR or MC. Accordingly, the firm's optimal level of output is unaffected. With the $50 rise in fixed cost, the firm's profit falls to $150. SECTION: 4
27. Demand for a firm’s product is: P = 36 - .2Q, The firm’s cost equation is: C = 200 + 20Q. a) Determine the firm’s optimal quantity and price. b) Suppose that costs change to C = 100 + 24Q‚. Determine the new optimal quantity and price. Explain why the results differ from those in part a. ANSWER: a) We can derive MR = 36 - .4Q and MC = 20. Setting MR = MC implies Q* = 40. From the price equation, it follows that P* = 36 – (.2)(40) = 28. Finally, profit is: = $1,120 – 1,000 = $120.
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b) With the new cost function, MC = 24. Setting MR = MC implies 36 - .4Q = 24, or Q* = 30. In turn, P* = 36 – (.2)(30) = 30. Finally, profit is: = $900 – 820 = $80. Here, the reduction in fixed cost has no impact on output, but the increase in marginal cost induces a smaller output quantity and a greater price. SECTION: 4
28. A firm faces the demand curve, P = 80 - 3Q, and has the cost equation C = 200 + 20Q. a) Find the optimal quantity and price for the firm. b) Now suppose that demand changes to P = 110 - 3Q. Find the new optimal quantity and price. Has there been an increase or a decrease in demand? Explain. ANSWER: a) Maximize profit by setting MR = MC. From the price equation, we know that MR = 80 - 6Q. Equating this to a MC of 20 implies 80 - 6Q = 20, or Q* = 10. In turn, P* = 80 - (3)(10) = 50. b) From the new price equation, P = 110 - 3Q, we find MR = 110 - 6Q. Setting MR = MC implies 110 6Q = 20, or Q* = 15. In turn, P* = 110 - (3)(15) = 65. The increase in demand (in this case a parallel outward shift in the demand curve) has induced the firm to increase both its price and quantity. SECTION: 4
29. Suppose that a firm sells in a competitive market at a fixed price of $12 per unit. The firm's cost function is: C = 200 + 4Q. In this case, how can the firm use MR and MC to maximize its profit? ANSWER: Here, R = 12Q so that MR = 12. In turn, MC = 4. Clearly, it is not possible to apply the rule MR = MC. However, we know that M = 12 – 8 = 4 > 0. So the firm gains additional profit by continuing to increase output. It should do so until it reaches the capacity limit of its production facility. SECTION: 3
30. In each case below, find the profit-maximizing level of output. Verify that each is a maximum by checking the second derivative. a) = -50 + 200Q - 20Q2. b) = -100 + 300Q - 4Q3. ANSWER: a) M = 200 - 20Q. Setting M = 0 implies: Q* = 10. b) M = 300 - 12Q2. Setting M = 0 implies: Q* = 5. The second derivative is negative, so Q* = 5 is the profit-maximizing level of output. SECTION: 5
31. Carefully explain the economic importance of the Lagrange multiplier. How might a manager use it in decision making? ANSWER: The Lagrange multiplier measures the marginal change in the objective function at the constrained optimum. Thus, it measures the cost to the firm (in terms of lost profit) of the binding constraint. Managers can use the value of the Lagrange multiplier to determine whether it is worthwhile to relax or shift the constraint. For example, suppose that the cost of relaxing a constraint (for instance, increasing the firm’s limited production capacity) is larger than the increase in profits that would result from the change. In this case, it does not pay to expand capacity. Management should accept the constrained level of profit as the optimal outcome. SECTION: 5
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ESSAY
32. According to the law of demand, an increase in price will lead to a drop in the quantity of units sold by a firm. What are the reasons for the decrease in quantity? ANSWER: There are three sources of the decrease: (1) decreased sales to the firm's current customers, as they choose to buy less at the higher price; (2) sales lost to competing suppliers; and (3) decrease in new customers, who choose to buy from competing suppliers. In particular circumstances, these will be important to a greater or lesser degree. SECTION: 1
33. Max Whitley, manager of Whitley Construction, builds new homes in a booming community in the Midwest. Although sales have slowed because of a national recession, it now looks as if the recession is about to end. Max wants to be ready with material, labor, and foremen to meet the demand for housing. Last year, Max built and sold 40 “starter homes,” the most popular model. Max thinks that his sales will increase to 50 units over the current year. The going market price for this model (which Max and his numerous competitors have charged) has been $175,000. In addition, Whitley Construction's marginal cost of building this model averages $155,000. a) Based on these facts, recommend a course of action for Max. b) Suppose that the economic boom raises the cost of labor and raw materials, so that the additional cost of a starter house rises to $165,000. What is Max's most profitable course of action? Explain. ANSWER: a) Since Max can expect to make $20,000 marginal profit on each home, he should attempt to build and sell a maximum number of units. He should monitor market demand (are home sales really robust enough to justify building 50 units?). If the price is truly market determined (note the “many competitors”), Max may not be able to increase his sale price very much. However, he should take advantage of every opportunity to sell more homes, since marginal revenue is above marginal cost. b) If the market price is competitively determined, Max will have little opportunity to pass on such a cost increase in the form of a higher price. (Whitley's new home sales would dwindle quickly if it charged a price above the competitive level). The most profitable course of action is to sell new homes at the lower profit margin of $10,000 per house. An alternative choice is to reduce construction of starter homes and increase production of larger, more expensive homes, assuming that the profit margins are greater on these. SECTION: 2
34. War Game, Inc. produces games that simulate historical battles. The market is small but loyal, and War Game is the largest manufacturer. It is thinking about introducing a new game in honor of the sixtieth anniversary of the end of World War II. Based on historical data regarding sales, War Game management forecasts demand for this game to be P = 50 - .002Q, where Q denotes unit sales per year, and P denotes price in dollars. The cost of manufacture (based on royalty payments to the designer of the game, and the costs of printing and distributing) is C = 140,000 + 10Q. a) If the goal of War Game is to maximize profit, calculate the optimal output and price. b) If instead the company's goal is to maximize sales revenue, what is its optimal price and quantity? ANSWER: a) The company's profit equation is: = 50Q - .002Q‚ - 10Q - 140,000. To maximize profit set M = 0. Therefore, 40 - .004Q = 0, implying Q = 10,000. In turn, P = 50 - (.002)(10,000) = $30 per game. b) The company's revenue equation is R = P•Q = 50Q - .002Q‚. To maximize revenue set MR = 0: Therefore, 50 - .004Q = 0, implying Q = 12,500. In turn, P = 50 - (.002)(12,500) = $25 per game. SECTION: 4
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35. Night Timers is a small company manufacturing glow-in-the-dark products. One of the hottest items the engineering department has developed is adhesive tape that can be applied to walls and floors. Night Timers' chief engineer anticipates that the product will be sold in ten-foot rolls. At present, the company's maximum production capacity is 140,000 rolls per year. The engineer believes the cost function to be described by: C = $50,000 + .25Q. (The high fixed costs represent development cost and tooling to prepare coating equipment). Night Timers' president seeks to establish a price that maximizes profit (since she is the chief stockholder). She thinks that the firm should be able to sell at least 125,000 rolls of tape per year. a) If Night Timers plans to sell 125,000 rolls per year, what is the necessary price if the firm is to break even? What if it can only sell 100,000? b) The marketing manager forecasts demand for the tape to be: Q = 350,000 - 200,000P. Find the firm's profit-maximizing output and price. c) If the demand forecast in part b is realized in the first year of production, should the company consider expanding capacity? Explain. ANSWER: a) Break even implies R = C or P•Q = 50,000 + .25Q at the level of output indicated. To find the break-even price, set Q = 125,000 and solve for P. Doing so, we find: P = $.65 per unit. If Q = 100,000, the break-even price rises to: P = $.75 per unit. b) After rearranging the demand equation, we have P = 1.75 - Q/200,000. Thus, MR = 1.75 - Q/100,000. From the cost function, we know that MC = .25. Set MR = MC to maximize profit: 1.75 - Q/100,000 = .25. Therefore, Q = (1.5)(100,000) = 150,000 rolls. However, maximum capacity is 140,000 rolls. Thus, an output of 140,000 is the best the company can expect to do. The requisite price is: P = 1.75 140,000/200,000 = $1.05. The firm's projected profit is: (1.05 - .25)(140,000) - 50,000 = $62,000. c) The relevant question is whether the increased profit of expanding capacity exceeds the increased cost of doing so. If it could produce and sell 150,000 rolls (by lowering price to $1), the company's profit would increase very slightly to: (1 - .25)(150,000) - 50,000 = $62,500. The extra $500 in profit is clearly not worth the cost of expansion. SECTION: 4
36. KopyKat specializes in printing business cards and résumé’s, using the latest laser technology. After analysis of the business, the manager has determined that weekly demand can be approximated by P = 25 – .001Q. The firm’s cost function is C = 25,000 + 13Q + .002Q 2, where Q is output per week. a) Determine the firm’s profit maximizing price and output. b) The night supervisor believes that extending KopyKat’s hours by two hours in the evening would substantially increase volume. The manager is willing to stay open for two hours over the next three months as an experiment. What results would lead you to recommend that the store remain open later in the evening on a permanent basis? c) A former employee decides to sue KopyKat, alleging employment discrimination. Although management claims innocence, they agree to settle out of court. The settlement requires KopyKat to pay the employee $10,000 per month for the next year. Determine the optimal price and output for the shop under these new conditions. ANSWER: a) The inverse demand function P = 25 - .001Q implies MR = 25 - .002Q. Also MC = dC/dQ = 13 + .004Q. Setting MR = MC, we have: 25 - .002Q = 13 + .004Q, or .006Q = 12. Thus, Q = 2,000 units per week. The optimal price is P = 25 - (.001)(2,000) = $23 per unit. b) Keeping KopyKat open additional hours means incurring some additional labor costs (If volume increases, production cost will increase as well). As always, the decision for the manager hinges on whether the increased volume from longer hours generates enough additional revenue to cover the increased cost of longer hours. An experiment for three months should presumably provide enough data to let the manager decide if the move is “worth it." c) The $10,000 a month payment represents an increase in the firm's fixed costs and has no impact on marginal revenue or marginal cost. Thus, the firm should not alter its pricing or production decisions. SECTION: 4 2-9
Optimal Decisions Using Marginal Analysis
37. The current manager of a small bicycle shop estimates the demand curve for a child’s starter bike to be: P = 80 - 2Q. Costs are given by C = 200 + 20Q. The former owner of the shop (now retired) urges the manager to keep prices low so as to increase sales and maximize revenue. (The shop pays the former owner 5% of each dollar of earned revenue.) If current management follows the former owner’s goal, what sales output and price should it set? What strategy would you recommend for management? ANSWER: If the manager obeys the wishes of the former owner and maximizes revenue, she would set output at the point where MR is equal to 0. From the demand curve, we have: R = P•Q = (80 - 2Q)Q = 80Q - 2Q‚ so that MR = dR/dQ = 80 - 4Q. Setting MR = 0 implies Q = 20 bikes. In turn, P = $40 per bike and = R - C = 800 - 600 = $200. But, the proper goal is to maximize profit. Thus, the manager should follow the optimal rule: MR = MC. We know that MC = 20. Therefore, 80 - 4Q = 20, or Q = 15 bikes. In turn, P = $50 per bike, and = R - C = 750 - 500 = $250. With an optimal output and pricing policy, the shop can increase its profit by 25% compared to the revenue-maximizing outcome. SECTION: 4
38. a) A manufacturer produces and sells small farm tractors. Its annual fixed costs are $15 million, and its marginal cost per tractor is $20,000 per unit. Demand for small tractors is given by: P = 30,000 - Q, where P denotes price in dollars and Q is annual sales. Find the firm's profit-maximizing output, price, and annual profit. b) Next year, agriculture prices fall and the farming sector faces a mild recession. Demand drops to: P = 26,000 – Q. Suppose the recession is only temporary, and demand will recover soon. What price and output adjustment should the firm make during the recession? Instead, what should the firm do if the demand drop is permanent? ANSWER: a) To maximize profit set MR = MC. Therefore, we have MR = 30,000 - 2Q = 20,000, implying Q* = 5,000 tractors, and P = 30,000 – 5000 = $25,000 per tractor. The firm’s total profit is: (25,000 – 20,000)(5,000) – 15,000,000 = $10,000,000. b) With the fall in demand, we find the firm’s new optimal output: MR = 26,000 - 2Q = 20,000, implying Q* = 3,000 and P* = 26,000 –3,000 = $23,000. Contribution now becomes (3,000)(3,000) = $9,000,000 and the firm’s total profit is –$6,000,000. During a temporary downturn, the firm should lower its price and output because it is making a positive contribution toward its fixed cost. This way it is minimizing its shortterm loss. If the fall in demand is permanent, the firm should eventually shut down to avoid continuing losses. SECTION: 4
39. Turbo produces two lines of flash-memory drives. Its deluxe model has the inverse demand equation: PD = 70 -.05QD where QD is the number of units sold per week. For its economy model, the price equation is: PE = 30 - .05QE. Turbo’s marginal cost is $10 per unit for either drive, and it produces both on a single assembly line that has a maximum capacity of 875 drives per week. a) Determine the profit-maximizing outputs and prices of the drives. b) Answer the questions in part a, supposing that demand for the economy drive increases to: PE = 50 .04QE.
ANSWER: a) Setting MD = 0 implies 60 - .1QD = 0 or QD = 600 drives. For the economy version, we have ME = 20 - .1QD = 0, so QE = 200 drives. The corresponding prices are: PD = $40 and PE = $20. The total output is within the firm’s capacity. b) Given the increase in economy demand, Turbo’s new optimal output becomes QE = 500 drives, so total output would exceed total capacity. The constrained optimization problem (using the Lagrangian 2-10
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approach) must satisfy the optimality condition: MD = ME, or 60 - .1QD = 40 - .08QE, as well as the capacity constraint, QD + QE = 875. Solving these two equations in two unknowns implies QD = 500 drives and QE = 375 drives. The new prices are: PD = $45 and PE = $35. SECTION: 5
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File: Ch03; CHAPTER 3: Demand Analysis and Optimal Pricing
Each question contains a code showing the section of the chapter text from which it was taken. The codes for this chapter are: Code 1 2 3 4
Section Determinants of Demand Elasticity of Demand Demand Analysis and Optimal Pricing Appendix: Consumer Preferences and Demand
MULTIPLE CHOICE
1. The demand equation a) Provides a qualitative list of possible factors affecting demand. b) Contains one or more explanatory variables on the right side of the equation. c) Perfectly predicts the number of units sold. d) Is useful in predicting a firm’s sales but not the sales of the total industry. e) None of the answers above is correct. ANSWER: b SECTION: 1
2. The firm’s demand equation is: Q = 600 – 60P + 2Y. If price increases by $2 and income increases by $80, then quantity will a) Increase by 160 units. b) Increase by 40 units. c) Decrease by 120 units. d) Decrease by 40 units. e) There is insufficient information to provide an answer. ANSWER: b SECTION: 1
3. Which of the following will cause the firm’s demand curve to shift? a) A change in the price of the good or service. b) A change in the amount offered for sale. c) A change in the seller’s profit associated with the good or service. d) A change in a non-price variable in the demand function. e) A change in production technology for the good or service. ANSWER: d SECTION: 1
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Demand Analysis and Optimal Pricing
4. If the price of a good or service increases, a) The demand curve shifts inward. b) The demand curve shifts outward. c) There is a movement along the demand curve. d) There is a movement along and a shift in the demand curve. e) The demand curve changes slope but does not shift. ANSWER: c SECTION: 1
5. If the price of MP3 players decreases, a) The price per downloaded song will also decrease. b) The demand for downloading songs will increase. c) The demand for downloading songs will be unaffected. d) Answers a and b are both correct. e) None of the answers above is correct. ANSWER: b SECTION: 1
6. Of the following goods and services, which is most likely to be inferior? a) Gasoline b) Air travel c) Ten-year-old used cars d) Wine e) DVDs ANSWER: c SECTION: 1
7. The price elasticity of demand is defined as the a) Ratio of the percentage change in quantity to the percentage change in price. b) Ratio of the change in quantity to the change in price. c) Absolute change in quantity resulting from a price change. d) Change in the slope of the demand curve when price changes. e) Ratio of the percentage change in price to the percentage change in quantity. ANSWER: a SECTION: 1
8. Which of the following is likely to affect demand elasticity? a) The availability of substitutes. b) Advertising spending that increases customer brand allegiance. c) The price level set by the firm. d) The overall size of the market. e) Answers a, b, and c are all correct.
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ANSWER: e SECTION: 2
9. The initial price for an item is $5.00, and the quantity demanded is 350 units. When the price is raised to $5.25, the quantity demanded falls to 300 units. The point price elasticity of demand is: a) -2.25 b) -2.86 c) -3.5 d) -4.05 e) -5.75 ANSWER: b SECTION: 2
10. Management estimates the firm’s demand curve to be: Q = 400 - 5P. At P = $15, the point elasticity of demand is a) -.23 b) -.013 c) -.85 d) -4.35 e) -5.00 ANSWER: a SECTION: 2
11. A product’s point price elasticity has been estimated at -1.5. If management cuts price from $20 to $17.50, quantity demanded and sold is expected to increase by a) 18.75% b) 6.67% c) 8.75% d) 10.33% e) None of the answers above is correct. ANSWER: a SECTION: 2
12. The cross price elasticity between two products has been measured at 2.0. If the price of the first product is increased by 8%, demand for the second product will a) Increase by 8% b) Decrease by 4% c) Increase by 4% d) Increase by 16% e) There is not enough information to provide an answer. ANSWER: d SECTION: 2
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Demand Analysis and Optimal Pricing
13. If demand is “inelastic”, then a) Sales are relatively responsive to price. b) The demand curve is relatively flat. c) Total revenue is insensitive to price. d) Unit sales are insensitive to price. e) Answers a and b are both correct. ANSWER: d SECTION: 2
14. Demand for a service depends upon price and income, where EP = -.6 and EY = 1.2. If price falls by 4% and income rises by 2%, service demand will a) Be approximately unchanged. b) Increase by about 6%. c) Increase by about 4.8%. d) Increase by about 9.6%. e) There is not enough information to provide an answer. ANSWER: c SECTION: 2
15. The goals of maximizing profit and maximizing revenue coincide when a) Variable costs are so small they can be ignored. b) Fixed costs can be ignored. c) Marginal revenue is zero. d) Demand is unitary elastic. e) Demand is very elastic. ANSWER: a SECTION: 3
16. If the price of a good is in the elastic range and the firm raises price, a) Quantity demanded will fall but revenue will increase. b) Revenue will be largely unchanged. c) Revenue will decrease. d) The fall in quantity demanded will be less than the increase in price. e) None of the answers above is correct. ANSWER: c SECTION: 3
17. The practices of full-cost pricing and optimal markup pricing correspond a) Very closely, because the logic behind them is similar. b) Very closely, although the logic behind them is different. c) Identically; the pricing policies go by different names but always arrive at the same answer. d) Not closely, because the logic behind them is different. e) Not closely, even though the logic behind them is similar.
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ANSWER: d SECTION: 3
18. In practicing price discrimination, the firm a) Must be able to identify separate market segments having different elasticities. b) Typically charges higher prices in the larger market segment. c) Must disguise the fact that it is charging different prices. d) Must face inelastic demand for its products. e) Sets price according to the different costs of serving different market segments. ANSWER: a SECTION: 3
19. If a firm price discriminates across two market segments (exhibiting the same marginal cost), a) Price will be lower in the market with the lower cross price elasticity of demand. b) Price will be lower in the market with less elastic demand. c) Price will be higher in the market with greater overall demand. d) Price will be higher in the market with less elastic demand. e) There is insufficient information to provide an answer. ANSWER: d SECTION: 3
20. In selling an “information” good or service, the firm should a) Set a relatively low price because the marginal cost of reproducing the good is very small. b) Set a price based on the average fixed cost of producing the good. c) Set a high price because information goods deliver great user value to customers. d) Set a low price to encourage usage and so enjoy positive network externalities. e) Answers a and d are both correct. ANSWER: e SECTION: 3
21. For a garage of fixed capacity, the owner sets different parking rates for short-term and long-term parkers. To maximize revenue, the operator should set prices and target the number of places for each segment such that a) The marginal revenues of the segments are equal. b) The total revenues of the segments are equal. c) Short-term parkers (exhibiting more inelastic demand) pay a higher hourly price. d) Short-term parkers (exhibiting more inelastic demand) pay a lower hourly price. e) Answers a and c are both correct. ANSWER: e SECTION: 3
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Demand Analysis and Optimal Pricing
22. If a firm sells several products with interdependent demands, a profit-maximizing output and pricing strategy a) Treats the different products as totally separate items. b) Lumps the products together as if they were homogeneous. c) Takes account of the interdependencies in making decisions. d) Maximizes revenue rather than profit. e) Employs full-cost markup rules in setting price. ANSWER: c SECTION: 3
23. If a firm sells two goods that are substitutes, a) Selling more of one good will reduce sales of the other. b) Selling more of one good will increase sales of the other. c) The firm should set higher prices than if the goods were independent. d) The firm should set similar prices for both goods. e) Answers a and c are both correct. ANSWER: e SECTION : 3
SHORT ANSWER
24. The Juice Shop sells iced soft drinks. Management has found that demand is well described by the equation: Q = 1,000 - 240P + 80PC, where Q denotes the number of drinks sold per day, P is the drink’s price, and PC is the price of drinks at a nearby café. a) How many drinks will be sold if P = $1.50 and PC = $1.20? b) Write down the equation for the firm’s demand curve for PC = $1.20. c) If the other café’s price increases to $1.50, what is the effect on Juice Shop’s demand curve? ANSWER: a) Q = 1,000 – (240)(1.50) + (80)(1.20) = 736. b) The demand curve is: Q = 1,000 – 240P + (80)(1.20) = 1,096 – 240P. c) The increase in PC causes Juice Shop’s demand to increase – that is, a rightward shift in the demand curve. The new demand curve is: Q = 1,120 – 240P. SECTION: 1
25. Carefully define the term demand function, and explain its importance to the study of managerial economics. ANSWER: A demand function shows in equation form the relationship between the quantity sold of a good or a service and one or more explanatory variables. A demand function is an important tool for predicting the demand, revenue, and profit impacts from changes in the firm’s own price and from changes in other variables such as consumer income, advertising spending, and the prices of competing or complementary goods. SECTION: 1
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26. If customer income increases over time, (while price is held constant), what is the most likely impact on unit sales? Explain. ANSWER: An increase in buyers' income will generally increase demand since most goods are normal. Thus, one can expect unit sales to increase at all prices – that is, this would be a rightward shift in the demand curve. SECTION: 1
27. As sales manager of an appliance store, you sometimes visit outlets run by your competitors. Six months ago, you noticed that rivals’ prices were very close to yours. However, in the last six months, your competitors have lowered their prices to about 15 percent below yours. Nevertheless, your total unit sales have increased slightly during this time period. Assuming rational buyers and no deceptive advertising, how can you account for this? ANSWER: If the only factors that have changed are prices in the stores, this result makes no sense. However, other factors may be at work that would increase demand at your store – factors that would more than offset the effects of lower competitor prices. One such factor would be an increase in customer income (assuming your store’s items are normal goods). Another is an increase in output of complementary products (for instance a boom in the construction of new apartments that need to be equipped with new appliances). SECTION: 1
28. Demand for DVD rentals at a video store is described by the equation: Q = 4,000 - 500P, where Q denotes the number of DVDs rented per week and P is the rental price in dollars. a) Determine the point price elasticity of demand at P = $3.00. b) What is the new point price elasticity if price is raised to P = $4.50? Comment on the change in elasticity. ANSWER: a) Q = 4,000 – (500)(3.00) = 2,500. EP = (dQ/dP)(P/Q) = (-500)(3.00/2,500) = -.6. b) Q = 4,000 – (500)(4.50) = 1,750, and EP = (-500)(4.50/1,750) = -1.29. At P = $3.00, demand is inelastic, but at P = $4.50, it is elastic. The increase in price along the linear demand curve has caused demand to become more elastic. SECTION: 2
29. Suppose that a firm faces the inverse demand curve: P = 20 – Q/40. a) Determine the firm’s revenue maximizing output and price. b) Now suppose there is a reduction in demand (a parallel leftward shift in the demand curve). Provide a new inverse demand equation consistent with this shift. What is the effect on the firm’s revenue maximizing output and price? ANSWER: a) Compute R = P•Q = 20Q – Q2/40. Therefore, MR = 20 – Q/20. Setting MR = 0 implies Q = 400. In turn, P = 20 – 10 = $10. b) Consistent with the shift in demand, suppose P = 16 – Q/40. After the demand shift, MR = 16 – Q/20. Setting MR = 0 implies Q = 320 and P = $8. The firm’s optimal response is to lower both output and price. SECTION: 2
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Demand Analysis and Optimal Pricing
30. What would you expect to happen to a firm’s price elasticity of demand if additional competitors enter the market and achieve significant market shares? Explain briefly. ANSWER: Increased competition provides more numerous purchase alternatives for buyers, so the firm’s demand naturally becomes more elastic (possibly much more so). SECTION: 2
31. You are co-owner of a small gift shop. Your colleague is urging that the shop hold a sale and reduce most prices by 10% to 20%. His parents owned a convenience store, and they said that they could always count on increased traffic when they cut prices. If a 10% price cut didn’t bring enough purchases, then cut by 20%, and the cash flow would cover all their needs. Do you agree with this? Why or why not? ANSWER: A price cut will always lead to some increase in the number of units sold. However, total revenue will increase only if demand is elastic. If demand is inelastic, a price cut will reduce total revenue. SECTION: 3
32. Which of the following settings approximate "pure selling” problems? Explain why or why not. a) A toll bridge b) CD sales in a music store c) Selling advertising time on a commercial radio station. d) Checking account services e) Amtrak seats f) Frozen vegetables in a store g) Fresh fish at the end of the business day ANSWER: a) Yes. Wear and tear on the bridge from an additional vehicle is fairly low. b) No. Additional inventory has a variable cost. c) Yes. As long as air time is available, the radio station’s marginal cost of selling extra minutes is zero. d) No. There are variable costs associated with clearing checks, mailing statements, and so on. e) Yes. Seating capacity involves fixed costs, but the marginal cost of filling an empty seat is close to zero. f) No. Vegetables can be stored for future sale, and it is costly to replenish inventory. g) Yes. There is little demand for day-old fish. SECTION: 3
33. Suppose that a firm is selling a good with a marginal cost of $35. Management estimates demand elasticity to be -2. What is the appropriate price to set in order to maximize profit? ANSWER: P = [EP/(1+EP)]•MC. Therefore, P = [-2/(1-2)]•35 = $70. SECTION: 3
34. Your company produces a hand-held global positioning system (GPS) used for hiking and sells it for $350 per unit in the United States. You also sell the same GPS unit in Europe at a price of $250 Euros (the equivalent of bout $290.) Several competing European producers have charged your company with “dumping” your units at unfairly low prices in Europe. What economic defense would you submit for your company’s pricing practice? ANSWER: Your main defense is that demand elasticities are different at home and abroad. Demand in international markets is more elastic, reflecting the wider variety of competitors in Europe. By contrast, the upscale hiking market in the United States might be a wealthier but relatively small niche market served by
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fewer GPS suppliers (your company and one rival). The result is less elastic demand and, therefore, a higher price. SECTION: 3
ESSAY
35. Seasons Four Equipment Corporation sells 200 riding lawn mowers per month at a sales price of $1,800 each. Overall, mower demand is described by the price equation: P = 2,600 – 4Q, and the firm’s estimated marginal cost is $1,000 per mower. The head of marketing points out that mower demand is quite elastic at the current $1,800 price. Therefore, he recommends cutting price in order to increase revenue and profit. a) Compute the point price elasticity for mower. Is the marketing chief correct? b) Do you agree (or disagree) about cutting price? Explain briefly. ANSWER: a) EP = (dQ/dP)(P/Q) = (-1/4)(1,800/200) = -2.25. Yes, demand is quite elastic. b) Here, the marketing chief is incorrect. The profit-maximizing price is determined by the markup rule. Therefore, P = = [EP/(1+EP)]•MC = [-2.25/(1 – 2.25)]•1,000 = $1,800. The current price of $1,800 is optimal. Price should not be cut. (One can confirm the same price and output by setting MR = MC.) SECTION: 3
36. INSITE Corporation produces advanced analytic software for computer simulations called Model It. Based on an analysis of product sales over a two-year period, INSITE’s marketing department estimates the demand for Model It to be: QM = 1,200 - 8PM + 4PS, where QM denotes units sold of Model It software, PM denotes Model It’s price, and PS denotes the price of a best-selling statistical software package (with both prices in dollars). a) Currently, PM = $200 and PS = $300. What is the predicted demand for Model It software? b) The price PS has been unchanged (at $300) during the last 6 months. Given this information, write down the equation for Model It’s demand curve (with QM as the left-side variable). Also determine its inverse demand curve (with PM as the left-side variable). c) An industry analyst comments that demand for Model It is not very sensitive to changes in the price of the statistical software package PS. (This package does perform some of the same operations as Model It, but not as quickly or conveniently.) Carefully assess this contention. Do you agree or disagree? d) As is true with many information goods, the marginal cost of producing Model It is negligible. However, the company incurred significant costs in developing the product for market (estimated to be about $350,000). Using the estimated demand curve of part b, determine the optimal price and output quantity for Model It. ANSWER: a) QM = 1,200 – (8)(200) + (4)(300) = 800 units. b) QM = 1,200 + (4)(300) – 8PM, or QM = 2,400 – 8PM. Equivalently, PM = 300 – (1/8)QM. c) The analyst’s argument probably rests on the fact that the coefficient for P S is only 4 (seemingly not very large). However, the best measure of price sensitivity is the cross price elasticity of demand: EPs = [dQ/dPS][PS/Q] = (4)(300)/800 = 1.5. This is greater than one, indicating that the software items are reasonably close substitutes. A 10% reduction in the rival price will cause a 15% drop in sales of Model It. The analyst’s contention appears to be wrong headed. d) With MC = 0, the objective is to maximize revenue. We know that PM = 300 – (1/8)QM. Setting MR = 0 implies 300 - .25QM = 0, or QM = 1,200 units. In turn, PM = $150. SECTION: 3
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37. Firm Z sells farm equipment and faces demand given by: P = 3,000 - Q, where P denotes price in dollars and Q is quantity of units sold per month. In its East coast factory, the firm’s fixed costs are $250,000 per month, and its marginal cost of manufacturing the equipment is $1,000 per unit. a) Find the firm's profit-maximizing output and price. What is its profit? b) Over the last year, the US dollar has appreciated (gained value) versus the Japanese yen with the result that Japanese imports of farm equipment to the US have become more competitive. Firm Z’s marketing department judges that it now would have to cut price by $500 per unit in order to sell the same quantity as in part a. (In short, the price equation has shifted down and in relative to part a.) Is such a price cut part of a profit-maximizing strategy? Explain. c) Suppose that a new market for the firm's product emerges in South America. Firm Z has begun selling the equipment in several test markets there and has found the elasticity of demand to be E P = -3 for a wide range of prices (between $1,500 and $2,500). The cost of shipping to South America is $200 per unit. One manager argues that the foreign price should be set at $200 above the domestic price (in part a) to cover the transportation cost. Do you agree that this is the optimal foreign price? Justify your answer. d) Suppose that the firm has produced the optimal level of output in part a. But before this quantity is sold, demand unexpectedly falls to: P = 2,800 - 2Q, (equivalently Q = 1,400 - .5P). One manager recommends cutting price to sell the entire inventory; another favors maintaining the price in part a (selling less than the total inventory). Do you agree with either manager? What optimal price would you set? ANSWER: a) Setting MR = MC implies: 3,000 - 2Q = 1,000. Thus, Q = 1,000 units and P = $2,000. In turn, Profit = R - C = 2,000,000 - 1,250,000 = $750,000. b) The downward shift in the demand curve implies a downward shift in the MR curve. With MC unchanged the new intersection of MR and MC must occur at a lower optimal level of output. The firm should not insist on maintaining its sales level. The needed price cut is too drastic. (Assuming a parallel demand shift, one can confirm this answer quantitatively. The new MR curve is MR = 2,500 - 2Q. Setting MR = MC implies Q* = 750 and P* = $1,750, not $1,500.) c) Using the markup rule, the optimal foreign price is: P = (-3/-2)(1,200) = $1,800. The manager is wrong. The price should be lowered by $200, not raised by $200. The foreign market is more price elastic than the domestic market, implying a lower final price (despite the higher cost per unit). d) The key is to recognize this as a pure selling problem. The units have already been produced and the costs already sunk. To maximize revenue, set MR = 0. Thus, 2,800 - 4Q = 0, and Q = 700 units. The associated price is $1,400, and revenue is $980,000. This is better than the other options. To sell all 1,000 units, the price must be $800, implying revenue of $800,000. If the firm maintains P = $2,000, then Q = 400 units and revenue is again $800,000. SECTION: 3
38. Will a profit-maximizing firm typically sell a good at a price that is in the inelastic portion of a demand curve? Why or why not? ANSWER: No, selling at an inelastic price cannot be profit maximizing. If demand is inelastic, then the firm can increase its profit simply by raising price. In the process, it increases its total revenue and reduces its total cost (because it produces and sells fewer units). In short, the firm should always raise price until it finds itself in the elastic portion of the demand curve. The same point can be confirmed by a graph of MR and MC, where their intersection (as long as MC is positive) always implies price and output in the elastic (northwest) portion of the demand curve. SECTION: 3
39. Recently, the major firms in the United States cigarette industry joined with the government in a settlement of liability claims. Under the tentative agreement, the industry would curb advertising and pay the equivalent of about $15 billion per year (for smoking-related state Medicaid expenses) in exchange for protection against smoker lawsuits.
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a) Before the settlement, a leading cigarette manufacturer estimated its marginal cost at $1.00 per pack and its elasticity of demand at -2. What is its optimal price? The firm’s share of the industry payment (based on its historic market share) will raise its average total cost per pack by $.60. What effect will this have on its optimal price? b) A marketing manager suggests that the firm should offer price discounts to the company’s long-term, older, most-loyal (addicted?) customers. Do you agree? Explain carefully. c) In the past, anti-smoking information campaigns have had some limited success in reducing smoking. What price reaction (if any) would the cigarette companies have to such programs? Explain carefully. ANSWER: a) Applying the markup rule, we find: P = [-2/(1-2)]1.00 = $2.00. Because the firm’s share of the industry payment is a fixed cost (does not varying with its current output), its MC is unchanged and, therefore, so is its price. b) This reasoning is wrong-headed. The long-term addicted smoker is much more insensitive to price changes than the new smoker. Thus, the firm should set higher prices for long-term prices and lower prices for new smokers. c) The limited success of antismoking campaigns implies an inward shift in the firm (and industry) demand curves. This shifts the MR curve inward and leads to lower optimal quantities and lower prices. SECTION: 3
40. Carefully define price discrimination. What conditions must exist for it to be possible? For it to be profitable? Explain. ANSWER: Price discrimination occurs when a firm sells the same good or service to customer segments at different prices. The difference in price is purely demand based. (Typically, there is no significant difference in the marginal cost of serving the different customer groups.) Two conditions must exist for a firm to practice price discrimination profitably. The firm must be able to identify market segments that have different price elasticities. It must also be able to enforce the difference in price – that is, resale must be impossible. Firms will charge higher prices in markets where demand is less elastic, and lower prices in markets where demand is more elastic. SECTION: 3
41. You are the marketing manager of a firm that produces Titanium and sells this metal to two distinct kinds of customers: aircraft producers and golf club manufacturers. Demand for Titanium by these two market segments is quite different, as described by the respective price equations: PA = 10 - QA./600 and PG = 12 - QG./100, where annual quantities are in thousands of pounds and prices are in dollars. Your firm estimates the marginal cost of titanium production at $4 per pound. a) For each segment, determine the firm’s profit-maximizing price and output. Is the firm practicing price discrimination? b) Because of Titanium shortages, the firm’s total production capacity drops to only 1.5 million pounds per year. Determine the firm’s optimal quantities and prices in this case. ANSWER: a) The profit-maximizing rule is to set MRA = MRG = MC. Thus, we have: 10 - QA/300 = 4, implying QA = 1,800 thousand pounds. In turn, PA = 10 – 1,800/600 = $7 per pound. For the golf segment, we have: 12 - QG/50 = 4, implying QG = 400 thousand pounds. In turn, PG = 12 – 400/100 = $8 per pound. The firm is practicing price discrimination (charging a higher price to the golf club segment). b) With total capacity limited to 1.5 million pounds, the total production in part a, 2.2 million pounds, is infeasible. Clearly, the firm should produce at full capacity (1.5 million pounds at a variable cost of $6 million) and divide sales between the two segments in order to maximize total revenue. Therefore, the revenue maximizing condition is: MRA = MRG, along with the constraint QA + QG = 1,500. Thus, we know that 10 - QA/300 = 12 – QG/50, and QA + QG = 1,500. Solving these two equations simultaneously implies: QA = 1,200 thousand pounds and QG = 300 thousand pounds. In turn, PA = $8.00 per pound and PG = $9.00.
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SECTION: 3
42. Amalgamated Popcorn, Inc. sells bags of flavored gourmet popcorn in a popular mall. As shop owner and operator, you have observed that weekly popcorn sales are well-described by the demand equation: Q = 1,200 - 800P + 2.0A, where A denotes advertising weekly spending (in dollars). You are currently charging $1.50 per bag of popcorn (for which the marginal cost is $.75) and spending $500 per week on advertising. a) Compute the store’s price elasticity and advertising elasticity. b) Check whether your current $1.50 price is profit maximizing. If not, determine the store’s optimal quantity and output. c) Should the store consider increasing its advertising spending? Why or why not. ANSWER: a) Q = 1,200 – (800)(1.50) + (2.0)(500) = 1,000 bags. Therefore, EP = (Q/P)(P/Q) = (800)(1.50/1,000) = -1.2, and EA = (2.0)(500/1,000) = 1.0. b) According to the markup rule, (P – MC)/P = -1/EP. At P = $1.50, the percentage markup on the left side of this equation is: (1.50 - .50)/1.50 = .667 or 66.7%. But the value of the right side of the equation calls for a markup of 1/1.2 = .833 or 83.3%. Thus, the store’s current price is too low. To determine the store’s optimal output and price, start with the demand equation: Q = 1,200 – 800P + (2.0)(500), or Q = 2,200 – 800P, after setting A = $500. Therefore, the price equation is: P = $2.75 – Q/800. Setting MR = MC implies: 2.75 – Q/400 = .75, or Q = 800 bags. In turn, P = 2.75 – 800/800 = $1.75. c) Yes, increasing advertising spending is profitable. Increasing A by $1 increases sales by (2)(1) = 2 bags. The contribution margin on each unit is: $1.75 - $.75 = $1.00. Thus, the additional total contribution of $2.00 is well-worth each extra dollar spent on advertising. SECTION: 3
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File: Ch04; CHAPTER 4: Estimating and Forecasting Demand
Each question contains a code showing the section of the chapter text from which it was taken. The codes for this chapter are: Code 1 2 3 4
Section Collecting Data Regression Analysis Interpreting Regression Statistics Forecasting
MULTIPLE CHOICE
1. Which of the following can one expect to get from a sound forecast? a) A precise numerical forecast (one with a minimal margin of error). b) The relationship between the forecast and the economic variables that influence it. c) An assessment of the accuracy of the forecast. d) A numerical estimate based on extending the past time trend into the future. e) Answers b and c are both correct. ANSWER: e SECTION: 1
2. Response bias occurs when a) Responses do not reflect the true preferences and attitudes of respondents. b) Insufficient sample size tends to bias the cross-section of responses. c) Questions are framed in ways that biases the answers. d) Different question versions are targeted to different segments of respondents. e) Answers b and c are both correct. ANSWER: a SECTION: 1
3. Is it always worthwhile gathering more information about customer needs and preferences? a) Yes, such information is highly valuable. b) Yes, provided that this information is relevant to the firm’s decisions. c) No, a good rule of thumb is not to spend on information more than 2% of what is at stake in the decision. d) No, the value of additional information must be compared to its additional cost. e) None of the answers above is correct. ANSWER: d SECTION: 1
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4. Which of the following is the best definition of a controlled market study? a) A carefully designed study of a market situation. b) A study of a single market. c) A study that varies key economic variables in one or more markets to determine the effects of the changes. d) A study that assumes differences in sales can be accounted for by unmeasured variables. e) A study that uses experiments to determine probable market outcomes. ANSWER: c SECTION: 1
5. If a study examines several different markets at the same time, and compares outcomes with conditions in each market, the study is using a) Time series data. b) Survey data. c) Controlled data. d) Experimental data. e) Cross-sectional data. ANSWER: e SECTION: 1
6. Can a researcher, in analyzing a market, use uncontrolled market data? a) Yes, it is valuable and useful data as is. b) Yes, by using appropriate statistical techniques. c) No, uncontrolled market data has little information value. d) Uncertain, it depends on how “noisy” the data is. e) No, valid causal predictions must be based on controlled data. ANSWER: b SECTION: 1
7. In estimating a regression equation, a) The main objective is to determine whether there is a valid correlation between two variables. b) One or more independent variables are contained on the right-side of the equation. c) Forecasts of one or more independent variables are statistically estimated. d) It is good practice to keep the number of explanatory variables to a minimum. e) Answers b and c are both correct. ANSWER: b SECTION: 2
8. A regression coefficient measures a) The change in the dependent variable due to a unit change in a particular independent variable. b) The correlation (always between –1 and 1) between the dependent and independent variables. c) The accuracy of the independent variable in explaining the value of the dependent variable. d) The fixed or “constant” term in the regression equation. e) The percentage of variation in the dependent variable explained by the independent variable.
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ANSWER: a SECTION: 2
9. In contrast to simple regression, multiple regression uses a) Several dependent variables rather than one. b) Several independent variables rather than one. c) Several dependent variables and several independent variables. d) Multiple equation specifications in order to find the best statistical fit. e) Both times-series data and cross-section data. ANSWER: b SECTION: 2
10. What is the best definition of R2, the coefficient of determination? a) The slope of the regression equation. b) The proportion of the variation of the dependent variable left unexplained by the regression. c) The variation in the dependent variable normalized to be between zero and one.. d) The standard error of the coefficient associated with an independent variable. e) The proportion of the variation of the dependent variable that is explained by the regression. ANSWER: e SECTION: 3
11. Suppose that the “goodness of fit” of an equation is nearly perfect. What is the value of the R 2 statistic in this case? a) Very close to zero. b) Very close to negative one. c) Very close to infinity. d) Very close to positive one. e) Very close to either positive or negative one. ANSWER: d SECTION: 3
12. Computing the F-statistic allows one to a) Measure the forecasting accuracy of the regression equation. b) Determine which variable contributes the most explanatory power to the regression. c) Increase the overall explanatory power of the regression. d) Predict the increased explanation of any additional variables that might be included. e) Test the overall statistical significance of the regression equation. ANSWER: e SECTION: 3
13. The t-statistic
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a) Is the coefficient estimate divided by its standard error. b) Is the coefficient estimate plus or minus its standard error. c) Is the coefficient’s standard error normalized to be between 0 and 1. d) Measures the overall statistical validity of the regression equation. e) None of the above answers is correct. ANSWER: a SECTION: 3
14. The standard error of the regression a) Measures the accuracy of the equation (and lies between 0 and 1). b) Measures the explained variation in the dependent variable. c) Measures the unexplained variation in the dependent variable. d) Provides a confidence interval for predicting the dependent variable. e) Answers c and d are both correct. ANSWER: d SECTION: 3
15. When multicollinearity occurs a) Dependent and independent variables change in a common pattern. b) Two or more explanatory variables tend to move together. c) Multiple independent variables enter linearly in the regression equation. d) The explanatory variables vary independently of one another. e) None of the answers above is correct. ANSWER: b SECTION: 3
16. Heteroscedasticity occurs when a) The variance of the random error is non-constant over the sample. b) The regression coefficient estimates are highly unstable. c) The random errors are correlated over time. d) Two or more explanatory variables are highly correlated. e) Answers b and d are both correct. ANSWER: a SECTION: 3
17. Serial correlation occurs when a) Value of the random error in one period depends on one or more independent variables. b) The random errors are correlated over time. c) The values of two or more coefficients are correlated. d) Two or more independent variables tend to move together. e) The size of the random error increases over time. ANSWER: b SECTION: 3
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18. An economic variable’s trend over time indicates a) A general tendency for an event to occur. b) A steady movement in an economic variable. c) An irregular pattern in the movement of an economic variable. d) A fixed path along which the variable must move. e) A steady and predictable increase in the variable. ANSWER: b SECTION: 4
19. Business cycles are a) Short-term patterns of increases and decreases in economic activity around a general trend. b) Irregular events, which rarely occur anymore. c) Predictable economic expansions above the long-term trend. d) Abrupt and unexpected departures from the current economic trend. e) None of the answers above is correct. ANSWER: a SECTION: 4
20. Some examples of economic variables that display seasonal variations include a) Tourism. b) Air travel. c) Clothing. d) New housing construction. e) All of answers above are correct. ANSWER: e SECTION: 4
21. Time-series patterns can be decomposed into a) Past fluctuations and future fluctuations. b) Changes caused by economic variables. c) Trends and seasonal variations. d) Business cycles and random fluctuations. e) Answers c and d are both correct. ANSWER: e SECTION: 4
22. The equation Q = a + bt represents a) An exponential trend. b) A linear trend. c) A stochastic model. d) A geometric trend.
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e) An increasing time trend. ANSWER: b SECTION: 4
23. The equation Q = a + bt + ct2 represents a) A quadratic trend. b) A linear trend. c) A stochastic model. d) A barometric trend. e) An exponential trend. ANSWER: a SECTION: 4
24. A time-series model attempts to identify a) Patterns of changes in a single variable over time. b) Possible links between a dependent variable and a single independent variable over time. c) Possible links between a dependent variable and one or more independent variables. d) Key factors that help predict future economic events. e) Patterns of forecast errors over time. ANSWER: a SECTION: 4
25. A barometric model a) Predicts changes in trends. b) Searches for systematic patterns in the timing of changes in variables. c) Explains the magnitude of changes in different variables. d) Is a reliable predictor of cause-and-effect relationships. e) All of the answers above are correct. ANSWER: b SECTION: 4
26. In the example “Forecasting the Fate of Euro Disney,” Disney’s problem stemmed from its a) Downsized launch plan due to the European recession during 1992-1994. b) Refusal to learn from mistakes made in opening its Tokyo theme park. c) Decision to locate Euro Disney near Paris. d) Inability to forecast fundamental demand for the theme park and related services. e) All of the answers above are correct. ANSWER: d SECTION: 4
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27. An equation’s root mean squared error is a) A measure of how closely its predictions match actual outcomes. b) A measure of how closely the equation explains past data. c) A measure of how well the equation predicts future discrete events. d) Derived from the R2 statistic. e) Answers b and d are both correct, ANSWER: a SECTION: 4
SHORT ANSWER
28. What are the four major pitfalls of using consumer surveys to forecast demand? ANSWER: 1. Sample bias, i.e., using an incorrect or inadequate sample. 2. Response bias, i.e., respondents did not answer surveys in a truthful manner. 3. Response accuracy, i.e., a respondent may not know the answer to a particular question. 4. The cost of conducting the survey and compiling the data into a useful form. SECTION: 1
29. You are a newly hired marketing trainee for a corporation in the local community. Senior management has wondered how other local firms view your company’s reputation. One suggestion is to call a variety of managers from a master contact list of firms that your firm has done business with over the last 12 months and ask them what they think of the company. How reliable is this kind of survey method? ANSWER: Using the firm’s own contact list is a very limited, non-random sample of the population of all local firms. The list suffers from sample bias (firms already doing business are likely to favorably view the firm) and probably response bias (respondents might provide ultra-favorable responses, what they believe the firm wants to hear). SECTION: 1
30. What are the major advantages and drawbacks of using controlled customer experiments to determine demand? ANSWER: An advantage is that experiments require subjects to make actual decisions, rather than indicating preferences and behavior. The results are more likely to reflect true preferences. A drawback is that subjects know they are part of an experiment, and may not respond accurately. Second, experiments tend to be of small scale and of short duration, so that accuracy is limited. SECTION: 1
31. What are the major advantages and drawbacks of using controlled market studies to estimate demand?
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ANSWER: The major advantage is that a firm can alter one or more key decision variables in one market and compare the outcome to another similar market in which the variables did not change, or were changed in a different manner. The method can generate valuable information about pricing and advertising policy. The main drawback is that all other factors (including population size and demographics, consumer incomes, tastes, competitor prices) must be comparable. Of course, this is not always possible. Controlled market studies are also expensive to conduct. SECTION: 1
32. What is regression analysis, and what are the major steps in using it? ANSWER: Regression analysis is a set of statistical techniques that quantify the dependence of a given economic variable on one or more other variables. The steps in using it are 1) collecting data on the variables in question, 2) specifying the form of the equation relating the variables, 3) estimating the equation coefficients, and 4) evaluating the accuracy of the equation. SECTION: 2
33. How can regression analysis use uncontrolled data to estimate demand? ANSWER: Regression analysis uses uncontrolled data to generate an equation that allows one to measure the separate influences of multiple explanatory variables (in the form of numerical coefficients) on total demand. In addition, the analysis provides statistics that measure the accuracy (goodness of fit) of the equation. Accordingly, the regression approach can produce the same kinds of results as a carefully controlled market study. SECTION: 2
34. Suppose that in some regression, the R2‚ = .945, the number of observations is 14, and the number of coefficients is 5. What is the adjusted R 2? ANSWER: In this case, the number of degrees of freedom is N - k = 14 - 5 = 9. The adjusted R2 is: R2 - [(k - 1)/(N - k)•(1 – R2)] = .925 SECTION: 3
35. Carefully explain why adjusted R2 is always less than R2. ANSWER: Mathematically, the formula for adjusted R2 is such that for a finite number of observations N, the adjusted R2 will always be less than R2. The adjustment corrects for the fact that adding explanatory variables necessarily increases the proportion of explained variation in the dependent variable. SECTION: 3
36. Jim Bradley is the manager of a bakery, located on a major intersection in a suburban area of Midwestern city. He has been collecting data on sales at his store for the past year. Recently, he has developed a model that he thinks explains sales at the bakery. Unfortunately, he never had a course in statistics, and isn’t sure that he has done his computing correctly and asks for your opinion. According to Jim, weekly sales at the Bradley Bakery can be described by the equation: Q = 5,000 - 1,000P + 10A + 1.5Y - 400Pc - 25Ac,
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where Q denotes unit sales, P is the firm’s price, A is the firm’s advertising spending, Y is the per capita income in the local area, Pc is the average price charged by a nearby competing bakery and Ac is the competitor’s advertising spending. Jim didn’t keep the printout from the analysis. He only kept the equation, which he is eager to use to plan for his likely sales in the next few months. What advice would you give Jim on using the equation? ANSWER: Without the regression’s statistical output, Jim’s equation is highly problematic. It is impossible to test the reliability or statistical significance, of any of the results. Specifically, there is no information on t-ratios to test the significance of any of the independent variables. There is no R 2‚ to test the significance of the regression as a whole. There is no standard error of the regression to compute confidence intervals for the dependent variable. Furthermore, it is possible that Pc and Ac are collinear. A competing firm might increase advertising while decreasing price at the same time. In short, Jim cannot use the results with any confidence. SECTION: 3
37. What role do leading indicators play in forecasting? What are some of their limitations? ANSWER: A leading indicator is a variable that moves in a predictable direction well in advance of another key economic variable. For instance, a downturn in the stock market might be an early indication (six to 12 months in advance) of a downturn in the economy. In other words, the indicator’s change “leads” the change in the other variable. Barometric forecasting relies on leading indicators (often an index of variables to improve accuracy) to make predictions. There are several problems with the leading indicator approach. First, leading indicators are not always accurate predictors. Second, there are variable and changing lags between movements in indicators and subsequent movements in the variable to be predicted. Third, leading indicators do not usually give information about the actual magnitude of the change in the variable predicted. SECTION: 4
38. A firm has prepared two different models to be used for forecasting. One has a fairly large root mean squared error (RMSE), the other has a much smaller RMSE. Which forecast would you expect to give the more accurate prediction? Explain. ANSWER: The model with the smaller RMSE will typically give the more accurate prediction. RMSE is a measure of the total error in the forecasting model, and is analogous to the R 2 statistic associated with regression models. The smaller the RMSE, the more accurately the model predictions match the actual outcomes of the predicted variable. Note, however, that if the underlying structure of an economic relationship changes, then the accuracy of a predictive model may fall. SECTION: 4
39. What role does uncertainty play in forecasting? Explain. ANSWER: The future is uncertain. No model or forecasting method can predict the course of future economic events with certainty. Consequently, forecasts are not infallible guides to the future. Significant margins of error must be attached to all forecasts. They are contingent upon various events that may or may not take place. Therefore, a manager, who relies on a forecast, should be prepared to cope with the unexpected. Note that one possible response to uncertainty is to prepare several forecasts based on different possible scenarios. Management could examine both a most-likely forecast and a “worst-case” forecast and determine how to respond in each case. SECTION: 4
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40. Sales at a store are currently $450,000 per year. If sales are predicted to increase by 5% per year, forecast sales for each of the next 4 years. ANSWER: For the first year, For the second year, For the third year, For the fourth year, SECTION: 4
($450)(1.05) = $472.5 thousand. ($450)(1.05)2 = $496.1 thousand. ($450)(1.05)3 = $520.9 thousand. ($450)(1.05)4 = $547.0 thousand.
41. If a forecaster is analyzing sales of gasoline in a large city during the next two years, which timeseries component is likely to be most important? What if the forecast is for the next ten years? ANSWER: a) The most important components during the next two years are (1) seasonal variations in gasoline demand, and (2) volume changes due to the business cycle. b) Over 10 years, the general growth trend in sales is likely to dominate all other components. SECTION: 4
42. How would a forecaster determine which functional form of an equation to use to predict a variable? ANSWER: A forecaster would most likely use regression analysis to find the best equation for explanation and prediction. An equation that has (1) high explanatory power (a high R 2, statistically significant coefficients) and which (2) makes economic sense (the signs and magnitudes of the coefficients makes sense) would be deemed superior. SECTION: 4
ESSAY
43. Rail Tours, Inc., sells packaged tours on rail lines, including gourmet meals and a reserved bed. The most popular tours are in the autumn, when foliage colors are at their peak. The overnight package for Saturday and Sunday morning are especially heavily booked. A market survey firm has just completed a study in which they conclude that if the package cost is $200 per couple, then Rail Tours can expect to sell 400 spaces on a typical Saturday. If the price is raised to $225, then unit sales will drop to 390. If the price is raised further to $250, unit sales drop to 380. a) From the data given, write down the demand equation and determine its intercepts. Are there any precautions needed when operating at the extreme ends of the demand curve? b) The survey firm also reports that if per capita income changes, Rail Tours can expect a large change in bookings. In particular, if per capita income falls by 1%, then bookings will tend to fall by about 2%. Are tour packages a normal good? Explain. c) If you were responsible for making a forecast for bookings, would you accept this forecast as is? Or would you want additional information about demand? Explain. ANSWER: a) For every $25 increase in price, Q decreases by 10 units, implying the slope P/Q = -2.5. The complete equation is: P = 1,200 – 2.5Q. Thus, Q = 0, and P = $1,200 is one intercept and P = 0 and Q = 480 is the other. One should be careful about this sort of extrapolation. The extreme ends of the
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curve are far from the current price and quantity, and it is not at all certain that such an extension of the curve will yield reliable predictions. b) Tours are normal goods. As income rises, so does demand. If income falls, demand also falls. c) The demand equation is deficient in several ways. There is no indication of R 2‚ or other statistics to determine accuracy. There is no mention (or inclusion) of other variables that might influence demand. In particular, the firm may wish to know of the effects of substitutes or complements on tour demand. Finally, although demand is highest on fall weekends, there is no indication of the degree of drop-off in offpeak periods. Thus, the tour operator needs to measure and track the seasonal trend in demand so it can adjust capacity accordingly. SECTION: 2
44. You have taken over your parents' small dry-cleaning shop, and are interested in forecasting demand for your services. Your parents never quite got around to trying to measure demand, but they have kept extensive price and sales records. Using this data, you employ multiple regression techniques and estimate the following equation: Q = .95P-.6Y.9 Pc.25, where Q = number of shirts laundered per week, P = price in dollars of a laundered shirt, Y = per capita income in the local area, and Pc = price charged by another dry cleaner two blocks away. The number of observations is 39 (i.e., nine months of weekly data).The equation’s R2 is .85, the standard error of the estimate is 200, and the standard errors for the variables are.45;.15; .39; and .18, respectively. a) Interpret the demand equation and discuss the associated regression statistics. b) If you were to raise the price per shirt, what would happen to total revenue? c) Evaluate the impact of the other dry cleaner’s price on your sales. (At the 95% confidence level, the relevant t-statistic is about 2.04 for 35 degrees of freedom). d) Were your parents maximizing profit? If not, suggest an appropriate course of action to increase profitability. ANSWER: a) The regression equation relates the number of shirts laundered weekly to the value of three variables: Price charged, P; per capita income, Y; and price charged by another firm, Pc. The individual coefficients of the equation provide estimates of the elasticity of each of the variables. The other statistics indicate the accuracy of the empirical estimation of the equation. For instance, the R 2 of .85 indicates that 85% of the variation in weekly sales are explained by the regression model. The standard error of the estimate provides information about the level of accuracy that a forecaster can expect when using this model. The standard error of each variable’s coefficient measures the accuracy of the coefficient. The smaller the size of the standard error, the greater the accuracy of the parameter estimate. b) Because each coefficient measures that variable’s elasticity of demand, demand at the current price is price inelastic (-.6). Increasing price is likely to increase revenue. Moreover, the t-ratio is (.6/.15) = 4, which easily is significant at the 95% confidence level. c) Compute the t-ratio. From the data given, the coefficient is .25, and the standard error is .18, implying a t-ratio of 1.389. At the 95% confidence level, this is not significantly different from 0. Therefore, the other dry cleaner’s price does not have a material effect on your sales. d) No. The fact that demand is inelastic is clear indication that your parents were not maximizing profit. The most direct way of increasing revenue and profit is to raise price. SECTION: 3
45. The Dodge City Bank is planning its loans for the next several years, and is using a model of loan demand developed from past experience. Fred Smith is responsible for developing the mortgage loan component of total loan demand. Fred estimates the following equation using 14 years of data: Q = 50 - .2P - .2D + .3Y + .15H, (17) (.13) (.16) (.08) (.06)
4-11
R2 = .844
Estimating and Forecasting Demand
Here, Q denotes mortgage loan demand (in $ millions), P denotes the prime interest rate, D is the discount rate, Y is per capita income ($ thousands), and H is an index of average city housing prices ($ thousands). The standard error of the regression is 22, and standard errors are shown in parentheses. a) Fully evaluate these regression results, including computation of t-statistics, adjusted R2, and the Fstatistic. b) Might there be multicollinearity in this model? If so, how should Fred adjust his forecast for this fact? c) Fred thinks that the discount rate will be 6% in the next year, the prime rate will be 7.75%, per capita income in Dodge City will be $21,000, and housing prices will be $165,000. How many loans can Dodge City Bank expect to make in the next year? ANSWER: a) The regression equation relates the amount of mortgage loans annually to the value of four variables: the prime interest rate; the discount rate; per capita income; and housing prices. The individual coefficients of the equation provide estimates of the impacts of the respective explanatory variables The equation’s R2 of .844 measures the proportion of total variation in annual mortgage loan volume explained by the regression model. The standard error of the regression provides information about the level of accuracy that a forecaster can expect when using this model. The standard error corresponds to the standard deviation of a probability distribution, and is used to estimate a confidence interval of a demand forecast. The standard errors of the coefficients measures the level of accuracy with which the relationships between the independent variables and the level of demand have been estimated. They can also be used to estimate confidence intervals or ranges regarding the true value of the parameter. In particular, the smaller the size of the standard error for the variable is, the greater the accuracy of the coefficient estimate. The respective t-statistics are: -.2/.13 = -1.54 for P,.-2/.16 = -1.25 for D, .3/.08 = 3.75 for Y, and .15/.06 = 2.50 for H. The t-statistics for P and D are not large enough to be significantly different from zero. The tstatistics for Y and H are highly significant. The adjusted R2 is R2 - [(k - 1)/(N - k)]•(1 – R2) = .844 - [(5 - 1)/(14 - 5)]•(1 - .844) = .775. 2 In turn, F = [R /(k - 1)]/[(1 – R2)/(N - k)] = [.844/(5 - 1)]/[(1 - .844)/(14 - 5)] = 12.173. The F-statistic is large, indicating that the equation as a whole has strong explanatory power. b) The variables P and D are likely to be collinear. Interest rates tend to move together (or, be closely correlated with each other). A good indicator of this is that the estimated coefficients of P and D are not statistically significant. Multicollinearity means that the estimate is unreliable, and must be taken with caution. Fred should be cautious in preparing a forecast of loan demand for the next year. c) Based on the data given, Predicted Q is: 50 - .2(8) - .2(7.75) + .3(21) + .15(165) = $77.9 million. SECTION: 3
46. What are the major sources of information that can be used to estimate demand? What are the major benefits and drawbacks of each? ANSWER: Consumer interviews and surveys are a direct way to gather information, through phone calls, mail surveys, or other marketing surveys. Such direct information can be very useful. Pitfalls of surveys include sample bias, response bias, response inaccuracy, and the cost of administering the survey. Controlled consumer experiments can generate data about actual decisions, rather than reported preferences and behavior. Drawbacks include the fact that subjects know it is an experiment, and the tests are generally of small scale and short duration, so that results may not forecast long-term effects well. Controlled market studies permit detailed tests of changes in key decision variables, such as price and advertising. Drawbacks include the fact that many other variables must be held constant, and the high cost of conducting experiments. Uncontrolled market data is inexpensive to generate and permits many variables to change at one time. Statistical techniques permit analysts to sort out the effects of the different variables. Finally, it is possible to purchase some data, such as consumer buying plans, and macroeconomic forecasts. SECTION: 1
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Chapter 4
47. Why is identification a problem in demand estimation? What management errors might occur if a demand relationship is not properly identified? ANSWER: Identification is the concept that there must be sufficient known information to permit precise identification of unknown variables. If several variables are changing simultaneously, it is essential to disentangle the changes, and assure proper estimation. Ideally, all of the variables are held constant (either in fact or with multiple regression). See Figure 4-2 in the main text for an example of identification problems. Using this example, improper estimation may lead management to believe that demand is very elastic. In fact, demand is much less elastic. A price cut, which management believes will lead to a large unit increase in sales, has much less impact on quantity. SECTION: 3
48. INSITE Corporation produces advanced analytic software for computer simulations called Model It. Based on a regression analysis of product sales in the first year after launch, INSITE’s marketing department estimates the demand for Model It to be: QM = 1,200 - 8PM + 4PS with adjusted R2 = 0.65, and with all of the above coefficients statistically significant. Here, QM denotes units sold of Model It software, PM denotes Model It’s price, and PS denotes the price of a best-selling statistical software package (with both prices in dollars). a) Currently, PM = $200 and PS = $300. What is the predicted demand for Model It software? The price PS has been unchanged (at $300) during the last 6 months. Given this information, write down the equation for Model It’s demand curve (with QM as the left-side variable). Also determine its inverse demand curve (with PM as the left-side variable). b) An industry analyst comments that demand for Model It is not very sensitive to changes in the price of the statistical software package PS. (This package does perform some of the same operations as Model It, but not as quickly or conveniently.) Carefully assess this contention. Do you agree or disagree? c) As is true with many information goods, the marginal cost of producing Model It is negligible. However, the company incurred significant costs in developing the product for market (estimated to be about $350,000). Given the estimated demand of part a, determine the optimal price and output quantity for Model It. d). A marketing department analyst realizes that a potentially important determinant of demand for Model It software is the price of computer workstations. The analyst reruns the regression model and now includes the price of workstations along with the other variables. The new model differs from the original regression of part a in the following ways: The adjusted R2 increases from .65 to .78. The coefficient of PM changes from -8 to -10, while the coefficient of PS is essentially unchanged. The new regression coefficient for PW (the workstation price) has a negative sign. Finally, all three price coefficients are highly significant. Is the new regression equation an improvement over the original? In the new regression, Q M is observed to be more sensitive to changes in PM than in the original regression. Explain why this might be the case? ANSWER: a) i) QM = 1,200 – (8)(200) + (4)(300) = 800 units. The demand curve is: QM = 1,200 + (4)(300) – 8PM, or QM = 2,400 – 8PM. Equivalently, PM = 300 – (1/8)QM. b) The analyst’s argument probably rests on the fact that the coefficient for P S is only 4 (seemingly not very large). However, the best measure of price sensitivity is the cross price elasticity of demand: EPs = [Q/PS][PS/Q] = (4)(300)/800 = 1.5. This is greater than one indicating that the software items are reasonably close substitutes. A 10% reduction in the rival price will cause a 15% drop in sales of Model It. The analyst’s conjecture appears to be wrong headed. c) With MC = 0, the objective is to maximize revenue. We know that PM = 300 – (1/8)QM. Setting MR = 0 implies 300 - .25QM = 0, or QM = 1,200. In turn, PM = $150. d) As indicated by the higher R2, the new equation explains variations in demand significantly better than the old equation. In addition, all of the coefficient signs make sense (the coefficient of P W is positive
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Estimating and Forecasting Demand
because PCs and applications software are obvious complements), and all coefficients are highly significant. The new equation shows the true sensitivity of QM to PM, accounting for the independent influence of PW. In the old equation (with PW missing), this sensitivity was obscured. For instance, if PM was increasing at the same time PW was declining, the former’s negative effect on sales would be partially offset by the latter’s positive effect. ) SECTION: 3
49 What are the component parts into which a time-series pattern can be broken? Briefly describe each. ANSWER: A time-series can be broken into four components: trends, business cycles, seasonal variation, and random fluctuations. See section 1 of the text for a complete discussion. SECTION: 4
50. Henry Goot is the owner of Discount Books, a bookseller housed in large warehouse. Sales have been growing rapidly since he opened his shop (in much smaller quarters) 4 years ago. Goot has been tracking sales and has observed that compound growth has been 25% a year since opening. At year’s end, gross sales have totaled about $1,250,000. a) Assuming that demand continues to grow at this rate, what will be gross sales in the next three years? b) Goot has observed that he needs to rent 1,000 square feet of warehouse space in order to stock sufficiently to sell $100,000 gross sales in a year. He can sign a long-term lease to rent space adjacent to his current space (of 17,000 square feet) and wants to do so in order to prevent overcrowding of the store. When should he arrange to have the space available for stocking books? c) How reliable is the forecast for the next three years of sales? Explain. List at least three specific weaknesses in the forecast. ANSWER: a) Sales in the past year are $1,250,000. Sales forecast in the coming year are: (1.25)($1,250,000) = $1,562,500. Sales in year 2 are: (1.25)2($1,250,000) = $1,953,125, and sales in year 3 are: (1.25)3($1,250,000) = $2,441,406. b) Current space is sufficient for sales of $1,700,000. Discount Books will surpass that amount of sales near the end of year 2. Therefore, Henry should sign a long-term lease starting about then, or risk overcrowding of the store. c) The forecast, as briefly described, is not particularly reliable. Some of the specific weaknesses are: (1) The model is non-structural. There is no attempt to specify the underlying factors that have produced strong sales growth to date. (2) There is no indication of the size of the year-to-year fluctuations during the first four years of business. Thus, it is difficult to estimate a confidence interval (or margin of error) for future sales. (3) Growth of 25% a year is not unusual for a new, growing business. However, it is rare for a more mature business. It is unlikely that this sort of growth rate will continue for long. SECTION: 4
51. Fred Smith of the Dodge City Bank has received several loan applications from local small businesses. The applications are supported by various documentation, including the business plans of the firms. Each applicant has submitted forecasts of sales and profits for his or her business. Smith must decide which (if any) loans to approve. Because the ability of the firms to pay off the loans depends on the accuracy of the forecasts, he is especially concerned. He has called on you, his newly hired assistant, to help determine the reliability of the forecasts. What do you tell him about these forecasts and their accuracy to help him make his decision? ANSWER: The forecast accuracy of a prediction (or the forecasting equation behind the prediction) is only as reliable as the methodology used to derive it. Your job as assistant is to examine each applicant’s
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Chapter 4
forecasting methodology to determine how reliable the forecasts might be. Refer to the discussion of forecast accuracy in the chapter. SECTION: 4
52. Gold Tracker monitors the price of precious metals and has developed a forecasting model for the sales of gold: Q = 4,000 - .01P + 1.5C - 1.25X + 1.0S, where Q = weekly sales of gold (in millions of ounces), P is the price of gold (dollars per ounce), C is the most recent one-month report of the consumer price index of inflation (in percent), X is an index of the exchange rate of the U.S. dollar compared to seven other currencies, and S is the market price of an ounce of silver (dollars per ounce). a) Recently, the price of gold has been $380 per ounce, inflation was measured at 0.2% for the month, the dollar has been trading at 99.7 on the foreign exchange index, and silver has been steady at $9.50 per ounce. What is the expected quantity of gold traded per week? b) Forecast sales of gold for the next two weeks if gold’s price is expected to rise by 1% per week, inflation is expected to remain constant, the dollar is expected to fall by 5% per week, and the price of silver is expected to rise by 2% per week. c) Discuss the importance of sensitivity analysis in relation to this forecasting equation. ANSWER: a) Q = 4,000 - .01P + 1.5C - 1.25X + 1.0S = 4,000 - (.01)(380) + (1.5)(0.2) - (1.25)(99.7) + (1)(9.50) = 3,881 million ounces per week. b) For the first week, Q = 4,000 - (.01)(383.8) + (1.5)(0.2) - (1.25)(94.7) + (1)(9.69) = 3,888 million ounces. For the second week, Q = 4,000 - (.01)(387.64) + (1.5)(0.2) - (1.25)(89.98) + (1)(9.88) = 3,894 million ounces. Notice that most of the changes during the next 2 weeks tend to be offsetting, leading to little change in predicted gold sales. c) Sensitivity analysis examines how forecasts would change if one or more economic factors change. Here, the forecast is largely invariant to the assumed changes in the variables. The coefficients on the variables are all small, so that a change in each explanatory variable will have a small effect on the value of the dependent (or forecasted) variable. In addition, the multiple effects are largely offsetting, leaving predicted gold sales mainly unchanged. SECTION: 4
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File: Ch05; CHAPTER 5: Production
Each question contains a code showing the section of the chapter text from which it was taken. The codes for this chapter are: Code 1 2 3 4 5
Section Basic Production Concepts Production with One Variable Input Production in the Long Run Measuring Production Functions Other Production Decisions
MULTIPLE CHOICE
1. The main task of a production manager is to determine a) Which goods to produce. b) The markets in which to sell finished products. c) When and how to increase production capacity. d) Profitable prices for finished products. e) How to produce a given level of output at minimum total cost. ANSWER: e SECTION: 1
2. For a given combination of inputs, a production function indicates the associated a) Average cost of production. b) Marginal cost of production. c) Maximum output level. d) Minimum cost. e) Profit-maximizing output level. ANSWER: c SECTION: 1
3. When considering efficient production, how many ways are there to make a finished good or service? a) Only one way that is efficient. b) Two ways, but never more than that. c) One way, until technological innovations cause this method to be displaced by a more efficient means. d) Many efficient methods usually exist. e) Uncertain. For a definitive answer, more information is needed. ANSWER: d SECTION: 1
4. The best definition of the short run is the period of time in which a) Management cannot change its decisions. 5-1
Production b) The amount of output cannot be varied. c) One or more inputs are fixed d) All inputs can be varied but at a high marginal cost. e) Economic conditions are relatively stable and unchanging. ANSWER: c SECTION: 2
5. In the long run, the firm can change a) All of its inputs. b) Only some of its inputs. c) None of its inputs. Its inputs are fixed in the long run. d) All of its inputs, provided they are changed in the same proportions. e) Uncertain. It depends on the specific industry. ANSWER: a SECTION: 2
6. Marginal product is defined as a) The additional output produced by an additional unit of input, all other factors held constant. b) The additional output produced by a scale increase in all inputs. c) The additional input required to produce one additional unit of output. d) Total output divided by the total units of an input. e) None of the answers above is correct. ANSWER: a SECTION: 2
7. Labor’s marginal product curve at first rises due to a) Increasing specialization of labor. b) Increasing returns to scale. c) Increasing efficiency of capital. d) Increasing profits from additional output produced and sold. e) Declining labor costs. ANSWER: a SECTION: 2
8. If marginal product is zero, then total product is a) At a minimum. b) Necessarily being produced at minimum total cost. c) At a maximum. d) Increasing at a maximum rate. e) Uncertain. More information is needed. ANSWER: c SECTION: 2
5-2
Chapter 5 9. According to the law of diminishing marginal returns, a) If all inputs are increased in equal proportions, output will eventually decrease. b) If one input is increased, with all other inputs unchanged, additions to output will eventually decrease. c) If one input is held constant, and all other inputs are increased, output will eventually decrease. d) If one input is increased, and all other factors are held constant, output will eventually decrease. e) If all inputs are increased, output will grow but by a smaller proportion. ANSWER: b SECTION: 2
10. Marginal revenue product denotes a) The extra revenue resulting from a unit increase in the input. b) The extra revenue resulting from a unit increase in output. c) The extra revenue that results from economizing on excess inputs. d) The extra output that results from a unit increase in the input. e) The extra revenue that results from an increase in technical efficiency. ANSWER: a SECTION: 2
11. In seeking to maximize profit, what rule should the firm follow regarding the amount of labor to hire? a) Hire as long as MRPL > MRPK. b) Hire until MRPL > MCL. c) Hire until MRPL = MCL. d) Hire until MRPL = 0. e) Hire until MR = MC. ANSWER: c SECTION: 2
12. Firm X sells output at P = $8 per unit and pays labor a wage of $20 per hour. The marginal product of labor is given by: MPL = 7 - .1L. The profit-maximizing quantity of labor is: a) L = 20 hours. b) L = 28 hours. c) L = 35 hours. d) L = 40 hours. e) L = 45 hours. ANSWER: e SECTION: 2
13. In the long run, can a firm change its scale of operation? a) Yes. This is a key decision in the long run. b) Yes, but only if technology changes. c) No. Scale cannot be changed in the long run. d) No, unless there are returns to scale. e) Uncertain, depends on the nature of the production function. ANSWER: a SECTION: 3 5-3
Production
14. If a firm faces constant returns to scale, when inputs are increased, a) Output will be constant. b) Output will increase at the same rate. c) Output will increase at a falling rate. c) Additions to output will eventually decrease. e) The firm will move to a new production point on the same isoquant. ANSWER: b SECTION: 3
15. Under increasing returns to scale, a) As one input increases, additions to output eventually decrease. b) As all inputs are varied, average cost increases. c) As inputs increase in a given proportion, output increases by a greater proportion. d) As output is increased, required inputs grow at a faster rate. e) As scale economies are reached, total costs escalate. ANSWER: c SECTION: 3
16. When choosing a least-cost production method, the firm considers a) Different production technologies to find efficient combinations of inputs. b) The marginal products of all inputs. c) The costs of all inputs. d) Answers b and c are both correct. e) Answers a, b, and c are all correct. ANSWER: e SECTION: 3
17. If there is a change in input prices, what is the most likely impact on production isoquants? a) They will shift leftward. b) They will shift downward. c) They will be unchanged. d) They will shift outward. e) Uncertain, depends on which input prices change. ANSWER: c SECTION: 3
18. In an isoquant map, which of the following best measures the trade-off between the inputs? a) The ratio of the inputs’ marginal products. b) The slope of the isoquant. c) The ratio of the inputs’ average products. d) The slope of the budget line. e) Answers a and b are both correct.
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Chapter 5 ANSWER: e SECTION: 3
19. The marginal rate of technical substitution is defined as a) The rate at which outputs can be substituted for one another. b) The rate at which one input can be reduced without reducing total production. c) The rate at which both inputs can be substituted between two isoquants. d) The rate at which one input substitutes for another without changing output. e) The rate at which new substitutes can be used for current inputs. ANSWER: d SECTION: 3
20. In the long run, a profit-maximizing firm produces such that a) The marginal products of all inputs are zero. b) The ratios of marginal products to input prices are equal across all inputs. c) Marginal products are equal for all inputs. d) Each input’s marginal revenue product equals the input’s marginal cost. e) Answers b and d are both correct. ANSWER: e SECTION: 3
21. If a production function is linear, the inputs used in the production process a) Are perfect complements. b) Are perfect substitutes. c) Exhibit diminishing returns. d) Are unrelated. e) Cannot be substituted for one another. ANSWER: b SECTION: 4
22. If production takes place with fixed proportions, the inputs used in the production process a) Are perfect substitutes. b) Are imperfect substitutes. c) Cannot be substituted for one another. d) Are combined in linear fashion to make output. e) Uncertain, depends on the nature of technology. ANSWER: c SECTION: 4
23. A Cobb-Douglas production function with exponents summing to 1.2 exhibits a) Increasing returns to scale. b) Constant returns to scale. c) Decreasing returns to scale. d) Increasing long-run average cost per unit. 5-5
Production e) Answers c and d are both correct. ANSWER: a SECTION: 4
24. In statistically estimating a production function, a manager can use a) Time series data. b) Cross-section data. c) A computer simulation of output levels under the new technology. d) Answers a and b are both correct. e) Answers a, b, and c are all correct. ANSWER: d SECTION: 4
25. In allocating a limited amount of an input among several plants that produce the same good, the firm should do so such that a) The total products of all facilities are equal. b) The marginal products of all facilities are positive. c) The marginal products of all facilities are equal. d) The average products of all facilities are equal. e) None of the answers above is correct. ANSWER: c SECTION: 5
26. Factory A produces output according to: QA = 100XA, where XA denotes the amount of input allocated to the factory. Factory B produces output according to: QB = 200XB - QB2. The total available amount of input X is 100 units. The firm’s profit-maximizing allocation is a) XA = 60 and XB = 40. b) XA = 50 and XB = 50. c) XA = 0 and XB = 100. d) There is not enough information to determine the answer. e) None of these answers is correct. ANSWER: b SECTION: 5
SHORT ANSWER
27. Carefully define the term production function, and explain its importance. ANSWER: A firm's production function is a quantitative relationship that indicates the maximum level of output the firm can produce for any combination of inputs. A production function is a guide to management for efficient production of the good or service. SECTION: 1
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Chapter 5
28. Dirt Diggers (DD) is a firm that excavates roadside ditches for laying drainpipe. Its output follows the production function: Q = 10L - .1L2, where L denotes labor hours and Q the length of the ditch in meters. The firm hires labor at a wage of $12 per hour. a) DD has received an offer to excavate 250 meters for a price of $500. Should it accept the offer? b) Answer part a assuming that DD is offered as much or as little excavation work as it desires at a price of $2.00 per meter dug. ANSWER: a) From the production function, we see that excavating 250 meters requires 50 labor hours. For this much labor, the total wage cost is ($12)(50) = $600. Clearly, DD should reject the $500 price. b) To determine a profit-maximizing quantity (of digging), DD should set: MRPL = MR•MPL = MCL. We know that MPL = dQ/dL = 10 - .2L. Thus, (2)(10 - .2L) = 12, implying L = 20. In turn, Q = 200 - 40 = 160, and DD's profit is ($2)(160) - ($12)(20) = 320 - 240 = $80. SECTION: 2
29. Carefully explain why the marginal product of labor first rises and then falls as use of labor increases. In which portion of the marginal product of labor curve will the firm typically produce? ANSWER: The marginal product of labor increases because with more labor, specialization can be exploited. In addition, any underutilized fixed factors can be used more intensively. Marginal product of labor then decreases as opportunities for specialization are exhausted, and more and more labor is applied to a fixed amount of machines and production capacity. The typical firm will produce at an input level for which MPL is falling. SECTION: 2
30. Will a profit-maximizing firm seek to maximize output from a variable input? Explain. ANSWER: No. Assume the variable input is labor. A firm will maximize profit when it equates MRP L = MCL. If the firm maximizes output from an input, then MPL = 0, and MRPL = 0. Because MCL is positive (i.e., there is a cost of hiring additional labor hours), the firm will not maximize profit in this case. Instead the firm will maximize profit by using less labor, so that MPL is still positive. SECTION: 2
31. Suppose that management increases the size of its plant. What is the most likely impact on total and marginal products of the other inputs? How will this affect usage of the variable inputs? ANSWER: The most likely impact is an increase in total product and marginal product for a given amount of labor. Graphically, the total product and marginal product curves would shift upward, and the peaks of the curves would occur at greater input levels than originally. Typically, this will result in increased usage of the variable input. SECTION: 2
32. Explain how a firm will respond to each of the following changes in the short run. a) A drop in the price of the good or service its sells. b) A drop in the hourly wage. c) A decline in the productive efficiency of labor. ANSWER: The firm’s optimal use of its variable input (here, labor) is governed by the rule: MRP L = MCL. The key is to trace the effect of each change on the factors entering into this rule.
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Production a) A drop in the good’s price reduces the firm’s marginal revenue product causing it to use less labor and to lower its output level. b) A drop in the hourly wage makes the use of labor more attractive. Labor use and output both increase. c) A decline in labor’s marginal product causes MRP to fall, so labor usage and output both decrease. SECTION: 2
33. Carefully define returns to scale, and explain how this differs from marginal returns. ANSWER: Returns to scale refer to the impact on output if all inputs are changed. For example, if a firm faces constant returns to scale and all inputs increase by 5%, then output will increase by 5%. Marginal returns refer to the impact on output if one input is changed while all other inputs are held fixed. Typically, we expect that as use of the input increases, the firm will experience diminishing marginal returns. This will be true regardless of returns to scale. SECTION: 3
34. A firm has carefully measured its production function, and thinks that it can be approximated by: Q = K.55L.45, where Q = units of output, K = units of capital, and L = units of labor. What is output elasticity in this case? What sort of returns to scale does the firm face? Explain. ANSWER: Output elasticity in this case is the sum of the exponents: .55 + .45 = 1. In addition, because the exponents sum to one, the firm faces constant returns to scale. SECTION: 3
35. Carefully explain the rule for the firm to follow in the long run if it wishes to produce at least cost. ANSWER: In the long run, the firm produces at least cost when the ratios of marginal products to input costs are equal across all inputs. This requires that the firm hire inputs so that: MPK/PK = MPL/PL = .... = MPi/Pi for all inputs. If a firm follows this rule, then the extra output per dollar of input will be the same for all inputs. No possible rearrangement of inputs will decrease cost for that level of output, or increase output for that level of expenditure on inputs. SECTION: 3
36. Specialty Steel has carefully measured production in its new plant to determine whether it is technically efficient in production. It has found that, for its two inputs K and L, it has the following marginal products: MPK = 15, and MPL = 22. The inputs are hired in perfectly competitive markets, and the firm faces input costs of PK = $7.50 and PL = $10 per unit. You have been hired as a consultant to assist Specialty in increasing profitability. What do you recommend about production planning? Explain. ANSWER: In the long run, the firm produces at least cost when the ratios of marginal products to input costs are equal across all inputs. This requires that MPK/PK = MPL/PL. Here, the respective rations are 15/$7.50 and 22/$10 and are not equal. Therefore, the firm is not maximizing profit. It can increase efficiency and profit by hiring more labor and/or less capital to bring this ratio into equality. As more L is used, MPL will decline; as less K is used, MPK will increase. SECTION: 3
37. Carefully define marginal rate of technical substitution. What assumptions are made in measuring it? 5-8
Chapter 5
ANSWER: MRTS denotes the rate at which one input substitutes for another in production. When using isoquants, it can be measured as: -MPL/MPK, and it is assumed that Q is constant; that is, we are moving along an isoquant. SECTION: 3
ESSAY
38. A firm produces according to the following production function: Q = K .25L.75 where Q = units of output, K = units of capital, and L = units of labor. Suppose that the price of K is $4 per unit, and the price of L is $6 per unit. What is the optimal capital/labor ratio? ANSWER: The firm employs inputs in an optimal ratio when MP K/PK = MPL/PL. We know that MPK = .25K-.75L.75 and MPL = .75K.25L-.25. By substitution, (.25K-.75L.75)/4 = (.75K.25L-.25)/6. Cross multiplying leads to : 6(.25K-.75L.75) = 4(.75K.25L-.25) or 1.5K-.75L.75 = 3K.25L-.25. This simplifies to 1.5L = 3K, or L = 2K. The firm should use twice as many units of labor as units of capital. SECTION: 3
39. Enpar manufactures engine parts for an automotive manufacturer. It operates two plants, A and B, which have the following production functions: QA = 30SA - .25SA2 and QB = 40SB - .5SB2, where QA and QB denote the outputs of engine parts from each plant and SA and SB denote the amounts of steel used in each plant. Suppose that total steel availability is 40 units. What is the optimal allocation between the two plants? ANSWER: Enpar maximizes profit when the marginal product for steel is equal at the two plants. MPA = 30 - .5SA and MPB = 40 – SB. So that 30 - .5SA = 40 – SB. In addition, SA + SB = 40, so that SB = 40 – SA. Substituting this last equation into MPA = MPB yields the single equation: 30 - .5SA = 40 - (40 - SA), so 30 = 1.5SA. Thus, SA = 20 and SB = 20. SECTION: 3
40. Standale Plastics produces plastic dustpans, using a semiautomated system of five machines to produce pans. The amount of labor to tend the machines, repair, adjust input flows, and remove completed pans, is variable, and output tends to follow the formula: Q = 300L .6, where Q = units of output produced per day and L = number of daily workers. a) Compute the total product and marginal product of labor for the first five workers. b) Standale sells the dustpans to retailers at a price of $1 each, and can hire labor at a wage of $125 per day. What is the optimal amount of labor to hire? What is the optimal output of dustpans? c) Suppose that the price of the dustpans increases to $1.25. What is the new optimal amount of labor? ANSWER: a) For L = 1 to 5, compute: Q = 300L.6 and MPL = Q/L = (.6)(300)(L)-.4. L Q MPL 1 300 180 2 455 136.4 3 580 116 4 689 103.4 5 788 94.6 b) Optimal use of an input requires that MRPL = (MR) • (MPL) = MCL. Based on the given data, ($1) • (MPL) = $125 or MPL = $125. The firm should use two workers because the marginal product of a third worker falls short of the threshold value of $125. Total output is 455 units. 5-9
Production c) The new threshold value for MPL becomes: ($1.25) • (MPL) = $125 or MPL = 100. The increase in price prompts the firm to increase its labor to four workers. SECTION: 2
41. Crew Brew produces a popular brand of beer in its mini-brewery located on a small river in Wisconsin. It uses a special formula, combined with the fresh water from the local stream, to produce a drink popular with local folks and tourists who visit during the summer fishing season, and autumn deer hunting season. The production function of Crew follows the formula: Q = 50K + 50L, where Q = barrels of beer, K = units of capital, and L = units of labor. a) Suppose that capital can be purchased for $8 per unit, and labor costs $6 per unit. What is the optimal combination of inputs for the firm to employ? b) Suppose that the cost of inputs changes to $7 for a unit of capital, and $9 for a unit of labor. What is the new optimal combination of inputs? c) Explain the results of a. and b. ANSWER: a) The marginal products for the inputs are: MPK = Q/K = 50 and MPL = Q/L = 50. Because the marginal products are identical, and labor is the cheaper input, Crew Brew should employ only labor to produce its product. Note that MPL/PL is always greater than MPK/PK. b) Now MPK/PK > MPL/PL, so the firm should use only capital. c) This unusual result is because the inputs are perfect substitutes. Graphically, isoquants are straight lines. The optimal solution is on one of the axes, use only labor or capital, depending on the price ratio. SECTION: 3
42. Ranger Construction is preparing to repair potholes, under contract to the local county road repair agency. Based on past experience, Ranger has found that output can be described by: Q = K .5L.5, where Q = pot holes filled, K = units of capital, and L = units of labor. Ranger can hire labor at $12 per hour, and the cost of capital is $8 per unit. Capacity limitations require that Ranger accept no more than $96,000 worth of filling this season. What is the optimal mix of inputs for Ranger? How many potholes should Ranger agree to fill? Use the method of Lagrange multipliers to find the solution. ANSWER: Ranger's objective is: Maximize Q = K.5L.5 subject to 8K + 12L = 96,000. The Lagrange multiplier is: G = K.5L.5 + (8K + 12L - 96,000). We compute three partial derivatives: (1) G/K = .5K.-5L.5+ 8 = 0 (2) G/L = .5K.5L-.5 + 12 = 0 (3) G/ = 8K + 12L - 96,000 = 0 Multiply (1) by 1.5: .75K-.5L.5 + 12 = 0 and equate this expression with (2) to get: .75K-.5L.5 + 12 = .5K.5L-.5 + 12. Cancel 12, and then combine terms and simplify: .75L = .5K, or K = 1.5L. Substitute this last expression into (3): 8(1.5L) + 12L - 96,000 = 0, or 24L = 96,000. Thus, L = 4,000 units and K = (1.5)(4,000) = 6,000 units. The firm’s level of output is: Q = (6,000) .5(4,000).5 = 4,899. Ranger should hire 4,000 units of labor, 6,000 units of capital, and agree to fill 4,899 potholes. SECTION: 3
43. Your firm produces a good in two factories: one in Tucson and one in Phoenix. Historically, the plants’ long-run average costs have been comparable. Engineers have found that output elasticity at the Tucson plant is 1.1, while at Phoenix it is .93. A senior production manager has recommended expanding the scale of production in Tucson over the next few years and cutting production in Phoenix. Does this proposal make sense? Explain. 5-10
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ANSWER: The production manager’s recommendation makes good sense. Tucson’s facility exhibits increasing returns to scale while Phoenix’s facility has decreasing returns to scale. The plants are starting from roughly the same average cost per unit. Increasing the scale of production in Tucson will lower its long run average cost. Conversely, because in Phoenix average costs are rising with output, the best thing to do is reduce the scale of operation and so downsize toward lower average costs. By shifting output from Phoenix to Tucson, the firm can produce the same total amount of output and lower the average cost per unit in both plants. SECTION: 3
44. Sleak Teak builds yard furniture, using domestic hardwoods and (in a smaller shop) handcrafted knick-knacks from the same sorts of wood. Although hardwoods were readily available in the past, recently they have been much more difficult to obtain. Consultation with the plant managers of the two lines has resulted in the following production functions for hardwood usage in the two products: Yard furniture Y = 2TY - .001TY2 Knick knack K = 20TK - .01TK2, where Y and K denote units of products and TY and TK denote teak used in each product. Yard furniture can be sold at a profit of $100 per unit, and knick-knacks can be sold at a profit of $25 each. Sleak Teak has 1,300 units of teak available. How should it be allocated? Explain. ANSWER: Compute the marginal products of teak in the two goods: MPY = 2 - .002TY and MPK = 20 .02TK. The marginal profits of the two activities are: MY = (100)MP Y = 200 - .2T Y, and MK = (25)MP K = 500 - .5T K. Equating the two marginal profits, we have: 200 - .2TY = 500 - .5TK. In addition, TY + TK = 1,300. Therefore, 200 - .2TY = 500 - .5(1,300 - TY), or 350 = .7TY. Thus, TY = 500. In turn, T K = 800. From the production functions, we find: Y = 750 and K = 12,800. SECTION: 4
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File: Ch06; CHAPTER 6: Cost Analysis
Each question contains a code showing the section of the chapter text from which it was taken. The codes for this chapter are: Code 1 2 3 4 5 6
Section Relevant Costs The Costs of Production Returns to Scale, Scope, and Learning Cost Analysis and Optimal Decisions Appendix: Transfer Pricing Special Appendix
MULTIPLE CHOICE
1. Accounting profit typically exceeds economic profit because a) Accounting profit includes intangible revenue sources. b) Economic cost includes all relevant opportunity costs. c) Accounting cost contains implicit costs. d) Accounting practice is to allocate fixed costs to other activities. e) This is incorrect. Economic profit is usually greater than accounting profit. ANSWER: b SECTION: 1
2. The opportunity cost of investing all of your savings in a new business is equal to a) The potential profits from the business. b) The discounted present value of future profits. c) The rate of return on your savings you could have earned in a comparable investment. d) The risk of losing all your savings. e) The growth rate of your savings in the business. ANSWER: c SECTION: 1
3. The total economic cost of pursuing a three-year Masters degree after college is equal to a) The total cost of tuition, books, and living expenses during the program. b) The total cost of tuition and books. c) All expenses incurred during the program. d) All educational expenses during the program plus three years of wages that the individual would have earned if she had not elected the program. e) None of the answers above is correct. ANSWER: d SECTION: 1
6-1
Cost Analysis
4. A manager considering alternative courses of action should a) Not consider costs that are fixed with respect to the alternatives. b) Include both variable and fixed costs. c) Consider all past, present, and future costs. d) Incorporate only accounting cost in the decision-making process. e) Include only a portion of sunk costs. ANSWER: a SECTION: 1
5. Money spent on past research and development should be considered a) Implicit costs. b) Variable costs. c) Sunk costs. d) Relevant costs. e) Opportunity costs. ANSWER: c SECTION: 1
6. A law firm will be paid $500 to send one of its lawyers to take a routine deposition. The firm can send a 2nd-year lawyer whose usual billing rate is $150 per hour and who will lose a half day from working on a lucrative tax deal. Or it can send a 4th-year associate (billing rate $200 per hour) who is currently overseeing the selection and hiring of law students as summer associates. The firm should a) Assign the 2nd-year lawyer because his billable rate is lower. b) Assign the 4th-year lawyer because her billable rate is higher. c) Assign the 2nd-year lawyer because he is currently more productive. d) Assign either one since the firm receives the same $500 fee. e) Assign the 4th-year lawyer because her current work is less valuable to the firm. ANSWER: e SECTION: 1
7. When computing economic profit, we assume that capital earns a a) Zero rate of return. b) Normal rate of return. c) Risk-free rate of return. d) Positive rate of return. e) None of the answers above is correct. ANSWER: b SECTION: 1
8. Fixed costs a) Must be allocated among different activities of the firm. b) Are incurred regardless of the firm's level of output.
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Chapter 6
c) Are identical to overhead expenses. d) Are reduced to zero if the firm produces no output. e) Represent the full costs of production. ANSWER: b SECTION: 2
9. After stopping production of its only product, the firm’s total cost is a) Zero. b) Its total fixed cost. c) Its total variable cost. d) Its opportunity cost. e) There is not enough information to answer. ANSWER: b SECTION: 2
10. A firm's average fixed cost a) Is constant at all levels of output. b) Always increases as output increases. c) Increases at first and then decreases. d) Decreases at first and then increases. e) Always decreases as output increases. ANSWER: e SECTION: 2
11. In the short run, if the marginal product of labor is decreasing, then a) Marginal cost must be increasing. b) Marginal cost must be decreasing. c) Average cost must be increasing. d) Average cost must be decreasing. e) None of the answers above is correct. ANSWER: a SECTION: 2
12. If short-run average cost is increasing then a) Short-run average fixed cost must be increasing also. b) Short-run marginal cost must be decreasing. c) Short-run marginal cost must be greater than short-run average cost. d) Decreasing returns to scale must be the norm. e) None of the answers above is correct. ANSWER: c SECTION: 2
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Cost Analysis
13. When average total cost is at a minimum, a) Marginal cost is also at a minimum. b) The firm is experiencing constant returns to scale. c) Marginal cost is constant. d) Average cost is equal to marginal cost. e) The firm is maximizing its profit. ANSWER: d SECTION: 2
14. A firm produces 100 units of output at an average variable cost of $5 per unit and incurs a total fixed cost of $700. Then, a) Average total cost is $12 per unit. b) Total variable cost is $1,200. c) Marginal cost is constant and equal to $5 per unit. d) Average fixed cost is $5 per unit. e) Total cost is $500. ANSWER: a SECTION: 2
15. In the long run, a) All costs are fixed. b) All costs are variable. c) Some costs are fixed and others are variable. d) The firm can expand or contract as long as it changes all inputs in the same proportion. e) Marginal cost will eventually increase due to diminishing returns. ANSWER: b SECTION: 2
16. Under constant returns to scale, a) The SAC curve will tend to be horizontal. b) The LAC curve will tend to be U-shaped. c) The LMC curve will tend to be upward sloping. d) An increase in scale will increase output more than proportionally. e) The LAC curve will tend to be horizontal. ANSWER: e SECTION: 2
17. Mexico is capable of producing 20 auto tires or 16 microcircuits per labor hour. Brazil is capable of producing 24 auto tires or 24 microcircuits per labor hour. a) Brazil has an absolute advantage in both goods. b) Brazil will be expected to export both goods to Mexico. c) Mexico has a comparative advantage in tires. d) Answers a and c are both correct.
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e) Answers a and b are both correct. ANSWER: d SECTION: 2
18. When the LAC curve is at a minimum a) The LMC curve is also at a minimum. b) The LMC curve is decreasing. c) The firm is operating at its profit-maximizing level of output. d) Total cost is at a minimum. e) LMC = LAC. ANSWER: e SECTION: 3
19. Minimum efficient scale is a) The output level that maximizes long-term profit. b) The point at the bottom of the firm’s learning or experience curve. c) The lowest output level where minimum LAC is achieved. d) The output level where average fixed cost is a minimum. e) The point where the firm is operating at full factory capacity. ANSWER: c SECTION: 3
20. Economies of scope describe the a) Increase in efficiency due to the joint production of many goods rather than one product at a time. b) Efficiency gained by firms that have longer time horizons. c) Cost savings of firms that focus their attention on the production of a single good. d) Gains attributed to specialization and division of labor. e) Cost reduction due to cumulative production experience and learning. ANSWER: a SECTION: 3
21. The minimum efficient scale for a typical firm in an industry is 2 million units. The estimated output for the whole industry is 6 million units. Therefore, the industry a) Is a natural monopoly. b) Is perfectly competitive. c) Has insufficient demand to allow positive economic profits. d) Is likely to support no more than 3 firms of efficient scale. e) Is likely to support a single dominant firm. ANSWER: d SECTION: 3
6-5
Cost Analysis
22. Minimum efficient scale is important in determining a) How much profit exists in a particular market. b) How much output can be profitably made in a production facility. c) How many firms will exit the industry. c) How readily fixed costs can be covered by industry demand. e) How many firms can profitably exist in a particular market. ANSWER: e SECTION: 3
23. A firm maximizes profit by a) Producing until marginal cost equals average cost. b) Producing where the average cost per unit is minimized. c) Raising price until revenue is maximized. d) Producing until marginal revenue equals marginal cost. e) Producing until price equals average cost. ANSWER: d SECTION: 4
24. The firm's price consistently exceeds its average cost. Therefore, a) The firm earns a normal rate of return. b) The firm is maximizing its long-run profit. c) The firm is producing at its most efficient level of output. d) The firm earns a positive economic profit. e) Answers c and d are both correct. ANSWER: d SECTION: 4
25. A firm that is maximizing profit should nonetheless shut down in the short run if a) Total sales revenue is less than total cost. b) Total sales revenue is less than total variable cost. c) The firm is earning less than a normal rate of return. d) The firm is not able to cover its overhead. e) Answers b, c, and d are all correct. ANSWER: b SECTION: 4
26. In the long run, a firm should continue to produce a) If and only if it earns at least a normal rate of return. b) If and only if it earns a positive economic profit. c) If and only if it makes a positive accounting profit. d) If and only if, each profit center is able to cover its share of allocated costs. e) Answers a and b are both correct. ANSWER: e
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SECTION: 4
SHORT ANSWER
27. A lawyer is contemplating quitting her current job with a major corporation (annual salary $110,000) to open her own law firm. She estimates that the total cost of operating the office will be approximately $118,000 per year. The potential revenue is estimated as $200,000 per year. Compute accounting cost, accounting profit, economic cost, and economic profit. ANSWER: Total accounting cost is $118,000. Total accounting profit is $82,000. In turn, total economic cost is $118,000 + $110,000 (old salary), and total economic profit is $200,000 - $118,000 - $110,000 = $28,000. SECTION: 1
28. Briefly describe the economic cost of a college graduate serving two years in the Peace Corps in a remote South American village. ANSWER: If the volunteer is “living off the land” in the village, her living expenses could well be negligible. (Of course, she may incur certain non-monetary costs such as sickness and deprivation.) Rather, her main cost is the opportunity cost of the two years of wage income and job advancement she would have enjoyed if she had not headed off to the Peace Corps. SECTION: 1
29. A firm’s production function is given by Q = 2K2 + 6L. Does this production function exhibits constant returns to scale? ANSWER: At K = L = 1, we find that Q = 8. In turn, at K = L = 2, we now have Q = 18 (output more than doubles). Therefore, this production function exhibits increasing returns to scale. SECTION: 2
30. The average variable cost at Q = 1, Q = 2, Q = 3, Q = 4 is respectively equal to $5, $6, $7, and $8 per unit. Find the marginal cost of the first four units of output. ANSWER: Q 1 2 3 4
AVC 5 6 7 8
VC 5 12 21 32
MC 5 7 9 11
SECTION: 2
31. A firm’s short-run average cost is described by the equation: SAC = 2,000/Q + 60 + 0.2Q. Determine the equation for the firm’s marginal cost. What is the MC of producing the tenth unit of output?
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Cost Analysis
ANSWER: We know that total cost is: C = (SAC)Q = 2,000 + 60Q + 0.2Q 2. In turn, MC = dC/dQ = 60 + 0.4Q. At Q = 10, it follows that MC is 64. SECTION: 2
32. A firm’s long-run average cost curve is estimated by the equation: LAC = 1,000 - 2.5Q + .005Q2. What is the minimum efficient scale of production? ANSWER: Long-run average cost is at a minimum when d(LAC)/dQ = 0. Therefore, (dLAC)/dQ = -2.5 + 0.01Q = 0, implying Q = 250. SECTION: 3
33. A firm produces 100 units of good A at a total cost of $1,500 and separately 200 units of good B at a cost of $2,000. By combining the production of A and B, it is possible to produce the same quantities of A and B respectively at a combined total cost of $2,800. Compute the economies of scope experienced by this firm. ANSWER: Economies of scope are measured by: (1,500 + 2,000- 2,800)/(1,500 + 2,000) = 700/3,500 = .20. Management can obtain a 20% cost savings via joint production. SECTION: 3
34. The production manager of a clothing manufacturer estimates that the total annual cost of producing men’s suits is given by the equation: C = 5,000 + 4,100Q - 8Q2 + .004Q3. If the market price of suits is constant, what is the shutdown level of output? What is the minimum price the firm can accept? ANSWER: The shutdown point under competitive conditions occurs at the minimum point of the AVC curve. We know that VC = 4,100Q - 8Q2 + .004Q3, and, in turn, AVC = 4,100 - 8Q + .004Q2. To find minimum average cost, set dAVC/dQ = -8 + .008Q equal to zero. The solution is Q = 1,000. The value of minimum AVC is: 4,100 - 8(1,000) + .004(1,000)2 = 100. Therefore, the lowest price the firm can accept is $100 per suit. SECTION: 4
35. A firm produces three products A, B, and C. Long-run projected sales per year are 10,000 units of A, 12,000 units of B, and 8,000 of C. a) Determine whether the firm should remain in business under the following conditions: Good A sells at $5.00 per unit, and AVC is $3.50. Good B sells at $7.50 per unit, and AVC is $5.00. Good C sells at $10.00 per unit, and AVC is $7.50. Total fixed cost is $60,000 per year. b) If the firm allocates fixed cost using standard accounting practices, what is the total accounting profit for each good? ANSWER: a) Compute the long-run profit from the business: = (5 - 3.5)(10,000) + (7.5 - 5)(12,000) + (10 - 7.5)(8,000) - 60,000 = $5,000. The firm should continue to operate in the long run. b) For good A: = (1.50)(10,000) - .33(60,000) = -$4,800. For good B: = (2.50)(12,000) - .4(60,000) = $6,000. For good C: = (2.50)(8,000) - .27(60,000) = $3,800. Allocating fixed costs makes it appear as if good A is unprofitable even though it is making a positive contribution and should continue to be sold. SECTION: 4
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Chapter 6
ESSAY
36. The table gives data for production in the short run for a manufacturing firm. Compute AC and MC for the output levels shown in the table. Q 0 1 2 3 4 5 6 7 8
FIXED COST 15
VARIABLE COST
AVERAGE COST
MARGINAL COST
AVERAGE COST -21 13 10 8.25 7.4 7 6.86 6.88
MARGINAL COST -6 5 4 3 4 5 6 7
6 11 15 18 22 27 33 40
ANSWER: Q 0 1 2 3 4 5 6 7 8
FIXED COST 15
VARIABLE COST 6 11 15 18 22 27 33 40
SECTION: 2
37. Explain how short-run average cost and long run average cost are related to each other. Draw an appropriate graph to illustrate your explanation. ANSWER: The graph should resemble Figure 6-3 in the text. The long-run average cost curve shows the lowest possible short-run average cost corresponding to each output level. As such, long-run average cost is the lower “envelope” (boundary) of the possible short-run average cost curves. SECTION: 2
38. Three college students consider the option of forming a lawn care and landscaping business during their summer vacation. They estimate the following costs: Insurance $2,600 Equipment Rental Fees 1,000 Fuel and Supplies $4 per lawn Miscellaneous Expenses $2 per lawn Their projected revenue depends on the number of lawns serviced. The price per job is $30. The going wage for a typical unskilled college student is about $2,400 for the summer months. a) Derive an equation for total accounting profit. b) Derive an equation for total economic profit.
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c) Realistically, the small business should expect to service about 200 lawn jobs during the summer. Should the three students launch the business? ANSWER: a) Accounting profit = (30 – 6)Q – 3,600 = 24Q – 3,600. b) The students’ total economic profit is: = 24Q - 10,800. (The opportunity cost of their labor is $7,200.) c) Total Revenue = (30)(200) = $6,000. Total Economic Cost = 3,600 + (6)(200) + 7,200 = $12,000. No. The students should not start the business because it will generate a $6,000 economic loss. SECTION: 1
39. The firm’s total cost function is: C = 50 + 6Q + 2Q 2. a) Compute the level of output that minimizes average total cost. b) At what level of output does MC = AVC? ANSWER: a) MC = 6 + 4Q and AC = 50/Q + 6 + 2Q. We know that the point of minimum AC occurs where AC = MC. Therefore, 6 + 4Q = 50/Q + 6 + 2Q, implying 2Q = 50/Q, or Q 2 = 25. Thus, QMIN = 5 units. b) We know that AVC = 6 + 2Q and MC = 6 + 4Q. Equating these implies Q = 0. SECTION: 2
40. DigiWatch plans to open a new production facility to produce digital watches. Previous experience at the firm suggested that the fixed costs of the plant will be $366,000 per year, and that average variable cost will be: AVC = $7.00 + $0.002Q, a) Compute the total cost and average cost for the first year of production at an output of 6,000 watches. b) In the second year of production, Digiwatch revamped its assembly operations to improve efficiency. The firm produced 8,000 watches at a total cost of $498,000. How much did learning reduce average cost in the second year? c) Explain how cost reductions due to learning should be distinguished from economies of scale. ANSWER: a) Total cost for the firm is: C = 366,000 + 7Q + 0.002Q 2 . For Q = 6,000, the firm’s total cost is: 366,000 + 42,000 + 72,000 = $480,000 and its average cost is: AC = 480,000/6,000 = $80 per watch. b) Assuming an unchanged cost function (no learning), the firm’s projected total cost at Q = 8,000 units in year 2 would have been: C = 366,000 + 56,000 + 128,000 = $550,000, implying, AC = 550,000/8,000 = $68.75. Thus, the change in scale (from 6,000 to 8,000 units) reduced AC by: 80 – 68.75 = $11.75 per unit. In year 2, the firm actually achieved average cost: AC = 498,000/8,000 = $62.25. Therefore, learning accounted for a reduction in AC of: 68.75 – 62.25 = $6.50 per unit (or about 9.5%). c) Learning effects shift the average cost curve downward. If the level of output changes at the same time, one must be careful to distinguish learning and scale effects. To identify learning effects, we compare average cost for the same output level (as we did in part b). SECTION: 3
41. Explain how each of the following events will affect the average and marginal cost curves of a firm: a) An increase in labor costs. b) An increase in lease payments for a facility. c) A decrease in the cost of utilities (electricity, water heat). d) Stricter environmental regulation requiring installation of scrubbers on smokestacks. e) An increase in learning on the part of labor. ANSWER: a) Labor costs are variable costs. Average and marginal costs will increase at all levels of output.
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b) Lease payments are a fixed cost in the short run. Average cost will increase, but there will be no change in marginal cost. c) Utilities can be both fixed costs (water, heat, lighting) and variable costs (power to run a machine to produce extra output, or the electric refining of metals). Average cost will decrease. Marginal cost will decrease to the extent that part of this expense varies with the level of output. d) Environmental regulation requiring scrubbers is an example of a fixed cost. Average cost will increase, marginal cost will be unchanged. e) As labor learns, it becomes more productive, lowering average cost and marginal cost at all levels of output. SECTION: 2
42. Explain the economic logic of the short-run shutdown rule. Why does it sometimes make sense to operate at a loss? ANSWER: A profit-maximizing firm faces two types of costs: fixed and variable. In the short-run, fixed costs must be paid regardless of the level of production, but the firm has discretion over variable costs. It may eliminate variable costs by closing down production. Suppose that the firm is profit-maximizing in the short run but finds that its total cost exceeds its total revenue (or equivalently P < AC). That is, it is suffering an economic loss. Nonetheless, it should continue to operate as long as it is making a positive contribution toward its unavoidable fixed costs – that is, as long as its revenue exceeds its variable cost (equivalently P > AVC). In this way, it minimizes its loss. However, If revenue is less than total variable cost (or, P < AVC), the firm is making a negative contribution and should immediately shut down. SECTION: 4
43. a) Firm K is a leading maker of light-weight, water-proof outerwear. During the winter months, demand for its main line of water-proof coats is given by: P = 800 - .2Q, where P denotes price in dollars and Q is quantity of units sold per month. The firm produces coats in a single plant (which it leases by the year). The total monthly cost of producing these coats is estimated to be: C = 150,000 + 400Q. (Leasing the plant accounts for almost all of the $150,000 fixed cost.) What is the firm’s marginal cost? Find the firm's profit-maximizing output and price. If the firm’s other outerwear products generate $50,000 in contribution, what is the firm’s total monthly profit? b) From time to time corporate customers place “special” orders for customized versions of Firm K’s coat. Corporate orders generate an average contribution of $100 per coat. Firm K tends to receive these orders at short notice usually during the winter when its factory is operating with little unused capacity. Firm K has just received an unexpected corporate order for up to 300 coats but has unused capacity to produce only 200. One manager recommends delivering 200 coats (The client would still be satisfied with 200 coats.) A second manger argues for cutting back production of standard coats (by 100) to fill the full corporate order. Who is right? Explain carefully. In general, can you suggest any other ways to free up capacity in the winter? ANSWER: a) To maximize profit set MR = MC. Therefore, we have MR = 800 - .4Q = 400, implying Q* = 1,000, and P = 800 – (.2)(1000) = $600 per coat. The firm’s total monthly profit is: (600 – 400)(1000) + 50,000 – 150,000 = $100,000. b) If the firm delivers 200 coats, its incremental contribution is ($100)(200) = $20,000, so that its total profit is $120,000. If it delivers 300 coats, its contribution is $30,000 from corporate coats. It now sells only 900 mainline coats (at a price of $620 each). Its contribution from this line is: (620 – 400)(900) = $198,000. Thus, its total profit is 198,000 + 30,000 + 50,000 – 150,000 = $128,000. This is the more profitable alternative. Another way of arriving at the same answer is to treat the $100 contribution as an opportunity cost, and add it to the MC of 400. Setting MR = 800 - .4Q = 500, implies Q* = 750. (The firm
6-11
Cost Analysis
should be willing to cut back its mainline coat output by 250 coats if needed.) However, it only needs to cut back 100 coats (to fill the corporate order), so Q* = 900 is optimal. Finally, the most direct way to free up winter capacity (as opposed to paying to expand it) is to produce extra coats during the slack summer and fall months and store them for sale in the winter. SECTION: 4
44. Doorway Computers manufactures PCs, and also produces the special DVD drives that go into each PC. Demand for computers is estimated to be: P = 2,000 - .1Q, where Q denotes units sold per month, and P is the price of the PC. The firm’s total cost is: C = 40,000 + 800Q + C D, where CD denotes the firm’s total cost of producing drives. Currently, CD = 100QD – that is, the firm’s cost per drive is $100. a) If there is no external market for DVD drives, how many computers should Doorway produce and sell in order to maximize profit? What transfer price should the firm set for disk drives? b) The manager of the disk drive division informs Doorway’s CEO that she has received offers to sell the specialty drives to outside customers for $200 each. In fact, the division has firm offers to sell up to 8,000 disk drives, which is the firm’s current maximum production capacity. If so, what is the optimal transfer price? c) Answer the questions of part b in the case that Doorway’s cost for producing drives is: C D = 80QD + .02QD2. Assume that Doorway can buy or sell drives at the $200 market price. ANSWER: a) Without an outside market for drives, the firm should value the drives at marginal cost. Thus, the appropriate transfer price is $100 per drive, and the firm’s total cost is: C = 40,000 + 900Q. To maximize profit, set MR = MC which implies 2,000 - .2Q = 900. Thus, Q* =5,500 units, and P* = $1,450 per PC. b) With a flourishing external market for drives, the firm should value each drive at it’s opportunity cost, the foregone price for which it could have sold the drive. (Equivalently, the contribution that could have been earned on each drive should be added to the production cost of the drive.) Thus, the appropriate transfer price is $200, increasing the effective marginal cost per PC to: 800 + 200 = 1,000. The firm’s new profit-maximizing output and price are: Q* = 5,000 units and P* = $1,500. Thus, the firm should produce 5,000 drives for its own use and 3,000 drives (the rest of its capacity) to sell to outside buyers. c) The transfer price for drives continues to be $200 and the firm continues to produce 5,000 PCs. It should produce drives in house up to the output at which MCD = 200. We know MCD = dCD/dQD = 80 + .04QD. Therefore,80 + 04QD = 200, implying QD = 3,000 drives. Thus, the firm should produce 3,000 drives for its own use and purchase 2,000 drives from the external market. SECTION: 5
6-12
File: Ch07; CHAPTER 7: Perfect Competition
Each question contains a code showing the section of the chapter text from which it was taken. The codes for this chapter are: Code 1 2 3 4
Section The Basics of Supply and Demand Competitive Equilibrium Market Efficiency International Trade
MULTIPLE CHOICE
1. Demand is given by QD = 100 – P and supply by QS = .5P – 20. Equilibrium price and output under perfect competition are a) P = $60 and Q = 10 units. b) P = $80 and Q = 20 units. c) P = $70 and Q = 30 units. d) P = $100 and Q = 30 units. e) None of the above answers is correct. ANSWER: b SECTION: 1
2. If for some reason the price of a good is above the equilibrium price, then a) Finding inventories building up, suppliers will cut output, and lower prices. b) Finding inventories depleted, suppliers will increase output and lower prices. c) The demand curve shifts to the right until equilibrium is established at the existing price. d) The supply curve shifts to the left until equilibrium is established at the existing price. e) Consumers will bid down the good’s price, but there will be no reduction in output. ANSWER: a SECTION: 1
3. When there is an increase in demand, a) The supply curve will shift to the right to meet the demand increase. b) There is a movement toward a higher price along the demand curve. c) The demand curve shifts to the right. d) Market output will increase and market price will tend to decline. e) None of the above answers is correct. ANSWER: c SECTION: 1
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Perfect Competition
4. Normally, an increase in the supply of a good (a shift in the supply curve) will cause a) A shift in the demand curve for the good. b) The cost of producing the good to increase. c) The price of the good to fall. d) Total consumption of the good to increase. e) Answers c and d are both correct. ANSWER: e SECTION: 1
5. Over the last 3 months, the price and quantity sold of coal have fallen. Which of the following events is consistent with this observation (everything else equal)? a) The price of oil fell. b) Coal miners received large wage increases. c) Coal producers installed more efficient coal mining equipment. d) New mine operators entered the coal industry. e) The supply of coal fell. ANSWER: a SECTION: 1
6. The price of fresh fish rose and the quantity sold fell. Which of the following events is consistent with this observation (everything else equal)? a) Consumers developed a taste for fish. b) The price of meat rose. c) Fishermen have learned to catch fish more efficiently. d) Fresh fish catches have been down in recent months. e) The supply of fresh fish increased. ANSWER: d SECTION: 1
7. The supply curve of eggs will shift down and to the right if a) A virus kills millions of chickens. b) Cholesterol is found to cause heart disease. c) Chicken feed prices fall. d) The government taxes poultry suppliers. e) None of the answers above is correct. ANSWER: c SECTION: 1
8. A severe freeze has once again severely damaged the Florida orange crop. Consequently, a) Because of the shortage, consumers will reduce their demand in order to economize. b) The supply curve will shift to the right. c) Both output and price will decrease. d) Both the supply curve and the demand curve will shift to the left. e) Output will fall and price will increase.
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Chapter 7
ANSWER: e SECTION: 1
9. One important characteristic of perfect competition is the existence of a) A large number of small firms. b) A small number of large firms. c) Moderate barriers to entry. d) Large economic profits in the long run. e) Product differentiation. ANSWER: a SECTION: 2
10. The demand curve faced by an individual firm under perfect competition is a) Downward sloping. b) The same as the market demand curve. c) Horizontal. d) Perfectly inelastic. e) Answers and b are both correct. ANSWER: c SECTION: 2
11. Firms under conditions of perfect competition are a) Price setters. b) Price takers. c) Price leaders. d) Price cutters. e) Price followers. ANSWER: b SECTION: 2
12. The good or service produced by firms under perfect competition are a) Perfectly complementary. b) Highly differentiated. c) Imperfect substitutes. d) Homogeneous. e) Heterogeneous. ANSWER: d SECTION: 2
13. In order to maximize profits, a perfectly competitive firm continues producing until a) It reaches its full capacity.
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Perfect Competition
b) The cost of producing the last unit equals the market price. c) The average cost per unit is minimized. d) Total sales revenue is maximized. e) None of the answers above is correct. ANSWER: b SECTION: 2
14. In the long run, perfectly competitive firms will most likely a) Suffer economic losses. b) Fluctuate between swings of large profits and losses. c) Shut down because of their inability to cover overhead costs. d) Continue to earn positive economic profit because of barriers to entry. e) Earn zero economic profits. ANSWER: e SECTION: 2
15. A perfectly competitive firm's supply curve is simply its a) MC curve above MR. b) MC curve above AC. c) MC curve above AVC. d) AC curve above AVC. e) AVC curve. ANSWER: c SECTION: 2
16. If the long-run market supply under perfect competition is upward sloping, the industry a) Is a constant-cost industry. b) Is an increasing-cost industry. c) Is a decreasing-cost industry. d) Exhibits increasing returns to scale. e) Is monopolistically competitive. ANSWER: b SECTION: 2
17. In the long run, perfectly competitive firms are at equilibrium when a) P = LMC > LAC. b) P = LMC = LAC. c) P = LAC > LMC. d) MR = LMC e) R = VC. ANSWER: b SECTION: 2
7-4
Chapter 7
18. Economists generally prefer competitive markets because a) They result in fair outcomes. b) They yield efficient outcomes. c) They provide some consumer surplus. d) They provide significant economic profits. e) All of the above answers are correct. ANSWER: b SECTION: 3
19. Consumer surplus represents the a) Net gain that buyers obtain from purchasing the good. b) Area under the demand curve and above the price line. c) Difference between the good’s price and its cost per unit. d) Maximum monetary amount that a person would be willing to pay for a good. e) Answers a and b are both correct. ANSWER: e SECTION: 3
20. The industry demand curve also measures a) The marginal cost of additional units. b) The marginal benefit of consumption. c) Consumer surplus. d) The total benefit of consumption. e) Marginal revenue. ANSWER: b SECTION: 3
21. The efficient industry outcome under perfect competition occurs at an output where a) MB = P = MC. b) MR = MC. c) P > MC. d) Consumer Surplus = Industry Profit. e) Consumers obtain a price subsidy: P < AC.
ANSWER: a SECTION: 3
22. What are the efficiency implications of subsidized, universal health care for the American population? a) The outcome would be inefficient. Marginal cost of providing the care is less than the marginal benefit. b) The outcome would be inefficient. Marginal benefit to consumers is less than the marginal cost of providing the care. c) The outcome would be efficient. The total benefit would be equal to the total cost of providing the care.
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Perfect Competition
d) The outcome would be efficient. Total net benefits would be maximized. e) There is not enough information to answer. ANSWER: b SECTION: 3
23. The pattern of trade is based on a) Relative profit opportunities. b) Specialization and comparative advantage. c) Relative demand and supply across countries. d) Absolute advantage. e) Answers b and c are both correct. ANSWER: e SECTION: 4
24. With free trade, the market for a particular good or service is in equilibrium a) At a world price below the domestic price. b) Where domestic supplies are less than domestic demand. c) When there are large differences in the traded good’s price across countries. d) When worldwide demand equals worldwide supply. e) When domestic demand equals domestic supply. ANSWER: d SECTION: 4
25. When all trade is prohibited in good X, the equilibrium price in the home country is P x. After free trade is instituted, the domestic country begins to import good X from the rest of the world. Therefore, a) The domestic price of good X will fall. b) The domestic price of good X will rise. c) The domestic price of good X will exceed the price in foreign countries. d) The domestic price of good X will be less than the price in foreign countries. e) There is insufficient information to predict the impact on the price of good X. ANSWER: a SECTION: 4
SHORT ANSWER
26. In a given market, demand is described by the equation Q D = 1,800 - 10P and supply is described by QS = 200 + 10P. a) Determine the equilibrium price and quantity. b) Determine the surplus or shortage that would exist if the price were $60. ANSWER: a) Setting QD = QS implies P = $80 and Q = 1,000 units. b) At P = $60, QD = 1,200 and QS = 800. There is a supply shortage of 1,200 – 800 = 400 units.
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Chapter 7
SECTION: 1
27. Provide two examples of events causing a shift in industry demand. Draw a graph to illustrate your answer. ANSWER: For an increase in demand, the graph should resemble Figure 7-2 (a) in the text. Factors that can cause a change in industry demand are changes in (1) consumer income or consumer preferences, (2) the prices of substitute or complementary goods, and (3) demographic factors that affect the size of the market. SECTION: 1
28. Provide two examples of events causing a shift in industry supply. Draw a graph to illustrate your answer. ANSWER: For an increase in supply (or a decrease in cost), the graph should resemble Figure 7-2 (b) in the text. Factors that can cause supply shifts include changes in (1) costs due to input prices or technological change, (2) the number of firms entering or exiting the industry, and (3) supply shocks (finding new oil, experiencing a poor harvest, and so on). SECTION: 1
29. Derive the short-run supply curve of a firm under perfect competition. ANSWER: See section 2 of the text. The supply curve is coincident with the portion of the firm’s marginal cost curve that is above the firm’s minimum average variable cost. The MC curve represents the amounts of output a profit-maximizing firm will supply at different prices. SECTION: 2
30. Explain why the demand curve for a competitive firm is horizontal. ANSWER: The assumption is that the individual competitive firm is far too small to have any influence over the price that it can obtain. As a price taker, it must adhere to the going price in the market. It can sell all the output that it wishes without influencing price. Therefore the demand curve is horizontal and P = MR. SECTION: 2
31. Explain why perfectly competitive firms cannot earn positive economic profits in the long run. ANSWER: In the model of perfect competition, there are no entry barriers to the industry. If there are economic profits in the industry, entry will occur. This increases supply and, therefore, puts downward pressure on price. Price declines until P = LAC and the typical firm earns a zero economic profit. SECTION: 2
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Perfect Competition
32. The marginal cost of a firm under perfect competition is given by the equation MC = 20 + 2Q F. The market price is $50 per unit. Determine the firm’s profit-maximizing level of output. Write down the equation for the firm’s supply curve. ANSWER: The firm maximizes its profit by setting: P = MC. Therefore, we have 50 = 20 + 2Q F, or QF = 15. The firm’s supply curve is derived as follows: P = 20 + 2Q F. Therefore, QF = (P – 20)/2. SECTION: 2
33. For a perfectly competitive firm, long-run average cost is: LAC = 300 - 20QF + .5QF2., where QF denotes the firm’s output. Determine the firm’s long-run profit-maximizing output and price. ANSWER: In the long run, under perfect competition, firms will produce at the minimum point on their LAC curve. To find the minimum of LAC, we set dLAC/dQ equal to 0. Therefore, -20 + QF = 0, so that QF = 20. The firm’s demand curve is horizontal and tangent to LAC. Therefore, price is equal to the minimum value of LAC. We find minimum LAC to be: 300 - (20)(20) + .5(20) = 100. Thus, PC = 100. SECTION: 2
34. Derive the long-run supply curve of a perfectly competitive increasing-cost industry. Use graphical analysis. ANSWER: Begin with an equilibrium of demand and current, short-run supply. Shift the demand curve outward, and shift the supply curve outward. The new equilibrium price should be higher than the initial equilibrium price. Connect the two equilibrium points to derive an upward-sloping long-run supply curve. Be sure to distinguish this long-run supply curve from the two short-run curves. SECTION: 2
35. How can supply and demand analysis be used to measure consumer surplus? How does consumer surplus change if the market price falls? ANSWER: An appropriate diagram should resemble Figure 7.6 in the text. The consumer surplus triangle necessarily increases when the market price falls. SECTION: 3
36. Between 2000 and 2002, the value of the dollar in international markets rose by about 15%. What would you predict about the trade balance of the United States over this time period? ANSWER: If the value of the dollar rises, then imports to the US become cheaper (in dollar terms), which will cause them to increase. With the rise in the value of the dollar, US exports become more expensive (in terms of foreign currencies). Thus, exports decline. For both reasons, the US trade balance should worsen – that is, a trade surplus will shrink, or a trade deficit will become larger. SECTION: 3
ESSAY
7-8
Chapter 7
37. Draw a graph of a market in equilibrium. Describe what might cause a change in demand or supply, and how this would affect the new equilibrium. Indicate the effect on equilibrium price and quantity and the effect on consumer surplus. ANSWER: Your diagrams should resemble Figure 7.2a and 7.2b in the text. Effects that might change demand include changes in: population, income of buyers, tastes, and prices of related goods (substitutes and complements). Effects that might change supply include: the size of the industry (entry or exit), technological progress, price of inputs, and prices of related goods. Consumer surplus, the triangle below the demand curve and above the price line, will increase or decrease, depending on the exact shifts in the curves. SECTION: 3
38. Demand for flower bouquets in a suburban town is described by: QD = 50 - 5P + 2Y, where Q is quantity, P is price per unit, and Y is an index of consumer income. Similarly, supply is described by: Q S = -5 + 10P. a) If Y = 100, what is equilibrium price and output? b) If Y rises to 122.5, what is the new equilibrium price and output? ANSWER: a) Equate the supply and demand equations, substituting 100 for Y. Thus, 50 - 5P + 2(100) = -5 + 10P. Therefore, 50 + 200 + 5 = 15P, implying P = $17 and Q = 165. b) Equate the supply and demand equations, substituting 122.5 for Y. Thus, 50 - 5P + 2(122.5) = -5 + 10P. Therefore, 50 + 245 + 5 = 15P, implying P = $20 and Q = 195. SECTION: 1
39. Discuss why many agricultural industries in the United States are primary examples of perfectly competitive markets. ANSWER: First, list the characteristics of competitive markets. Next, explain that many actual agricultural markets possess most or all of those characteristics. The most important in the list are many small firms, too small to affect the price of the good, and many small buyers, also too small to affect the price. In addition, there are fairly low entry barriers to most products within the agricultural sector. SECTION: 2
40. A perfectly competitive market is described by the demand curve Q D= 60 - 2P, and the supply curve QS = 5P - 10. A typical firm in the market has total cost equation: C = 16 + 2Q F + QF2. a) Calculate the equilibrium price in the market. b) Calculate the profit-maximizing output for the firm. c) Compute the firm's total revenue, total cost, and total profit. ANSWER: a) Set demand equal to supply: 60 - 2P = 5P – 10. Therefore, 7P = 70, or P = $10. b) To maximize profit, set P = MC, where MC = dC/dQF = 2QF + 2. Therefore,10 = 2QF + 2, implying QF = 4. c) The firm’s revenue and cost are: R = PQ = (4)(10) = 40, and C = 16 + 8 + 16 = 40, implying an economic profit of zero. SECTION: 2
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Perfect Competition
41. In some western states, federal water projects sell water to farmers at a fraction of the total cost to dam and transport the water, and at a fraction of the cost charged to city dwellers who draw from the same water source. Is this likely to result in economic efficiency? Explain why or why not. ANSWER: No. If the price is held below the marginal cost, the result is inefficient overuse of the resource. Society will give up more resources to dam and transport the water than farmers gain. Society would be better off if the water price to farmers were raised to the marginal cost of providing the water. SECTION: 3
42. Is an efficient market allocation fair? Explain why or why not. ANSWER: Efficiency and equity are separate notions. An equitable allocation need not be efficient. An efficient allocation is not necessarily fair. Because competitive markets respond to demand and supply, they generate efficient outcomes, but these are not always fair. After all, demand is based upon willingness and ability to pay. Wealthy individuals will see their desires met in markets. Lower-income individuals might not be willing or able to pay the market price for a good or service and must do without. SECTION: 3
43. A firm sells in a competitive industry, in which the price is $10 per unit. Its fixed cost is $14 and its variable costs are given in the table below. Compute the firm’s revenues and costs for output over the range 0 to 8 units. Determine the profit-maximizing level of output for the firm. If this firm is typical of the industry, will entry occur? Explain why or why not. OUTPUT 1 2 3 4 5 6 7 8
VARIABLE COST 2 3 5 10 16 24 35 48
ANSWER: OUTPUT 0 1 2 3 4 5 6 7 8
COST 12 14 15 17 22 28 36 47 60
REVENUE 0 10 20 30 40 50 60 70 80
PROFIT -12 -4 5 13 18 22 24 23 20
By producing 6 units, the firm earns a maximum profit of 24. The presence of positive economic profit will attract new entrants, bidding down the price. SECTION: 2
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Chapter 7
44. You are the manager of a division of a paper firm that produces copier paper and sells it on the wholesale market. Your firm’s output represents about 1.5% of total copier paper sales. The wholesale price of copier paper is $3.95 per standard package. Your plant engineers report that, at your projected volume, labor costs are $1.00 per package, material costs are $2.00 per package, and other average fixed costs are about $.75 per package. What price should you charge for your product? ANSWER: This situation is as close to perfectly competitive as possible. The going price is $3.95, and the firm is too small to make any difference. This price more than covers the variable costs ($3.75) of production. The firm should produce and sell as much copier paper as it can at a price of $3.95. SECTION: 2
45. In a perfectly competitive market, LAC = LMC = $8 per unit for the typical firm. However, one of the firms discovers a technological innovation lowering its AC and MC to $7. How will this affect the equilibrium price? If all firms can take advantage of the innovation, what is the impact on the market price and industry profits? ANSWER: Because only one firm has a lower MC, this has no effect on the intersection of supply and demand. The market price, P = MC = $8, will be unchanged. However, the uniquely efficient small firm will earn a positive economic profit of $1 on each unit of output. If all firms implement the innovation, the industry supply curve shifts downward to $7. The new market price is P = MC = $7, and at this price, firms again make no economic profit. Consumers are the ones who gain from the industry-wide cost reduction. SECTION: 2
46. Does international trade increase economic efficiency? How do trade barriers and tariffs affect efficiency? Explain. ANSWER: Yes, international trade widens markets and increases the range of choice for consumers. Thus, international trade promotes global efficiency. Conversely, a trade barrier can serve as an entry barrier, which will make a market less competitive. A reduction in trade barriers will increase market efficiency and increase consumer surplus as well. SECTION: 4
47. Previously, a small nation has permitted free trade in good X. At the good’s free-trade price, P = $8, domestic firms supply 6 million units and imports account for 4 million units. Recently, the small country has erected trade barriers with the result that imports have fallen to 0 units, price has risen to P = $10, and domestic supply has increased to 8 million units. Calculate the change in consumer surplus and producer profit resulting from the trade barrier. What is the deadweight loss? ANSWER: The fall in consumer surplus is: (10 – 8)(10 + 8)/2 = $9 million. The increase in producer profit is: (10 – 8)(6 + 8)/2 = $7 million. Thus, the deadweight loss due to the trade barrier is; 9 - 7 = $2 million. SECTION: 4
7-11
File: Ch08; CHAPTER 8: Monopoly
Each question contains a code showing the section of the chapter text from which it was taken. The codes for this chapter are: Code 1 2 3
Section Pure Monopoly Perfect Competition Versus Pure Monopoly Monopolistic Competition
MULTIPLE CHOICE
1. A pure monopoly a) Can raise price indefinitely. a) Typically is more efficient than other firms in the market. a) Is the only seller in an industry. d) Always restricts output below the competitive level. e) Answers c and d are both correct. ANSWER: e SECTION: 1
2. A monopolist maximizes profit by a) Maximizing the markup of price over marginal cost. b) Producing until average cost is minimized. c) Producing until the cost of the last unit of output is equal to the price of the unit. d) Producing an output level such that marginal revenue equals marginal cost. e) Answers b and c are both correct. ANSWER: d SECTION: 1
3. A monopoly earns positive economic profits in the long run due to a) Barriers to entry. b) Perfectly elastic demand. c) A kinked demand curve. d) Diseconomies of scale. e) Operating with an optimal plant size. ANSWER: a SECTION: 1
4. Which of these factors contributes to the existence of monopoly power? a) A continuously decreasing long-run average cost curve.
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Monopoly
b) Possession of a patent. c) Control of essential inputs in the production process. d) A pure cost or quality advantage. e) All of the answers above are correct. ANSWER: e SECTION: 1
5. If a natural monopoly is broken up into two smaller firms, a) The market price will be unchanged. b) Industry output will increase. c) Production costs will increase. d) Production costs will decrease. e) Industry profits will increase. ANSWER: c SECTION: 2
6. Monopoly reduces overall economic welfare because a) Monopolies earns excess economic profits. b) Monopolies overproduce to maximize profits. c) Monopolies are usually anticompetitive. d) Monopolies engage in excessive product differentiation. e) Monopolies restrict output below efficient levels. ANSWER: e SECTION: 2
7. A pure monopoly occurs when a) All firms sell homogeneous goods. b) There is a single buyer of a good. c) A single firm produces a good that is similar in use to goods produced by other industries. d) A few firms produce a good for which other industries offer no substitutes. e) Entry barriers prevent other firms from competing. ANSWER: e SECTION: 1
8. Is the monopolist supply decision fundamentally different than the competitive supply decision? a) Yes, because the monopolist must determine both price and output quantity. b) Yes, because the monopolist sells a unique product. c) No, because industry demand determines the output level in both markets. d) No, because firms set price and quantity in both markets. e) Yes, because the monopolist’s average cost is typically lower than the competitive firm’s. ANSWER: a SECTION: 1
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Chapter 8
9. In a mid-size town in South Dakota, which of the following is most likely to be a monopoly? a) A local electric utility. b) A local grocery store. c) A local restaurant. d) A local farmer selling produce. e) A local gas station ANSWER: a SECTION: 2
10. Which of the following is most likely to result in a natural monopoly? a) High fixed costs and low variable and marginal costs. b) High fixed costs and high variable costs. c) Low fixed costs and high variable costs. d) Control of a natural resource. e) Answers a and d are both correct. ANSWER: a SECTION: 2
11. Compared to a perfectly competitive industry, a monopolist will generally produce a) A greater level of output and sell it at a lower price. b) A greater level of output and sell it at a higher price. c) A smaller level of output and sell it at a lower price. d) A smaller level of output and sell it at a higher price. e) Roughly the same level of output but sell it at a higher price. ANSWER: d SECTION: 2
12. Industry demand is given by: P = 200 - .4Q and long-run industry costs are: AC = MC = $80. a) If the market is a pure monopoly, QM = 200 and PM = $120. b) If the market is a perfectly competitive, QC = 300. c) If the market is a perfectly competitive, PC = $100. d) Under both monopoly and perfect competition, industry MR = MC. e) Answers a and b are both correct. ANSWER: b SECTION: 2
13. The basic objective of a cartel is to a) Maximize profit for the largest, most powerful members. b) Negotiate the division of the cartel’s profit. c) Produce the highest output level possible. d) Maximize the cartel’s collective profit. e) Price discriminate.
8-3
Monopoly
ANSWER: d SECTION: 2
14. Cartels are inherently unstable because individual members a) Tend to produce below their quotas. b) Tend to produce above their quotas. c) Are culturally and politically heterogeneous. d) Produce highly differentiated products. e) Tend to elevate their prices to increase their own profits at the expense of other members. ANSWER: b SECTION: 2
15. In the United States, monopolies are a) Common, producing about 20% of all GDP. b) Always and everywhere illegal. c) Actually quite rare, producing less than 3% of GDP. d) Usually based on natural-resource cartels. e) Prevalent only in manufacturing. ANSWER: c SECTION: 2
16. In the United States, the most common response to natural monopoly is a) Deregulation. b) Public ownership of the natural monopoly. c) Regulation in the form of average-cost pricing. d) Regulation in the form of marginal-cost pricing e) Breaking up the natural monopolist. ANSWER: c SECTION: 2
17. Which of the following is true for a profit-maximizing competitive firm in the long run but untrue for a monopolist? a) Economic profit is zero. b) AC = MC when AC achieves a minimum c) The industry demand curve is downward sloping. d) P = MC. e) Answers a and d are both correct. ANSWER: e SECTION: 2
18. Monopolistic competition is common in the United States, particularly in the a) Utility industry.
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b) Automobile industry. c) Retail trade industry. d) Steel industry. e) Electronics industry. ANSWER: c SECTION: 3
19. The distinguishing characteristic of monopolistic competition is a) Barriers to entry. b) Homogeneous goods. c) The existence of a few, large firms. d) Economies of scale. e) Differentiated products. ANSWER: e SECTION: 3
20. In the long run, firms under monopolistic competition a) Earn zero economic profit. b) Face perfectly elastic demand curves. c) Standardize their products. d) Produce output at minimum average cost. e) Merge and form a few dominant firms. ANSWER: a SECTION: 3
21. The demand curve faced by individual firms under monopolistic competition is a) Perfectly elastic. b) Perfectly inelastic. c) Relatively elastic. d) Fixed, i.e. does not vary with the entry or exit of other firms. e) The same as the market demand curve. ANSWER: c SECTION: 3
22. In comparing monopolistic competition to perfect competition, the major difference is a) The number of firms in each industry. b) The typical firm size in each industry. c) The degree of entry barriers in each industry. d) The demand curves faced by individual firms in each industry. e) The long-run profits of firms in each industry. ANSWER: d SECTION: 3
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Monopoly
23. Under monopolistic competition, firms earn zero economic profits in the long run due to a) Excess capacity that bids down prices. b) Price wars among a limited number of firms. c) Free entry. d) Excessive advertising. e) Collusive behavior. ANSWER: c SECTION: 3
24. The demand curve for a monopolistic competitor slopes downward because a) Demand drops to zero after a slight price increase. b) There are close but not perfect substitutes for the firm’s product. c) Customers have little loyalty for competing sellers’ products. d) Customers are largely uninfluenced by advertising. e) Products in the market are undifferentiated. ANSWER: b SECTION: 3
25. Which of the following distinguishes monopolist competition from pure monopoly? a) Different profit-maximizing rules. b) Downward slope of demand curve. c) Entry barriers. d) Short-run economic profits. e) Answers a and c are both correct. ANSWER: c SECTION: 3
26. Under monopolist competition in long-run equilibrium, a) P = AC = MC. b) MR = MC and P = AC. c) P > AC > MC. d) P > AC = MC. e) None of the answers above is correct. ANSWER: b SECTION: 3
27. Profit margins for fast food firms like Wendy's have fallen as has the value of a franchise because of an increase in competition from similar fast food chains and microwaveable food available in supermarkets. This scenario best describes a) Perfect competition. b) Monopoly. c) Monopolistic competition.
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d) Oligopoly. e) A market evolving from monopoly to perfect competition. ANSWER: c SECTION: 3
SHORT ANSWER
28. Carefully define and describe a natural monopoly. ANSWER: A natural monopoly is an industry in which advantages of large-scale production make it possible for a single firm to produce the entire output of the market at lower average cost than if the market were split among many firms, each producing a smaller quantity. Most natural monopolies are regulated utilities. SECTION: 2
29. Explain why monopolies are economically inefficient. ANSWER: A monopoly is inefficient because it charges a higher price and sells a lower quantity than does a competitive industry. Therefore, the price (or marginal benefit) of the last unit bought generally exceeds the marginal cost. From a social perspective, output is too small. SECTION: 2
30. Why are substantial economies of scale considered a barrier to entry? ANSWER: Economies of scale allow a large firm to charge a lower price than a small firm and still break even. Small firms find it hard to compete on price in this case, and tend to grow smaller or go out of business. Because initial entry is often at a small scale, new firms face high costs and initial large losses. This makes successful entry difficult. SECTION: 1
31. A monopolist faces the demand curve P = 100 - 2Q and has total cost of C = 50 + 20Q. Determine its profit-maximizing price and output. ANSWER: We now that MC = 20. In turn, R = PQ = 100Q - 2Q2‚, so that MR = 100 - 4Q. The monopolist produces according to: MR = MC, implying that 100 - 4Q = 20, so Q = 20. In turn, P = 100 – (2)(20) = $60. SECTION: 1
32. When competing firms or nations collude to form a cartel, the intention is to set one common price. This tendency to avoid competition should bring about stability. Paradoxically, however, cartels are usually unstable. Why?
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Monopoly
ANSWER: Cartel members have incentives to cheat on the agreed price. Because the price is far above marginal and average cost, firms can cut price slightly and increase output and gain profits. Once widespread cheating sets in, the cartel is likely to collapse. SECTION: 2
33. Why do monopolistic competitors have a tendency to advertise much more than perfectly competitive firms? ANSWER: Product differentiation, a key feature of monopolistic competition, is reinforced by firm advertising. By contrast, perfectly competitive firms sell homogeneous goods or services; they have no method to distinguish their offerings and little incentive to advertise. SECTION: 3
34. Based on your understanding of monopolistic competition, list five examples of real firms fitting the model. ANSWER: Local bars, dentists, shoe stores, restaurants, barber shops, beauty shops, and gasoline stations among many other examples all fit the model. SECTION: 3
35. How useful is the Lerner index as a measure of monopoly power? ANSWER: The Lerner index is L = (P - MC)/P. For a profit-maximizing monopolist, the Lerner index is equal to the inverse of the industry's price elasticity of demand. It is a useful measure of the degree to which monopoly raises price above marginal cost. However, it does not take into account the monopolist’s volume of production, and so does not measure the actual magnitude of monopoly profits. SECTION: 1
36. Many natural monopolies are regulated. Explain the rationale for such regulation. ANSWER: Natural monopolies exhibit falling average cost over a large range of output. Thus, it is economically efficient for a single large firm to produce a large output. However, the unregulated monopolist has an incentive to reduce output and raise price and profit. Regulation is an attempt to obtain the cost economies of natural monopoly by regulating a low price. SECTION: 2
ESSAY
37. Describe the different types of entry barriers and their importance to the study of monopoly. ANSWER: The chapter discusses seven types of entry barriers: (1) Economies of scale give large firms a cost advantage over smaller firms.
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Chapter 8
(2) Large sunk costs of entry discourages new entrants because a great deal must be put into the effort to enter, with no alternative economic value to the resources. The risk of failure increases when sunk costs increase. (3) Technical superiority may confer a monopoly, because rivals are unable to keep up with the leader. This may give a quality and/or cost advantage to the monopolist. (4) Product differentiation, often backed by advertising, may create a “unique” product or brand name. Examples include many retail products, such as breakfast cereals. (5) Control of a scarce resource or input, such as raw materials. Examples include French fine wine, DeBeers (in diamonds), and OPEC. (6) Legal restrictions on entry, including patents, trademarks, and copyrights. Examples include local franchises for various goods or services, or exclusive licenses for local utilities; e.g., cable TV. (7) Strategic barriers are erected by firms currently in the market to deter entry by others. One method is to sue competitors to scare them away; another is heavy spending on advertising to secure high customer loyalty. Entry barriers are critical to the study of monopoly because a monopoly cannot persist unless there is a barrier to prevent other firms from entering. The lure of profits is strong, and only a barrier will keep other firms out of the industry. SECTION: 1
38. A monopolist faces the price equation: P = 1,000 - .5Q, and total cost: C = 50,000 + 100Q + .4Q2. a) Determine the price and output that maximize total revenue, and the level of profit. b) Determine the price and output that maximize profit, and the level of profit. c) Compare the answers in parts a and b, and comment on the appropriate goal of the firm. ANSWER: a) To maximize total revenue R = 1000Q - .5Q2, the firm sets MR = 1000 - Q = 0. Therefore, Q = 1,000, P = $500, and = (500)(1,000) – [50,000 + (100)(1,000) + (.4)(1,000)2 = -$50,000. b) To maximize profit, the firm sets MR = MC. Therefore, 1,000 - Q = 100 + .8Q, or Q = 500. In turn, P = 1,000 – (.5)(500) = $750, and = (750)(500) – [50,000 + (100)(500) + (.4)(500)2 = $175,000. c) Here, there is a stark profit difference between the two goals. The wrong-headed pursuit of maximum revenue implies economic losses for the monopolist! SECTION: 1
39. Economists tend to be concerned about barriers to entry. Why are barriers so important? ANSWER: Economists see entry barriers as the primary reason why monopoly and oligopoly occur. In the absence of barriers, neither type of industry could long exist. Entry barriers imply anticompetitive and economically inefficient market outcomes, where P > MC. Entry barriers also support positive economic profits in the long run. SECTION: 1
40. Carefully explain how short-run equilibrium and long-run equilibrium in monopolistic competition differ. Use graphs to illustrate your answer. ANSWER: See Figure 8-5 in the chapter. The short-run equilibrium for the monopolistic competitor is akin to that of monopoly. The firm can expect to earn positive economic profit. However, in the long run, the lure of economic profits induces entry. New firms will take away some demand from existing firms, causing the firm’s demand curve to shift to the left. In the long run, the typical firm earn zero economic profit. Profit maximization occurs where MC = MR, which is at the quantity where P = AC, and where the AC curve is tangent to the demand curve. When profits are zero, no further entry or exit occurs.
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Monopoly
SECTION: 3
41. Demand for a firm has been reliably measured by: P = 100 – 5Q, where P is price in dollars and Q is output. Total cost is in the table below (see next page). Complete the table and indicate the price and level of output that a profit-maximizing firm would choose, and the same for a revenue-maximizing firm. OUTPUT PRICE REVENUE COST PROFIT 1 200 2 210 3 220 4 231 5 243 6 256 7 270 8 285 9 301 10 320 11 345 12 375 ANSWER: OUTPUT PRICE REVENUE COST PROFIT 1 95 95 200 -105 2 90 180 210 -30 3 85 255 220 35 4 80 320 231 89 5 75 375 243 132 6 70 420 256 164 7 65 455 270 185 8 60 480 285 195 9 55 495 301 194 10 50 500 320 180 11 45 495 345 150 12 40 480 375 105 From the table, the profit-maximizing firm will produce and sell an output of 8 units at a price of $60, generating a profit of $195. The revenue-maximizer would sell a greater output (10 units) at a reduced price of $50. SECTION: 1
42. Kiwi, Inc. dominates the wholesale chicken market in New Zealand. Its production cost is: LAC = LMC = $2 per pound and demand is given by: P = 6 - 2Q, where Q denotes output (in millions of pounds). a) Determine Kiwi’s output and price (presuming it faces no other competitors). b) Over the last five years, a Southeast Asian nation has dramatically increased its exports of chicken to New Zealand. That nation’s cost structure (with lower labor costs and higher shipping costs) is the same as Kiwi’s. Find the long-run output and price under perfect competition. c) New Zealand lawmakers have decided to enact a $1 per pound tariff on all chicken imports. What is the new equilibrium price? Suppose that imports fall to QI = .5 million pounds, what is Kiwi’s output? Compute consumer surplus and Kiwi’s profit. How has the tariff affected total welfare? ANSWER: a) As a monopolist, Kiwi maximizes profit by setting MR = MC. Therefore, MR = 6 -4Q = $2, imply QM = 1 million pounds and PM = $4 per pound. b) Under perfect competition, PC = LAC = $2 per pound and QC = 2 million pounds.
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c) The new price is $2 + $1 = $3. Total demand is 1.5 million pounds, so Kiwi’s output is 1.5 - .5 = 1 million pounds. Consumer surplus is: (.5)(6 – 3)(1.5) = $2.25 million and Kiwi’s profit is: (3 – 2)(1) = $1 million, for a total of $3.25 million. Without the tariff, total welfare in the form of consumer surplus was: (.5)(6 - 2)(2) = $4 million. So the tariff has reduced welfare by $.75 million.
43. Under patent protection, a firm has a monopoly in the production of a high-tech component. Market demand is estimated to be: P = 100 - .2Q. The firm’s economic costs are given by: AC = MC = $60 per component. a) Determine the firm’s output and price. b) After the firm’s patent expires, predict the new market output and price. (Assume that competing suppliers have the same economic costs as the original producer.) Compute the resulting change in consumer surplus. Calculate the net welfare gain ANSWER: a) The monopolist produces in accord with MR = MC. Therefore, 100 - .4Q = 60, or QM = 100 and PM = $80. Its economic profit is: (80 – 60)(100) = $2,000. b) After the patent expires, the market should approximate perfect competition. Therefore, P C = AC = $60, and QC = 200. Under monopoly, the consumer surplus triangle is: (.5)(100 – 80)(100) = $1,000. Under perfect competition, the consumer surplus triangle is: (.5)(100 – 60)(200) = $4,000. Consumer surplus is expected to increase by $3,000. At the same time, industry profit falls from $2,000 to $0. Therefore, the net welfare gain is: 3,000 – 2,000 = $1,000. SECTION: 2
44. In a perfectly competitive market, industry demand is: P = 850 - 2Q, and industry supply is: P = 250 + 4Q. (Supply is the sum of the marginal cost curves of the firms in the industry). a) Determine price and output under perfect competition. b) Now suppose that all the firms collude to form a single monopoly cartel. (There is no change in the demand or cost conditions of the industry). What price and total output would the cartel set? Compare the monopoly outcome with the competitive outcome in part a. ANSWER: a) The perfectly competitive market will reach equilibrium at the intersection of demand and supply: 850 - 2Q = 250 + 4Q, implying QC = 100. In turn, the competitive price is: PC = 850 – (2)(100) = $650. b) By contrast, the cartel will set total output such that MR = MC. We know that MR = 850 - 4Q, and MC = 250 + 4Q (i.e., is simply the supply curve). Therefore, 250 + 4Q = 850 - 4Q, implying QM = 75. In turn, the monopoly price is: PM = 850 - 2(75) = $700. The monopolist charges a higher price and produces a lower output than a perfectly competitive industry. SECTION: 2
45. Most people believe that monopolies always have high profits, yet some unregulated monopolies might have very low earnings. a) Why might a monopoly have little or no economic value? Explain. b) If you were given a chance to enter a perfectly competitive industry, or a monopolistic industry, which would you choose? Explain. ANSWER: a) A monopoly may exist for a good or service for which there is very little demand. Examples in the text include various legal patents for items that have never been sold. b) The answer depends on the expected profit opportunities in the respective industries. Other things equal, one can expect a successful monopoly to earn higher profits than a successful competitive firm. SECTION: 1
8-11
File: Ch09; CHAPTER 9: Oligopoly
Each question contains a code showing the section of the chapter text from which it was taken. The codes for this chapter are: Code 1 2 3 4 5
Section Oligopoly Quantity Competition Price Competition Other Dimensions of Competition Appendix: Bundling and Tying
MULTIPLE CHOICE
1. The term “loose oligopoly” refers to an industry with a) A four-firm industry concentration ratio of 90%. b) A four-firm industry concentration ratio between 40% and 60%. c) Significant price competition. d) A four-firm industry concentration ratio between 60% and 80%. e) A large number of differentiated sellers. ANSWER: b SECTION: 1
2. A competitive market has a four-firm concentration ratio that is a) Greater than 90%. b) Greater than 40% but less than 60%. c) Greater than 60% but less than 90%. d) Less than 40%. e) Less than 50%. ANSWER: d SECTION: 1
3. A monopoly industry is characterized by a a) Single-firm concentration ratio greater than 90% b) Single firm concentration ratio greater than 70%. c) Four-firm concentration of 90% and a HHI of 1,000. d) Small number of large firms dominating the industry. e) Large number of small firms dominating the industry. ANSWER: a SECTION: 1
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Oligopoly
4. Statistical evidence shows that there exists a) An inverse relationship between the degree of concentration and price. b) A positive relationship between the degree of concentration and price. c) An inverse relationship between seller concentration and efficiency. d) No significant correlation between seller concentration and price. e) An inverse relationship between price and cost. ANSWER: b SECTION: 1
5. Oligopoly differs from other forms of market structure (monopoly and perfect competition) because a) Firms frequently engage in collusion. b) Firms are protected by high barriers to entry. c) Firms’ decisions have direct effects on their rivals’ profits. d) Firms' price decisions are extremely limited. e) All of the answers above are correct. ANSWER: c SECTION: 1
6. A key characteristic of oligopoly is a) That each firm must consider its rivals' actions and reactions. b) Standardized products. c) Explicit or tacit collusion to raise industry profits. d) Unused capacity. e) Few or no entry barriers. ANSWER: a SECTION: 1
7. In the 1990s, the U. S. cigarette industry was dominated by four major firms that charged similar prices for the cigarettes they sold under a variety of brand names. When one firm raised its prices, the others generally followed. The cigarette industry was best characterized as a) Oligopolistic. b) Monopolistic competition. c) A monopoly. d) Perfectly competitive. e) A cartel. ANSWER: a SECTION: 1
8. In the U.S. cigarette industry during the 1990s, either R.J. Reynolds or Phillip Morris (Marlboro) would raise prices once or twice a year by about 50 cents per carton. Other firms in the industry typically raised their prices by the same amount. This is an example of a) Predatory pricing. b) A price war.
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c) Price leadership. d) Sales maximization. e) Kinked demand curve oligopoly. ANSWER: c SECTION: 2
9. Between 1950 and 1956, the three leading aluminum producers changed prices 9 times by exactly the same amount each time and usually within one to three days of the initial price increase. Economists call this pattern of behavior a) Destructive competition. b) Price leadership. c) Price discrimination. d) Monopoly. e) Price fixing. ANSWER: b SECTION: 2
10. The dominant firm serving as the price leader in an oligopolistic industry will charge a price that a) Is fair to all other oligopolists. b) Is consistent with the MR = MC profit-maximizing criterion. c) Maximizes total revenue for the firm. d) Maximizes total profits for the industry as a whole. e) Minimizes average cost. ANSWER: b SECTION: 2
11. The Cournot model concludes that the equilibrium price in a duopoly will be a) The same as the monopoly price. b) Higher than the monopoly price. c) Lower than the competitive-industry price. d) Set by collusive agreement between the firms. e) Between the competitive-industry price and the monopoly price. ANSWER: e SECTION: 2
12. The demand function in a duopoly is: P = 100 - 2(Q1 + Q2). The first firm decides to sell 10 units while the second firm sells 20 units. Therefore, a) The second firm earns twice as much revenue as the first. b) The second firm sells at a lower price than the first. c) An increase in one firm’s output will have no effect on the other’s revenue. d) An increase in one firm’s output will decrease the other’s revenue. e) Answers a and d are both correct. ANSWER: e
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Oligopoly
SECTION: 2
13. In the Cournot model of quantity competition, as the number of firms increases, total industry output a) Declines asymptotically. b) Grows indefinitely. c) Approaches the equilibrium output of perfect competition. d) Approaches the profit-maximizing output of a pure monopoly. e) Approaches the output of a cartel. ANSWER: c SECTION: 2
14. The model of the kinked demand curve implies that a) Strong brand loyalty means there is little incentive for firms to cut price. b) Free entry will eventually reduce economic profits to zero. c) A firm's competitors will follow it in a price decrease but not in a price increase. d) Firms will coordinate prices so as to maximize group profit. e) Rivals will match any price increases but tend to ignore any price cuts a firm makes. ANSWER: c SECTION: 3
15. An oligopolist's effective demand curve will be kinked if the firm a) Is acting as a price leader in the industry. b) Expects other firms to match price cuts but not price increases. c) Expects other firms to match all price changes. d) Fears new entry into the industry. e) Has succeeded in differentiating its product. ANSWER: b SECTION: 3
16. The model of the kinked demand curve is used to explain a) Advertising battles to build brand loyalty. b) Sales maximization. c) Price wars. d) Sticky prices in oligopolies. e) Collusive price agreements. ANSWER: d SECTION: 3
17. Under Bertrand competition, a) The firm setting the higher price attains a low market share. b) The firm setting the lower price claims the entire market. c) The total output supplied by the firms determines the market price.
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d) Firms compete on multiple dimensions: quantity, price, and advertising. e) Firms face kinked demand curves. ANSWER: b SECTION: 3
18. A price war is likely to occur when a) Some oligopolists irrationally cut prices. b) Any firm’s price change causes large market share swings. c) It is more profitable to match a price cut than to be undercut. d) Competing firms sell differentiated products. e) Answers b and c are both correct. ANSWER: e
SECTION: 3
19. In the paradigm of the prisoner’s dilemma, a) Participants’ interests are strictly opposed. b) Neither side has a dominant strategy. c) Pursuit of each person’s self-interest leads to a poor group outcome. d) Cooperation is achieved by the freedom to communicate. e) None of the answers above is correct. ANSWER: c SECTION: 3
20. The breakfast cereal industry is dominated by a number of large firms that advertise heavily. Many customers make purchase decisions according to image and brand loyalty. The cereal industry is a) Perfectly competitive. b) Monopolistically competitive. c) A differentiated oligopoly. d) A monopoly. e) A prisoner’s dilemma. ANSWER: c SECTION: 4
21. High advertising spending by oligopolists is likely to be profitable if it a) Helps buyers compare competing products. b) Raises entry barriers. c) Generates some additional sales. d) Reduces the cross-price elasticity of demand. e) Answers b and d are both correct. ANSWER: e SECTION: 4
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Oligopoly
22. Competition involves strategic substitutes when a) One firm’s best response varies in the same direction as its rival’s behavior. b) Competing goods are very close substitutes for one another. c) Firms have many choices – price, quantity, advertising – as to how to compete. d) One firm’s best response varies inversely with its rival’s behavior. e) Answers a, b, and c are all correct. ANSWER: d SECTION: 4
23. Informational advertising a) Tends to increase brand loyalty. b) Forces firms to compete more vigorously for informed customers. c) Can represent a kind of prisoner’s dilemma for competing oligopolists. d) Answers b and c are both correct. e) None of the answers above is correct. ANSWER: d SECTION: 4
SHORT ANSWER
24. Define market power, and explain why it is important to the study of managerial economics. ANSWER: Market power is the ability of a firm to raise its price significantly above the competitive price level and to maintain this high price profitably for a considerable period. Pricing power is a source of economic profit for the firm but means a higher than competitive price (and lower consumption and consumer surplus) for buyers. SECTION: 1
25. How does firm behavior in an oligopoly differ from behavior in other market structures? ANSWER: An oligopoly is a market dominated by a few sellers, several of which are large enough relative to the total market to be able to influence the market price. Much of U.S. manufacturing is characterized by oligopoly. It differs from monopoly in that there are several firms rather than one. It differs from competition in that the firms are aware of each other and their profits are interdependent. The various models of oligopoly are based on different predictions about the type of interactions between the firms. By contrast, strategic interactions are absent in monopoly and in perfect competition. SECTION: 1
26. What is the concentration ratio? How is it used to measure oligopoly? What are its drawbacks? ANSWER: The concentration ratio is the percentage of total sales accounted for by the top number (4, 8, or 20) of firms. See Section 1 of the chapter for a complete discussion. SECTION: 1
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Chapter 9
27. Why do antitrust authorities prefer to use the Herfindahl-Hirschman Index for their analyses instead of concentration ratios? ANSWER: There are three reasons: (1) The index counts the market shares of all firms, not merely the top four or eight. (2) The more unequal the market shares of a collection of firms, the greater the index because shares are squared. (3) Other things equal, the more numerous the firms, the lower the index. SECTION: 1
28. Five oligopoly firms have market shares of 40%, 20%, 18%, 12%, and 10%. Compute the four-firm concentration ratio, and the Herfindahl-Hirschman index for the industry. ANSWER: CR4 = 40 + 20 + 18 + 12 = 90%. In turn, HHI = (40)2 + (20)2 + (18)2 + (12)2 + (10)2 = 2,568. SECTION: 1
29. Distinguish between the degree of concentration for U.S. sales and the degree of concentration for U.S. production. Give at least two examples of U.S. industries that have significantly different production and sales ratios. ANSWER: Concentration ratios for domestic sales and domestic production will differ if imports represent a significant portion of the former. For example, the ”Big Three” U.S. automobile companies comprise more than 80% of domestic production, but only about 60 to 65% of domestic sales (since imports account for the other 15 to 20%). Industries with a large degree of import penetration include electronics, textiles, wines, and so on. SECTION: 1
30. Briefly explain the concept of price leadership and why it occurs in oligopolistic markets. ANSWER: The price leadership model of oligopoly combines elements of pure competition and pure monopoly. A dominant firm (in terms of market share) sets a profit-maximizing price (as a monopolist would), while the remaining small firms determine their optimal output taking this price as given; that is, they act competitively. The presence of this competitive supply makes the leader's demand curve more elastic than it would otherwise be. SECTION: 2
31. The kinked demand curve in an oligopolistic market is defined by the equations: P = 140 - .5Q, and P = 200 - 2Q. a) Derive equations for the marginal revenue curves. b) Determine the price and quantity at the "kink" of the demand curve. ANSWER: a) Derive the total revenue (TR) equations, and take the derivative of each. The curves are: R = 140Q - .5Q2‚ and MR = 140 – Q, and R = 200Q - 2Q2‚ and MR = 200 - 4Q. b) Set the two demand curves segments equal to each other, and solve for Q at the point of intersection. Therefore, 140 - .5Q = 200 - 2Q, implying 1.5Q = 60, or Q = 40. In turn, P = 140 – (.5)(40) = $120. SECTION: 3
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Oligopoly
32. In the Cournot model of duopoly, are the quantities chosen by the firms strategic complements or strategic substitutes? Explain. ANSWER: The firms’ quantities are strategic substitutes. As a rival firm’s output increases, the other firm’s net demand curve falls (shifts to the left). Thus, its marginal revenue also falls, and its optimal quantity of output decreases as well. Thus, the firm’s optimal output varies inversely with the output decision of the other firms, marking the output decisions as strategic substitutes. SECTION: 4
ESSAY
33. George Stigler, a Nobel laureate in economics, suggested that one reason why oligopolies have prices higher than competitive industries is that tacit coordination concerning output and price is much easier when there are only a few competing firms. In addition, it is easier to detect "cheating" on some agreed-upon price or output level. Evaluate this argument. ANSWER: Drawing upon knowledge of cartels (and the attendant problems of detecting and preventing cheating), the idea makes sense. Oligopolies are industries dominated by a small number of firms, and the profits of these firms are interdependent. Thus, the firms have a clear and common interest in avoiding price reductions and price wars. Stigler's analysis may be valid. SECTION: 1
34. The Department of Justice (DOJ) merger guidelines calls for the DOJ to examine proposed mergers, and approve or disapprove them. Mergers which are disapproved, and which are nonetheless consummated, face potential court challenge. The guidelines are based on the post-merger HHI. If the HHI after the merger is less than 1,000, the DOJ hardly ever disapproves the proposed merger. If the HHI after the merger is above 1,800, and has increased by more than 100 points, the DOJ is very likely to contest the proposed merger. Is this a reasonable stance on merger activity by the antitrust authorities? ANSWER: Yes, assuming one believes that increases in market power will tend to lead to increased prices and, therefore, a decrease in consumer welfare. A post-merger HHI below 1,000 is consistent with a fairly competitive industry. However, if the post-merger HHI is above 1,800, and would increase by 100 points, this could be viewed as a “significant decrease in competition,” which the antitrust authorities would find worrisome. SECTION: 1
35. Statistical evidence suggests that concentrated industries have higher profits than competitive industries. Is this necessarily harmful to consumer interests? ANSWER: No. As noted in the text, large firm size and high concentration are sometimes a reflection of superior efficiency. In other words, a firm might have grown to obtain a large market share because it was particularly efficient at producing high-quality, low-cost goods and services. Thus, such a larger firm might start with a lower average cost than a smaller competitor but have significant market power to mark up price above its unit costs. (This is the source of its increased profit.) In terms of consumer benefit, the question is whether the final price that prevails in the concentrated industry is higher or lower than it would have been under a less-concentrated market but with a higher cost structure. SECTION: 1
9-8
Chapter 9
36. The demand function for an oligopolistic market is given by the equation, Q = 180 - 4P. The industry has one dominant firm whose marginal cost function is: MC = 12 + .1Q D, and many small firms, with a total supply function: QS = 20 + P. a) Derive the demand equation for the dominant oligopolist. b) Determine the oligopolist’s profit-maximizing output and price. c) Determine the total output of the small firms. ANSWER: a) The demand equation for the dominant oligopolist is: Q D = Q - QS = 180 - 4P - (20 + P) = 160 - 5P. b) The marginal revenue equation for the dominant firm can be derived from its demand equation. Since QD = 160 - 5P, it follows that P = 32 - .2QD and, therefore, MR = 32 - .4QD. To maximize profit, equate MR = MC, implying 32 - .4QD = 12 + .1QD, so that QD = 40, and P = 32 – (.2)(40) = $24. c) The price of the smaller firms in the industry is the same as the leader, and their output is determined from their supply function: QS = 20 + 24 = 44. SECTION: 2
37. Demand in a market dominated by two firms (a duopoly) is determined according to: P = 300 - 4(Q1 + Q2). The marginal cost for each firm is constant, MC = 60. a) Derive an equation for Firm 1’s revenue (as it depends on Q1 and Q2). b) Determine each firm’s profit-maximizing output level and the resulting market price. c) What is the profit-maximizing level of output if the duopolists merged and formed a single monopoly? ANSWER: a) R1 = 300Q1 – 4(Q1 + Q2)Q1. b) As always, Firm 1 maximizes its profit by setting MR1 = MC. Thus, we have: MR1 = 300 - 8Q1 – 4Q2 = 60, implying Q1 = 30 - .5Q2. By symmetry, an analogous equation holds for Q2, and it must be the case that Q1 = Q2. Replacing Q2 by Q1 in the previous equation gives: Q1 = 30 - .5Q1, implying Q1 = Q2 = 20. The market price is: P = 300 – (4)(40) = $140. c) The merged monopoly faces the demand curve: P = 300 - 4Q. Setting MR = MC, we find that: 300 8Q = 60, implying Q = 30, and P = $180. Duopoly competition results in a larger combined output (Q = 40) than for the merged monopoly (Q = 30) and a lower price. SECTION: 2
38. What are the assumptions of the kinked demand curve model? What is its main conclusion about oligopoly behavior? How realistic is the model? ANSWER: The model has two main assumptions: The firm believes that rivals will match a price cut but ignore a price increase. The result is that demand is much more elastic above the current price (because sales volume will drop off quickly if rivals do not match a price increase), and fairly inelastic below the current price (rivals will cut price to prevent the firm from increasing market share). The main conclusion of the model is that oligopolists will tend to stick to their current prices unless there is a dramatic shift in demand and/or cost. The model is not complete. It does not explain why the kink occurs at a particular price, nor does it justify the price-cutting behavior of rivals. SECTION: 3
39. An oligopolist faces a kinked demand curve with segments given by: P = 100 - Q and P = 120 - 2Q. The firm has a constant marginal cost, MC = $45. a) Determine the profit-maximizing level of output and price.
9-9
Oligopoly
b) Calculate the (upper and lower) limits within which marginal cost may vary without affecting either the profit-maximizing output or the price. ANSWER: a) The total revenue equations and marginal revenue equations for the two demand segments are: R = 100Q – Q2 and MR = 100 - 2Q, and R = 120Q - 2Q2 and MR = 120 - 4Q. Set the two demand curves equal to each other to determine Q. Therefore, 100 - Q = 120 - 2Q, so that Q = 20. The profit-maximizing price is at the kink: P = 100 - 20 = $80. b) The upper and lower limits are computed by substituting Q = 20 into the two marginal revenue equations: MR = 100 - 2(20) = 60 and MR = 120 - 4(20) = 40. The current MC of 45 falls within these limits, so that the results are consistent with the model of kinked demand curve oligopoly. SECTION: 3
40. The matrix below displays the advertising rates and profit results of the two rival newspapers in a major city. FIRM B Firm A High Ad Rate Low Ad Rate High Ad Rate 20, 20 12, 26 Low Ad Rate 26, 12 15, 15 a) The newspapers set their advertising rates independently. Determine the optimal strategy for each firm. Explain briefly. b) If the newspaper firms were to merge and both newspapers were managed as a single business, how would this affect advertising pricing? Explain. ANSWER: a) The optimal strategy for each paper is to set a low advertising rate. If either charges a high rate, the other maximizes its profit by charging a low rate. Similarly, against a rival setting a low rate, the newspaper can improve its profits by switching to a low rate. The result is that the firms end up in the lower-right cell, each earning a profit of 15. b) After the newspapers merge, their common interest is to maximize the new organization’s total profit. Thus, each newspaper should set a high advertising rate (and total profit is 40). They effectively agree on the cooperative (or collusive) outcome. SECTION: 3
41. What is the “prisoner's dilemma”? Why is it important to the study of managerial decision making? ANSWER: The prisoner's dilemma is an example of a situation in which there are collective gains from cooperation, but individual gains from refusing to cooperate. Unfortunately, refusal by one or more parties leads to a breakdown, so that all parties end up losing. If one is interested in overcoming the prisoner's dilemma, there needs to be a binding agreement to take appropriate cooperative action. Besides firms engaged in price wars, or cartel members increasing their own outputs and profits at the expense of other cartel members, other dilemmas include overexploitation of a limited natural resource (overfishing), free riding by firms, and industry failures to set common standards for new products (such as the next generating DVD player). SECTION: 3
42. Compare and contrast equilibrium profitability for strategic substitutes versus strategic complements.
9-10
Chapter 9
ANSWER: Competition with strategic complements is more intense and leads to lower equilibrium profits compared to competition with strategic substitutes. Competition is self-limiting under SS, but reinforcing (magnifying) under SC. See section 4 of the chapter for a full analysis. SECTION: 4
43. Antitrust laws in the United States generally forbid tying arrangements. What reasons might firms give to justify tying? What reasons might antitrust authorities state to prevent it? ANSWER: Firms seeking to tie will clearly see the profit potential for the tie-in. It makes demand for the tied product less elastic, permitting a higher price and profit. Price discrimination becomes more likely with tying. In addition, a firm may argue that one product works better when used with another produced by the same firm. An example might be applications software bundled with a particular operating system software, such as Windows. The firm may be able to offer a group of products at a savings, compared to offering each separately. There may be legitimate quality control issues for requiring a tie-in. Antitrust regulation is concerned with tying because it may lead to less competition in the tied product and serve as an entry barrier. Tying that serves a legitimate business purpose is generally permitted. Ties and bundling that are seen as creating an entry barrier are less likely to pass antitrust scrutiny. SECTION: 5
9-11
File: Ch08; CHAPTER 10: Game Theory and Competitive Strategy
Each question contains a code showing the section of the chapter text from which it was taken. The codes for this chapter are: Code 1. 2. 3. 4.
Section Sizing Up Competitive Situations Analyzing Payoff Tables Competitive Strategy Appendix: Mixed Strategies
MULTIPLE CHOICE 1. Game theory offers insight into a) Pricing behavior in perfectly competitive markets. b) The optimal strategy of a monopolist. c) Making decisions within firms using optimal information. d) Strategic behavior of oligopolists. e) All of the answers above are correct. ANSWER: d SECTION: 1
2. The key assumption used in game theory is that each player a) Pursues its self-interest (maximizes its payoff). b) Seeks to win at the rival’s expense. c) Makes probabilistic predictions about competitor behavior. d) Seeks to maximize the players’ collective profits. e) Acts in a predictable manner. ANSWER: a SECTION: 1
3. In a zero-sum game, a) The equilibrium payoff is zero. b) Each player always has a dominant strategy. c) The players’ payoffs are in complete conflict; when one gains the other loses. d) The players may suffer the prisoner’s dilemma. e) Answers a and b are both correct. ANSWER: c SECTION: 2
4. In a zero-sum game, a) The players’ payoffs are in complete conflict; when one gains the other loses. b) There is never an advantage from communication or cooperation.
10-1
Game Theory and Competitive Strategy
c) Some outcomes may be mutually preferred to other outcomes. d) It is always an advantage to move first. e) Answers a and b are both correct. ANSWER: e SECTION: 2
5. A dominant strategy a) Guarantees a player a higher payoff than its competitor. b) Calls for a contingent course of action. c) Is the best response to any strategy that the other player might select. d) Minimizes the other player’s payoff. e) Achieves the player’s greatest entry in the payoff table. ANSWER: c SECTION: 2
6. The equilibrium of the following zero-sum game is:
Firm 1 R1 R2 R3
C1 6 -1 3
Firm 2 C2 -6 3 2
C3 -4 0 1
a) R1 versus C1. b) R1 versus C2. c) R2 versus C2. d) R3 versus C3. e) R2 versus C3. ANSWER: d SECTION: 2
7. An equilibrium strategy can be defined as one that a) The players would reach if they were allowed to communicate. b) Is unique and invariant to the strategy chosen by the other. c) Maximizes the sum of the players’ payoffs. d) Is a dominant strategy. e) Maximizes each player’s payoff against the strategy chosen by the other. ANSWER: e SECTION: 2
8. In the following non-zero-sum game, Firm 2
10-2
Chapter 10
Firm 1 R1 R2
C1 4, 5 2, 8
C2 10, 4 8, 7
a) Firm 1’s dominant strategy is R1. b) Firm 2’s dominant strategy is C2. c) The equilibrium outcome represents a prisoner’s dilemma. d) The equilibrium payoffs are 10 and 4. e) Answers a and c are both correct. ANSWER: e SECTION: 2
9. When two firms are poised to enter a new market, it is generally advantageous a) For both to enter simultaneously. b) For each firm to “wait and see.” c) To enter the market first. d) To enter the market last. e) For the firms to hide their intentions. ANSWER: c SECTION: 3
10. One effective way of deterring other firms from entering a new market is for the incumbent firm to practice a) Credible limit pricing. b) Selective price increases. c) Collusive pricing. d) Predatory pricing. e) Answers a and d are both correct. ANSWER: a SECTION: 3
11. In competition to determine which standard will become the industry norm, a) Each group should always adopt its own preferred standard. b) A compromise standard (even if it is inefficient) should be adopted. c) There is a prisoner’s dilemma, leading to different conflicting standards. d) There are multiple equilibria with one or the other standard adopted by all. e) Answers c and d are both correct ANSWER: d SECTION: 3
12. In a bargaining setting with perfect information, a) Backward induction determines the equilibrium outcome. b) The difficulty is that there may be many possible equilibrium outcomes. c) An equilibrium in pure strategies may not exist.
10-3
Game Theory and Competitive Strategy
d) The situation amounts to a constant-sum game. e) An equilibrium is not possible unless there is communication. ANSWER: b SECTION: 3
13. A key difference between a one-shot game and a repeated game is that a) The repeated game allows a player the opportunity to use a mixed strategy. b) In the repeated game, each player’s objective is to beat or outlast the other. c) The repeated game permits opportunities for cooperation. d) In the one-shot game, a player’s reputation might be important in influencing the other’s action. e) Answers c and d are both correct. ANSWER: c SECTION: 3
14. The global use of languages (English versus Spanish versus Chinese) for business purposes a) Should be relatively stable over long periods of time. b) Is likely to be marked by multiple equilibria. c) Depends mainly on population trends in the languages’ home countries. d) should evolve to be dominated by a few languages. e) Answers b and d are both correct. ANSWER: e SECTION: 3
15. In an infinitely repeated prisoner’s dilemma (such as a repeated price war), a) Repeated defection is the only equilibrium. b) There are two different equilibria: repeated defection and repeated cooperation. c) Repeated cooperation is the only equilibrium. d) Each player cooperates in the early stages, but defects near the end of the game. e) There is no equilibrium strategy for either player. ANSWER: b SECTION: 3
16. Which one of the following is NOT a feature of the tit-for-tat strategy? a) It delivers limited punishments for an opponent’s defections. b) It supports a cooperative equilibrium. c) It is unforgiving. d) It is never the first to defect. e) None of the answers above is correct. ANSWER: c SECTION: 3
10-4
Chapter 10
17. The pattern of fishing boats dividing themselves between maritime region A (with more fish) and region B (with less fish) should a) Have almost all boats fishing in region A. b) Exhibit two equilibria, one favoring A and the other favoring B. c) Equalize the rate of profit between the two regions. d) Have more boats fishing in region A than in B. e) Answers c and d are both correct. ANSWER: e SECTION: 3
18. A mixed strategy is optimal a) When there is no pure-strategy equilibrium. b) When the firm earns the same payoffs from multiple strategies. c) When there is no dominant strategy. d) Only in zero-sum games. e) When the firm wants to confuse its competitor. ANSWER: a SECTION: 4
SHORT ANSWER
19. How do constant-sum games and non-constant-sum games differ from each other? Give an example of each. ANSWER: A constant-sum game is one of pure conflict—that is, one player's gain is another player's loss. A non-constant-sum game is one with at least some common interest. Some outcomes may be “lose-lose,” others “win-win.” Competing for a market of constant size (i.e. how to split the total available profit) or vying to be elected President (by winning the most electoral votes) are constant-sum games. Price competition or negotiating mutually beneficial agreements are non-constant-sum games. SECTION: 1
20. The payoff table shows the competition between a new entrant and an incumbent firm. Determine each firm’s equilibrium strategy.
FIRM 1
ENTER NOT ENTER
FIGHT -10, 15 0, 20
FIRM 2 HIGH PRICE 10, 10 0, 20
ANSWER: Firm 1’s equilibrium strategy is not to enter. Firm 2’s equilibrium strategy is to fight. SECTION: 2
21. Define the concept of Nash equilibrium. Why is it important?
10-5
Game Theory and Competitive Strategy
ANSWER: In a Nash equilibrium, each player uses an optimal (payoff-maximizing) strategy, against the (optimal) strategy of the other player(s). In other words, all players are simultaneously maximizing their individual payoffs, and, therefore, none has any reason to change strategies. SECTION: 2
22. For the payoff table listed, determine the equilibrium outcome. Does either firm have a dominant strategy?
FIRM 1
LOW PRICE HIGH PRICE
FIRM 2 LOW PRICE HIGH PRICE 28, 12 48, 20 8, 50 30, 22
ANSWER: The equilibrium is for Firm 1 to set a low price and Firm 2 to set a high price. The firms' equilibrium profits are 48 and 20. Charging a low price is a dominant strategy for Firm 1. Firm 2 does not have a dominant strategy. Against a low price, Firm 2 should set a high price. But, against a high price, Firm 2 should set a low price. SECTION: 2
23. Why is communication an important factor in competitive situations? ANSWER: Communication allows rivals to state intentions and permits coordination of decisions. Indeed, it permits binding decisions. In general, the more that players' interests coincide, the more significant communication (or lack of it) becomes. In a pure common-interest game, the problem is completely one of communication. In a zero-sum game, communication cannot help because the parties’ interests are completely opposed (there is nothing to communicate about). SECTION: 1
24. What is the dilemma in the prisoner's dilemma? What is the key assumption about behavior? Suggest one way to overcome the dilemma. ANSWER: The general dilemma is that optimal individual actions inevitably lead to inferior group outcomes. The critical assumption is that the players cannot communicate, and therefore cannot coordinate their actions to optimize the group interest. If communication is possible, then the players can overcome the dilemma by explicitly entering into binding cooperative agreements. SECTION: 2
25. Define limit pricing. Under what conditions is it an optimal strategy? ANSWER: Limit pricing occurs when a dominant firm, or monopolist, maintains a below-monopoly price to deter entry. The sole objective of limit pricing is entry deterrence. Without the threat of entry, charging a price below the optimal monopoly price makes no sense. Limit pricing is optimal as a form of communication to potential entrants of intent to compete aggressively for market share or dominance. It makes sense if entry barriers are fairly low (so entry is a real threat) and if low pricing establishes a credible commitment that the incumbent will fight any new entrants. (If barriers are already high or insurmountable, there is no need to limit price.) SECTION: 3
10-6
Chapter 10
26. List and briefly explain the main entry deterrence policies that an oligopolist might employ to prevent other firms from entering a market. ANSWER: Entry deterrence policies include: limit pricing, maintaining excess production capacity (to be used should a new firm achieve entry), pursuing product differentiation strategies, and filing patent infringement suits. SECTION: 3
27. List and explain the various forms of oligopolistic cooperation, which may benefit all firms, and lead to greater profitability. ANSWER: Cooperative actions include (but are not limited to): Colluding to set noncompetitive prices, output restrictions or quotas (such as OPEC), and agreeing not to compete in rivals' home markets. SECTION: 3
28. Why is backward induction important in competitive strategy? ANSWER: Backward induction is the practice of solving a competitive situation (in the form of a game tree) from right to left – that is, by making and anticipating optimal future moves in order to determine optimal present moves. Backward induction teaches a strategist to think ahead, that is, to see the desired outcome, and the steps necessary to get there (or alternatively, the undesired outcome, and the steps necessary to avoid it). SECTION: 3
29. Discuss the role of “reputation” in competitive settings. ANSWER: The notion of reputation represents rivals' expectations of how a player will act or react in particular situations. It is most important in repeated competition, that is, in situations in which players continue to meet each other. Establishing a reputation (sometimes for toughness, other times for trust and cooperation) is important because one’s reputation affects the behavior of rival players to one’s advantage. For example, a firm might establish a reputation for price-cutting to limit entry or to retain market share. SECTION: 3
30. a) When is it optimal for players to adopt mixed strategies? b) What condition must an optimal mixed strategy satisfy? ANSWER: a) A mixed strategy is optimal when there is no pure-strategy equilibrium. (If he does X, I should do A, but if I do A, he should do Y, but if he does Y, I should do B, but if I do B, he should do X, with the process never settling down.) In this case, playing a pure strategy is a real problem. A player who always selects the same strategy is predictable and can be explointed. b) To be optimal, a player's chosen probabilities of strategies in his or her mixture must ensure that the other player earns the same expected payoff from any of the pure strategies making up his or her mixture. SECTION: 4
10-7
Game Theory and Competitive Strategy
ESSAY
31. What are the essential elements of a competitive situation (modeled as a game)? ANSWER: Any competitive situation can be described as a “game,” having the following common elements: (1) Players and their actions: Players are decision-makers and actors in a situation. Actions are decisions related to competition. (2) Outcomes and payoffs: A player's actions, together with actions taken by rivals, determine the outcome(s) of competition. Each outcome yields a payoff. (3) The underlying “rules.” There are formal and informal rules that govern competitive behavior. Rules include laws, regulations, what rivals know about the others, and whether moves are sequential or simultaneous. SECTION: 1
32. How does strategy formulation differ for zero-sum and non-zero-sum games? ANSWER: Zero-sum games are situations of pure rivalry. Players have no incentive to communicate or to establish reputation. In non-zero-sum games, players have at least some common interests. Communication is more important, and may be essential in order to reach a mutually satisfactory outcome. Reputation and commitment also play a role. SECTION: 1
33. Discuss the merits of cooperation and the advantages of bargaining (compared to the alternative of setting strategies individually and independently). ANSWER: The price war example of Chapter 9 (or any other prisoner’s dilemma) offers an apt illustration of the difference between competition (low prices result in low profits) and cooperation (a high-price agreement delivers greater profits for both firms). Bargaining over the terms of an agreement or over a common technology standard are other examples. SECTION: 2
34. a) Construct a payoff table that depicts duopolists, each facing a kinked demand curve. b) What assumption leads to the kinked demand result? ANSWER: a) The conclusion of the model is that all firms maintain the current price (at the kink in demand) unless conditions change drastically. Therefore, the payoff table should have each firm maximizing its payoff by setting its current price (with lower profit if it switched to a higher price or to a lower price). b) The key assumption is that a rival will always match any price cut but will not match a price hike. SECTION: 3
35. Why does the strategy of tit-for-tat support cooperative equilibrium? ANSWER: Tit-for-tat is a punishment strategy that makes sense in a strategic situation of repeated bargaining and confrontation. It has four virtues that make it attractive: It is (1) “nice”, (2) retaliatory, (3)
10-8
Chapter 10
clear, and (4) forgiving. If both players use tit-for-tat, each starts by cooperating and continues to cooperate (since neither is the first to defect). SECTION: 3
36. Predatory pricing is a practice of deliberately pricing at a loss in order to bankrupt a rival. a) Is predatory pricing rational? b) Should predatory pricing be illegal? Explain why or why not. ANSWER: a) Predatory pricing can be viewed as an extreme form of pricing to limit competition. It acts as a punishment to induce a rival to exit the market. The strategy is certainly rational as long as it succeeds in its intended effect. b) Predatory pricing is an antitrust offense. A firm can be found guilty of predation provided a number of conditions are proved: (1) The predatory price is below average variable cost (computed in various ways), (2) The predatory price caused or would cause the rival to leave the market, and (3) The rival’s exit would then allow the predator to raise its price to an anticompetitive level. SECTION: 3
37. What is the first mover advantage? Why is it an important strategy? Give an example to illustrate your answer. ANSWER: The first mover advantage lies in the fact that the first firm to commit to a strategy – enter a market, announce a price, or set quantity, for instance – gains an advantage by dictating or inducing rival firms’ reactions. For instance, a firm might take the first move of announcing a major capacity increase, with the aim of forestalling entry or production increases by rivals. (Entry by a new firm at a sufficient scale would depress the market price sufficiently to be unprofitable.) Another example is a firm that takes a lead in technology development that rivals may be unable to profitably match. SECTION: 3
38. Provide an example of a competitive situation where there is a second-mover advantage. ANSWER: Here are two examples. Suppose duopolists compete by setting prices and have identical demand and cost structures. Firm A sets its prices first, Firm B second. Clearly, Firm B has a potential second-mover advantage. It can always match Firm A’s price and earn an equal profit, and it might well gain by selecting a different price and earning a greater profit for itself (and a greater profit than A). Another second-mover example occurs in a zero-sum game without a pure strategy equilibrium. The second firm can always optimize its payoff after it sees the actual strategy move of the first firm. SECTION: 3
39. Nintendo and Sony Playstation are each planning to introduce one new game into the market. Each is considering three different kinds of games: an urban action game like Grand Theft Auto, an adventure game like Tomb Raiders, or a strategy game like SimCity The table shows each firm’s profits (Sony’s profit first) in millions of dollars. Nintendo Grand Theft Grand Theft
2,
2
10-9
Tomb Raiders 7,
3
Sim Cit 8,
4
Game Theory and Competitive Strategy
Sony
Tomb Raiders Sim City
3, 10
-3, -3
1,
4,
2,
-7, -7
8
1
2
a) Assuming the firms act independently, find the (Nash) equilibrium(a). Briefly, explain your answer. Is this game an example of the prisoner’s dilemma? b) Nintendo knows for a fact that Sony will not decide on its new project for four months. As CEO of Nintendo, what would you do immediately based on the analysis above? c) If the firms were free to coordinate their decisions, what agreement (and actions) would they take? Explain briefly. ANSWER : a) Using the method of circles and squares, we find two equilibria with one firm introducing an urban action game (for a $8 million profit) and the other the strategy game (for a $4 million profit). b) Given the first move, Nintendo should launch the action game (similar to Grand Theft) and claim its preferred equilibrium. c) A coordinated agreement would have Nintendo launching Grand Theft and Sony launching Tomb Raiders for a total gain of $13 million. Sony should expect to receive dollar compensation from Nintendo.
40. Consider the following game: Two players must choose one of three options: rock paper, or scissors. The winner is determined as follows: Paper slaps rock (and wins); rock crushes scissors (and wins); scissors cuts paper (and wins). Choosing the same option results in a draw. Does the game have a dominant strategy? Does it have an optimal pure strategy? ANSWER: As many will recognize quickly, the game has no dominant or equilibrium pure strategy. An optimal mixed strategy requires randomly choosing among the three options (i.e. select each with probability 1/3). SECTION: 4
41. Determine all possible equilibrium outcomes in the following non-zero-sum game.
FIRM K
STRATEGY S STRATEGY T
FIRM L STRATEGY P STRATEGY Q 16, 10 10, 14 20, 18 5, 7
ANSWER: Using the method of circles and squares, we identify two different equilibria: T versus P and S versus Q. SECTION: 3
42. The payoff table below depicts price competition between two electronics stores. (Payoffs are weekly profits in thousands of dollars for each store.)
Best Buy’s Prices
High Medium Low
High 100, 100 120, 65 110, 50
10-10
Circuit City’s Prices Medium Low 75, 120 70, 90 80, 80 65, 110 85, 75 60, 60
Chapter 10
a) Assuming they determine their strategies independently of one another, what are the stores’ respective equilibrium strategies? Explain briefly. b) Suppose that Circuit City can make the “first move” in setting its pricing policy, and then Best Buy sets its policy (knowing CC’s move). What pricing policy should CC set and what is BB’s optimal pricing response? Does Circuit City gain (relative to the equilibrium outcome in part a) from having the first move? c) Now suppose that each store adopts a “price matching” strategy – that is, each pledges to instantly match any lower price by its rival. What will be the effect on the stores’ chosen prices? Will consumers benefit from such policies? Explain briefly. ANSWER: a) Neither side has a dominant strategy. Circuit City’s high price is dominated by a medium price. The (Nash) equilibrium has Best Buy charging a low price and CC a medium price. b) If CC can make the first move, it should set a low price. Best Buy’s best response is a high price. CC’s profit is 90, an improvement of 15 relative to the original equilibrium. c) If price matching is the rule, the stores' choice is between High prices, Medium prices, or Low prices. Obviously, the mutually preferred outcome is for both to charge high prices. With automatic price matching, neither side has an incentive to deviate from the high price (i.e. to discount). The promise of price matching for consumers is empty; it actually sustains a high-price equilibrium. Consumers are worse off. SECTION: 3
43. Determine each player’s equilibrium mixed strategy in the following non-zero-sum game.
Firm A
Strategy X Strategy Y
Firm B Strategy W Strategy Z 16 4 6 10
ANSWER: Firm A should use strategy X with probability: x = (10 – 6)/[(10 - 6) + (16 – 4)] = 4/16 = .25. Firm B should use strategy W with probability: w = (10 – 4)/[(10 - 4) + (16 – 6)] = 6/16 = 3/8. Thus, the optimal mixed strategies are (.25X, .75Y) versus ((3/8)W, (5/8)Z). SECTION: 4
44. Determine each player’s equilibrium mixed strategy in the following non-zero-sum game.
Firm M
Strategy S Strategy T
Firm N Strategy P Strategy Q 16, 10 12, 8 20, 10 4, 12
ANSWER: Firm M should use probabilities s and 1 – s to ensure that Firm N earns the same expected profit from Strategy P and Strategy Q. Strategy P’s expected profit is: 10s + 10(1-s), while Strategy Q’s expected profit is: 8s + 12(1-s). Equating these two expressions yields: 10 = 12 – 4s, so s = .5. In turn, Firm N should use probabilities p and 1 – p to ensure that Firm M earns the same expected profit from Strategy S and Strategy T. Strategy S’s expected profit is: 16p + 12(1-p), while Strategy T’s expected profit is: 20p + 4(1-p). Equating these two expressions yields: 8 = 12p, so p = 2/3. Thus, the optimal mixed strategies are (.5S, .5T) versus ((2/3)P, (1/3)Q). SECTION: 4
10-11
File: Ch11; CHAPTER 11: Regulation, Public Goods, and Benefit-Cost Analysis
Each question contains a code showing the section of the chapter text from which it was taken. The codes for this chapter are: Code 1 2 3 4 5 6 7
Section Market Failure Due to Monopoly Market Failure Due to Externalities Market Failure Due to Imperfect Information Public Goods The Basics of Benefit-Cost Analysis Evaluating a Public Project Valuing Benefits and Costs
MULTIPLE CHOICE
1. Market efficiency is typically achieved by a) A small number of dominant oligopolists whose large size ensures low cost. b) Leading firms that practice genuine social responsibility. c) Competitive firms that produce goods at minimum cost and that maximize benefits for consumers. d) Command-and-control type regulations. e) Answers b and c are both correct. ANSWER: c SECTION: 1
2. An efficient competitive outcome means that a) The market maximizes total net benefits (the sum of consumer surplus and producer profit). b) Both consumer surplus and producer profit are strictly positive. c) The market is generating positive (beneficial) externalities. d) Normal shifts in demand and supply will result in a new, efficient industry output and price. e) Answers a and d are both correct. ANSWER: e SECTION: 1
3. Market failures are usually caused by a) Unexpected shifts in demand and supply. b) The persistence of monopoly power. c) Diseconomies of scale. d) Destructive price wars. e) Answers a, b, and c are all correct. ANSWER: b SECTION: 1
11-1
Regulation, Public Goods, and Benefit-Cost Analysis
4. Compared to perfect competition, monopolized markets result in a) Higher prices and greater total output. b) Higher prices and decreased total output. c) Greater producer profit but lower consumer surplus. d) A smaller total deadweight loss. e) Answers b and c are both correct. ANSWER: e SECTION: 1
5. Antitrust actions are intended to a) Remedy problems caused by imperfect information. b) Break up mega-firms when they grow too large. c) Reduce excessive windfall profits earned by firms. d) Prevent firm behavior that leads to the monopolization of markets. e) Answers b, c, and d are all correct. ANSWER: d SECTION: 1
6. The normal regulatory response in the case of a natural monopoly is a) Not to intervene at all. b) To set the regulated price equal to average cost. c) To break up the natural monopolist. d) To set the regulated price such that marginal revenue equals marginal cost. e) None of the answers above is correct. ANSWER: b SECTION: 1
7. The inefficiencies that result from negative externalities can be eliminated by a) Subsidizing consumers so as to decrease the effective price and increase output. b) Taxing consumers so as to increase the effective price and make production profitable. c) Taxing producers so as to internalize the marginal cost of the externality. d) Subsidizing producers so as to decrease cost. e) Mandating the elimination of the externality. ANSWER: c SECTION: 2
8. In the absence of regulation, if a good or service generates a positive externality, a) Market supply will tend to be less than the socially optimal level. b) Suppliers will be able to capture these positive benefits in the form of increased profits. c) Market supply will tend to be greater than the socially optimal level. d) The market price tends to be lower than the socially optimal price. e) Answers a and b are both correct.
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ANSWER: a SECTION: 2
9. When firms are required to internalize the external cost of producing a good or service, a) Price increases, output decreases, and economic costs are transferred from society to purchasers of the product. b) Price increases, causing firms to have less incentive to reduce the externality. c) Suppliers will seek the least-cost means of dealing with the externality. d) Price and output remain roughly the same but producer profits decrease. e) Answers a and c are both correct. ANSWER: e SECTION: 2
10. In regulating pollution, fees or taxes are preferred to standards because a) They involve less guesswork about clean up costs. b) They involve less guesswork about benefits. c) They allow greater flexibility and adjustments. d) The cost of a cleanup is efficiently distributed among all polluters e) All of the answers above are correct. ANSWER: e SECTION: 2
11. Market failures resulting from consumer misinformation or lack of information a) Justify government regulation to ensure better production and consumption decisions. b) Rarely justify regulation because government regulation usually increases costs more than benefits. c) Are best regulated by industry associations who have the best knowledge about the market. d) Are best regulated by the government mandating quality and prices. e) Are best handled by the firms themselves. It is in their best interest to inform consumers. ANSWER: a SECTION: 3
12. A pure public good a) Is provided by private firms for the benefit of the public. b) Is an expenditure on a good or service by the government. c) If provided for anyone, can be consumed by everyone at little or no additional cost. d) Generates the same benefit to all affected parties. e) Answers c and d are both correct. ANSWER: c SECTION: 4
13. Which of the following is the best example of a pure public good?
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Regulation, Public Goods, and Benefit-Cost Analysis
a) Medical care. b) Textbooks. c) Used clothing. d) The interstate highway system. e) Social security payments. ANSWER: d SECTION: 4
14. As a tool for public-sector managers, benefit-cost analysis a) Is useful for evaluating the profitability of infra-structure projects, such as dams, highways, bridges. b) Should not be used for budget planning purposes. c) Is valuable for evaluating the costs and benefits of government regulations and projects. d) Should not be used for evaluating projects that take more than a fiscal year to complete. e) Is problematic in evaluating safety programs because the value of life cannot be measured in dollars. ANSWER: c SECTION: 5
15. Using benefit-cost analysis a) Will typically eliminate projects whose costs and benefits stretch over decades. b) Is an attempt by public managers to ensure that society's resources are used optimally. c) Is not possible because some benefit-cost studies do not use actual market prices. d) Is a way for the government to maximize its profit from public projects. e) Answers b and d are both correct. ANSWER: b SECTION: 5
16. In deciding among mutually exclusive projects, a public manager should choose a) All projects with benefit-cost ratios greater than one. b) All projects with positive benefit-cost ratios. c) The project with the greatest benefit-cost ratio. d) The project with the greatest positive net benefit. e) Answers c and d are both correct. ANSWER: d SECTION: 5
17. Concerning benefit-cost analysis, the efficiency versus equity conflict a) Means that the analysis is of little value when benefits are inequitably distributed. b) Is partly answered by having “gainers” compensate “losers.” c) Is partly answered by using the tax and redistribution systems to address economic inequities. d) Holds that equity is more important than efficiency in a market economy. e) Answers b and c are both correct. ANSWER: e SECTION: 5
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18. When comparing benefit-cost analysis with profit analysis, a) Profit maximization is broader and more comprehensive than benefit-cost analysis. b) A public program might be implemented on benefit-cost grounds even if it is unprofitable. c) Benefit-cost analysis is more comprehensive because it includes consumer surplus and externalities. d) A public program is sustainable in the long run only if it is profitable. e) Answers b and c are both correct. ANSWER: e SECTION: 5
19. A proposed public convention center is expected to generate annual net revenues ($100,000), additional city taxes and other financial benefits ($50,000), additional after-tax business profits ($120,000), and consumer surplus ($80,000). Annual costs associated with the center include street maintenance and repair ($60,000) and traffic congestion ($70,000). Annual net benefits are a) $140,000. b) $220,000. c) $240,000. d) $290,000. e) There is insufficient information to state an answer. ANSWER: b SECTION: 6
20. Two mutually exclusive projects, expected to last indefinitely, are being compared. Program A has annual profits and consumer surplus of $10 million and a one-time capital expenditure of $50 million. Program B has consumer surplus of $15 million and a one-time capital expenditure of $100 million. Using net present value as a criterion, which alternative should be selected? a) If the discount rate is 12%, Program B should be selected. b) If the discount rate is less than 10%, Program B should be selected. c) If the discount rate is 22%, neither program should be selected. d) The programs have the same net present value regardless of the discount rate used. e) Answers b and c are both correct. ANSWER: e SECTION: 6
21. The annual net benefits (B) of a program are expected to continue forever. Its net present value is a) B/r b) B/(1+r) c) (1+r)B. d) rB e) There is insufficient information to provide an answer. ANSWER: a SECTION: 6
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Regulation, Public Goods, and Benefit-Cost Analysis
22. The discount rate used to evaluate public projects should a) Be the rate at which the government can borrow money. b) Be the rate at which the most credit-worthy firms can borrow money. c) Be determined by the social value of the project. d) Consider risk and generally be held to comparable rates of return as private investments. e) Be set significantly below comparable private market rates. ANSWER: d SECTION: 7
23. Benefit-cost analysis values non-marketed goods a) Using an index of market prices. b) At a $0 value, since such goods carry a $0 price and, therefore, generate no revenue. c) Using surveys and indirect proxies based on market prices. d) At relatively low values because their benefits are largely intangible. e) At relatively high values in recognition of their public, non-rival benefits. ANSWER: c SECTION: 7
SHORT ANSWER
24. Janet's Silk Printing company is located in a small university town. The major portion of their business is custom printed sweatshirts for university bookstores. As a sideline they also retail printed sweatshirts locally. The local demand for sweatshirts is: Q = 200 - 5P. The average and marginal cost per printed sweatshirt is $8.00. a) Calculate output, price, and profit under the monopoly conditions they enjoy locally. b) To test other markets they contemplate opening retail outlets in several university towns where there will be numerous competitors. Calculate price and output under these perfectly competitive conditions. c) Compare the competitive and the monopoly price and output situations. Calculate the deadweight loss due to their monopoly position and explain its meaning. ANSWER: a) Demand is Q = 200 - 5P or, equivalently, P = 40 - .2Q. The monopolist maximizes profit by setting MR = MC. Therefore, MR = 40 - .4Q = 8, implying Q = 80 sweatshirts per week. In turn, P = 40 - .2(80) = $24. b) Under perfect competition P = MC = AC = $8 and Q = 160. Under monopoly, price is considerably higher and output is considerably lower than under perfect competition. c) The deadweight loss is: D = (1/2)(24 - 8)(160 - 80) = $640. When Janet's charges the monopoly price ($24) as opposed to the competitive price ($8), consumer surplus is reduced. The increase in producer surplus is not sufficient to offset the consumer surplus loss and the difference is a deadweight loss. SECTION: 1
25. Brown City Pet Food Co. produces a complete line of dry pet foods. During the past year they have been test marketing a meat-based dog food. The firm's plant is located in an industrial park adjacent to the Brown River. The city's water system as well as much of its tourism industry is tied to the river. Recent tests show that a higher-than-normal bacteria count in the river stems from the effluent dumped into the
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river by the company. Experts are certain that the bacteria are generated from production of the new meat-based dog food. The firm’s long-run cost of production is: LAC = LMC = $10 per case. a) The company faces a number of competitors but still has some degree of market power. In particular, the firm’s long-run price elasticity is: EP = -3. Determine its optimal price and resulting profit margin. b) The current high bacteria count makes the river unsuitable and unsafe for swimming and other recreation – a result that has enormous cost to the town. A possible remedy is for the town to treat and clean the river water at a feasible cost of about $2 per thousand grams of effluent. The town has also petitioned Brown to remedy the discharge by installing expensive pollution equipment. However, under current town ordinances, the company is under no obligation to install the equipment and management has indicated that the plant would probably be forced to shut down if they were required to do so. Suggest a means by which the town might regulate the pollution problem. c) Is a complete solution to the problems of market failure possible? Explain briefly ANSWER: a) Using the markup rule, we find: P = [-3/(-3 + 1)]10 = $15. Profit per case is $5. b) The best solution would be for the city to implement an ordinance that imposes a fee (tax) of $2 per thousand grams on all firms that discharge effluent into the river. This tax represents the town’s cost of eliminating the externality. If Brown can find no efficient remedies to reduce the pollution, it will pay the tax and the town will at least be compensated for its cost of cleanup. Alternatively, the tax provides Brown the incentive to find cost-effective ways of reducing the effluent. Perhaps, it could re-engineer the production process to reduce or eliminate the discharge at a cost of $1.20 per thousand grams. Thus, this could well be the most cost-effective response. Of course, any increase in the firm’s marginal cost would be (partially) passed on in a higher markup price. c) This regulation is not a complete solution, because the firm’s limited market power to raise price creates a measure of deadweight loss (relative to the efficient perfectly competitive outcome). SECTION: 2
26. Use economic reasoning to comment on the following statement: “In a market where products appear to be similar but significant quality and performance differences exist, lack of information about product quality by some proportion of customers justifies government intervention.” ANSWER: Decisions about government intervention in such markets involve value judgments. The majority of customers, those with “information,” will select the better quality products. Thus, the question is how small a minority of customers are poorly informed and, therefore, are apt to make poor decisions. A second question is how effective (and costly) are government programs to disseminate better information and will consumers observe and use this information. For instance, suppose only 10% of consumers are poorly informed. Then the odds are that the market share of firms producing quality products will increase over time. In such markets word of mouth, failure of poor quality products, success of good quality products, and informative advertising would tend to drive poor quality products out of the market. Thus, intervention would not be justified. (Also, relative prices are important for consumer product choices. If prices were similar, poor quality products would tend to disappear more quickly. Alternatively, low quality products might continue to exist to satisfy a customer segment satisfied with such products as long as prices are lower.) By contrast, if most customers are poorly informed, and the consequences of quality failures are serious, there might be no effective market means to drive out poor quality products. In this case, government intervention to ensure sufficient minimum quality could be justified. SECTION: 3
27. A port authority is in the process of deciding the optimal depth (in feet) of a harbor dredging project. Both commercial shippers and pleasure boaters use the harbor. The total cost of dredging the harbor (in hundreds of thousand dollars) is C = 2F + .25F2, where F is harbor depth in feet. The total benefits to commercial shippers and pleasure boaters are: BCS = 18F - .5F2 and BPB = 8F - .25F2, respectively. a) Determine the optimal harbor depth.
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Regulation, Public Goods, and Benefit-Cost Analysis
b) Comment on the following statement: “If the cost of dredging the harbor were zero we would, of course, dredge the harbor 20 or even 25 feet deep.” ANSWER: a) Derive the optimal solution by setting the sum of the marginal benefits equal to the marginal cost. MBCS = dBCS/dF = 18 - F, MBPB = dBPB/dF = 8 - .5F, and MC = dC/dF = 2 + .5F. Therefore, MBCS + MBPB = MC implies: 26 - 1.5F = 2 + .5F, or F = 12 feet. b) Using the MB formulas, we see that both groups’ marginal benefits are negative beyond 18 feet. Thus, there is no additional apparent benefit to dredging beyond this depth. SECTION: 4
28. Explain why a private golf club might charge (1) an initiation fee, (2) an annual membership fee, (3) rental fees for carts on the golf course, and (4) dining fees for eating a required number of meals in the club’s restaurant. (Hint: Use the concepts of an individual's downward-sloping demand curve and consumer surplus). ANSWER: The law of downward sloping demand suggests that benefit for the last unit consumed is less than the benefit of the previous unit. A downward-sloping demand curve shows the price consumers are willing to pay for each unit consumed. When individuals join country clubs, the value they receive is at least equal to but very likely greater than the price they pay. Thus, the extra fees and required charges are attempts on the part of the club to capture some of this extra consumer surplus. Of course, the user charges also incorporate the marginal cost of the activities. SECTION: 5
29. Suppose that a public project (for example, a golf course) is funded out of general tax revenues. The population benefiting from the project is split into a high-income group and a low-income group, and 75% of the benefits go to the high-income group. How does this information affect a benefit-cost analysis? ANSWER: In general, by applying the efficiency criterion, analysis and policy decisions should be based on total benefits and costs of the combined population. One could, however, argue that since the benefits are so obviously skewed, weights should be applied to the benefits of each of the population groups. For example, one could deliberately weight the dollar benefits to the high-income group at only a fraction (70% say) of the benefits to the low-income group. As a result, such a public project might have positive total net benefits but be rejected by a weighted benefit-cost analysis. SECTION: 5
30. The city council of Anderson is evaluating several projects. Agreement has been reached to appropriate funds for the two projects with the highest net present value. The discount rate is 8% and the projects are expected to continue indefinitely. Which projects should be funded? Project (1) Sidewalk ramps (2) Street paving (3) Hockey arena
Annual Benefits $100,000 $600,000 $300,000
Capital Expenditures $ 450,000 $5,000,000 $4,000,000
ANSWER: NPV(1) = 100,000/.08 - 450,000 = $800,000, NPV(2) = 600,000/.08 - 5,000,000 = $2,500,000, and NPV(3) = $300,000/.08 - 4,000,000 = $250,000. The city should fund projects 1 and 2. SECTION: 6
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31. Why is selecting a discount rate so important? How does the discount rate affect benefit-cost valuations? ANSWER: Selecting the proper discount rate is important because it affects both the number of projects selected and the ranking of the projects. A higher discount rate favors projects whose benefits occur in the early years of a project and reduces the number of projects selected. SECTION: 7
ESSAY
32. The Federal Communications Commission (FCC) is trying to decide how to allocate an unused part of the radio spectrum for personal communication services (PCS). (These are advanced cellular communication services.) Monthly demand for the service in a major city is given by: Q = 1000 - 10P, or equivalently, P = 100 - 0.1Q, where Q is the number of subscribers (in thousands) and P is the monthly service price (in $). A typical firm can provide PCS service at the cost: MC = AC = $20 per subscriber per month. a) The FCC is considering licensing the exclusive right to use the spectrum to a single firm. i) What price should the firm set, and what is the resulting total number of subscribers? ii) Suppose the FCC charges the firm to license the spectrum. What is the maximum monetary amount that the FCC could expect to receive for exclusive spectrum rights? b) An alternative FCC policy is to allow multiple firms to share the spectrum in order to promote competition in the PCS market. If competition among multiple firms approximates perfect competition, what price and total number of subscribers will result? c) Which of the allocation programs in (a) or (b) do you recommend and why? ANSWER: a) i) Given its monopoly status, the firm maximizes its profit using the MR = MC rule. Accordingly, MR = 100 - .2Q = 20, implying QM = 400 thousand subscribers, and PM = 100 – (.1)(400) = $60. ii) The FCC could set a license fee equal to the firm’s total economic profit. This profit is: (60 – 20)(400,000) = $1.6 million per month. This is the maximum amount that the FCC could expect. b) Under perfect competition, PC = LAC = $20 per subscriber, and QC = 800 thousand subscribers. c) The allocation program in part (b) is best. It represents the perfectly competitive outcome and therefore is socially efficient (i.e. maximizes total net benefit). For the FCC, as an agency that seeks to further the public interest and therefore maximize social welfare, this is the appropriate goal (not simply to extract revenue from the industry). SECTION: 1
33. What is an externality? List the various types of externalities. Discuss why externalities justify government intervention. ANSWER: Externalities are side effects of production and consumption processes that affect individuals and which occur outside of markets. Externalities are classified as either positive (beneficial) or negative (harmful). Externalities distort markets and cause misallocation of resources, incorrect prices and inefficient output levels. Negative externalities understate production costs, tend to result in lower (than socially optimal) prices, and greater (than socially optimal) output levels. Positive externalities have the opposite effects. If externalities affect small numbers of individuals, then bargaining or negotiations between the parties can solve the problem. If large numbers of individuals are affected by the externality, government regulation (for instance, via a tax on the externality) is likely to be an effective response. SECTION: 2
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Regulation, Public Goods, and Benefit-Cost Analysis
34. The following (incomplete) payoff table depicts the net benefits to the United States and the European Union (EU) of reducing carbon emissions (so-called greenhouse gases). Carbon quantities are in billions of tons and monetary amounts are in billions of dollars. For the United States, the marginal benefit is $40 for each ton reduced; for the EU, MB = $50 per ton. Each side benefits regardless of who reduces the emissions. For instance, if the EU reduces by .6 billion tons and the US does nothing, the US enjoys a benefit of (40)(.6) = $24 billion, as indicated in the table. For the US, the marginal cost of reducing emissions is $60 per ton; for the EU, MC = $70 per ton. EU Reduction (billions) US Reduction 0 tons .6 tons (billions) 0 tons $0, $0 24, ___ .4 tons
___, 20
___, ___
a) Complete the missing entries in the table by computing each side’s net benefit. (Net benefit is simply total benefit minus total cost and can be positive or negative.) b) i) Determine the (Nash) equilibrium outcome when each side acts independently of the other (state the reduction each side will choose in equilibrium). Is this a prisoner’s dilemma? ii) If the two sides were able to negotiate an emissions agreement, what would be the likely outcome? c) Alternatively, suppose the US and the EU allot permits allowing the holder to release carbon emissions, (where the total amount of permits sets the maximum amount of carbon emissions a region can produce). Some commentators urge that the two sides go beyond the 1 billion ton total reduction indicated in the table. Would this increase overall social net benefits? Explain briefly. (Provide a qualitative answer). d) Currently, the US and the EU release approximately equal total emissions, and each would receive a total permit allocation proportionally less than its current level – that is, the US and EU might be provided permits equal to 70% (or some other percentage) of their pre-permit emission levels. Do you expect there to be permit trades between the US and the EU? If so, which side will be buying (selling) permits? Explain.
ANSWER: a) The completed table is EU Reduction (billions) US Reduction 0 tons .6 tons (billions) 0 tons $0, $0 24, -12 .4 tons
-8, 20
16,
8
b) Each side’s dominant strategy (and the resulting equilibrium) is 0 reductions (the top left cell). Yes, this is a prisoner’s dilemma. Reciprocal reductions (lower right cell) are mutually beneficial, but the individual incentives of each player push them to a less mutually beneficial outcome (0 reductions). ii) Under a negotiated agreement, the sides should settle on reciprocal reductions – at least the lower right cell, and presumably even greater mutual reductions. This presumes, however, that the parties can find a way to monitor and police the reductions agreement. c) Yes, going beyond the proposed reductions in the table will further increase social net benefits. This is so because the total marginal benefit from reductions is: 40 + 50 = $90 per ton. The MC of reduction is only $60 and $70 per ton. With MB > MC, further reductions would increase total social benefit. Reductions should stop at the point such that MB = MCUS = MCEU. d) With approximately equal emissions between the sides and the same proportional allocations, the sides will have comparable shortfalls between current emissions and allotted permits. But the MC of reduction in the US is cheaper than in the EU. Therefore, more emission reduction will take place in the US, inducing sales of unneeded permits from the US to the EU. For instance, if the permit price settled at a level such as P = $66 per ton, it pays to reduce emissions in the US, while the EU would find it cheaper to purchase permits rather than clean up emissions.
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SECTION: 2
35. Fisherburg is a growing industrial and tourism community with a population of 50,000 and a regional labor force pool of 40,000. A multinational corporation operates an aging paper producing plant in the community. The plant employs almost 1,500 workers and there is some concern that the current recession will force the plant to cut back production. There is even some risk that the plant will close permanently. During the past year a group of resort owners, riverfront homeowners, and outdoor sports enthusiasts have formed a committee to address river pollution. Their petition for placing a “clean river” amendment on the ballot in the upcoming local election will soon be considered by the city council. The council president is concerned about the impact of such a ballot issue, and has requested you, an economic consultant, to prepare an objective economic evaluation of potential problems the community faces. ANSWER: The most immediate concern is the pollution issue. If the paper plant is found to pollute the river, the question of who should bear the external cost and how it should be handled must be solved. As the text suggests, a pollution tax on the company is a fair way of handling the externality. The imposition of the tax will, however, increase the cost of production, and if the recession has weakened demand, production and employment will likely decrease. The extent of the reduction depends on how far the tax shifts the supply curve and on the elasticity of the demand curve. If the paper industry is competitive, which it appears to be, the decrease in production and employment could be large. The potentially larger issue is the primary and secondary effects on the local economy if the imposition of a tax results in a permanent plant shutdown. Recent anecdotal economic evidence suggests that firms recognize this potential and as a result tend to use it as leverage in bargaining with towns on regulatory remedies. SECTION: 2
36. Define a public good. How are private and public goods different? Discuss the free-rider problem and how it affects the demand curve for public goods. ANSWER: A public good is one, which if supplied to one person, can be supplied to others at (little or) no extra cost. A public good is said to be non-rival; that is, one person's consumption does not reduce its availability to others. Private goods, on the other hand, are goods that when consumed by one person cannot be consumed by another person. Thus one person's consumption excludes another person's consumption of that good. A public good when produced is equally available for all, regardless of whether they pay for the good or contribute to its production. Individuals who do not pay for the good yet consume that good are free riders. Since it is possible to consume public goods without paying for them, it is hard to get individuals to express their true preference for the good. Free riding may justify the intervention of government, since government has the authority to coerce individuals to pay for public goods through taxes. SECTION: 4
37. Outline the major steps required to construct a benefit-cost analysis for a government project. Describe the problems encountered and the decisions required for each step of the outline. ANSWER: A typical outline might include the following: 1) Identify community goals. 2) List objectives of the project. 3) Develop and evaluate alternatives for meeting project objectives. 4) List constraints. 5) Estimate the cost of each option.
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6) Estimate the dollar value of benefits for each option. On the basis of benefits and costs, select the best option. Goals tend to be very general and can be used to develop specific objectives. For example, if a goal is to improve the quality of life in a community, a specific objective might be to improve the flow of traffic. Alternatives for accomplishing this might be improved roads, improved public transportation, or simply rerouting traffic. Major constraints are typically lack of funding and lack of technology. Both of these types of constraints are important to recognize because they help set parameters for the size and kind of alternatives to consider. Costs and benefits can be either direct or indirect (external), and each must be evaluated before a project can be selected on the basis of net total benefits. SECTION: 5
38. What are some of the major problems of benefit-cost analysis? How can they be minimized? ANSWER: The major problems with benefit-cost analysis involve valuation, tradeoffs between efficiency and equity, and discount rate selection. Critics of benefit-cost analysis point to the difficulty of determining intangible values. How, for example, does one estimate the value of clean air, stronger national defense, or saving a life? Proponents argue that not considering a project because of procedural problems is equivalent to making a decision without the benefit of at least highlighting the tradeoffs. By valuing projects on the basis of market prices or proxies for market prices, different options will at least have sized up and valued (even if not precisely). Benefit-cost analysis is justified on the basis of efficiency by arguing that (1) dollar compensation can help equalize uneven benefits and costs, (2) distribution problems can be addressed via tax and other transfer programs, and (3) that in the long-run, inequities tend to even out across the population, while applying the benefit-cost rule maximizes total net benefits. The appropriate discount rate should either correspond to a comparable private rate or be determined on the basis of public policy. Projects of comparable risk should be evaluated at the same rate. SECTION 5
39. A city is deliberating whether to offer undertake a major infrastructure investment to provide free, high-speed WIFI internet access within its city limits. Alternatively, the city could rely on the private sector to provide access. The city estimates internet demand to be: P = 20 – 5Q, where Q denotes number of users (in millions) and P is price per month in dollars. The emerging private market for internet access is considered to be highly competitive, and the typical provider exhibits: LAC = LMC = $5 per subscriber per month. According to the city’s estimates, the initial cost for constructing the high-speed network is $600 million and network maintenance costs are $80 million per year. Prepare a benefit-cost analysis to guide the city’s decision. Assume that the public and private alternatives will last indefinitely, and that each will be held to a 5% discount rate. ANSWER: Consider first the private Internet alternative under perfect competition. We know that P = LAC = $5 and Q = 3 million subscribers. The industry’s economic profit is zero. From the demand curve, we know that consumer surplus is: (.5)(20 – 5)(3) = $22.5 million per month or $270 million per year. Thus, the present value of net social benefits is: 270/.05 = $5.4 billion. In turn, the public network exhibits MC = 0 and will be free of charge, implying P = $0 and Q = 4 million users. Thus, consumer surplus is: (.5)(20)(4) = $40 million per month or $480 million per year. Therefore, the present value of net social benefits is: (480 – 80)/.05 – 600 = $7.4 billion. Here, the public internet network generates far greater total benefit than the private alternative. SECTION: 6
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40. Recently, the annual interest rate that the City of Marion pays on new bonds has increased from 7% to 10%. On average the rate on the city's outstanding bonds is 8%. Which, if any, of these rates should be used by the city as a discount rate for valuing the benefits and costs of the city's current public projects? ANSWER: Probably none of them. For a given program, the city should estimate rate of return on private investments of comparable risk and use that rate. SECTION: 7
41. How does benefit-cost analysis handle the problem of valuing "priceless" human life? ANSWER: Projects that involve saving human lives, such as health and accident prevention programs, are among the most difficult to analyze. The two most common techniques for valuing human life are (1) to calculate the present value of future earnings and (2) to estimate how much individuals are willing to pay for reducing hazards and risks to life. The second method might use actual market behavior (wage rates for risky jobs) or it might rely on questionnaires asking individuals how much they are willing to pay for programs that will reduce the risk of injury or death. SECTION: 7
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File: Ch12; CHAPTER 12: Decision Making under Uncertainty
Each question contains a code showing the section of the chapter text from which it was taken. The codes for this chapter are: Code 1 2 3 4
Section Uncertainty, Probability, and Expected Value Decision Trees Sequential Decisions Risk Aversion
MULTIPLE CHOICE
1. The degree of uncertainty depends on a) The expected value of an unknown event. b) The chance that a particular outcome occurs. c) The number of possible outcomes. d) The unpredictable nature of life. e) The future trend of an economic variable. ANSWER: c SECTION: 1
2. Expected value is defined as a) The value of the outcome with the highest probability. b) The mid-point of the extreme (high and low) possible values. c) The benchmark scenario or most-likely scenario. d) The sum of the products of the probabilities of all outcomes and their values. e) The equally-weighted average of all outcomes. ANSWER: d SECTION: 1
3. An investment has the possibility of earning $10,000, $8,000 or $2,000 depending on the state of the economy. The probabilities of prosperity, moderate growth, or recession are .4, .3, and .3 respectively. The expected value of the investment is a) $10,000. b) $21,000. c) $7,000. d) $3,000. e) $8,000. ANSWER: c SECTION: 1
4. Probability may sometimes be estimated as 12-1
Decision Making Under Uncertainty a) A long-run frequency. b) An educated guess. c) The degree of uncertainty. d) The expected value. e) The degree of variation around the mean. ANSWER: a SECTION: 1
5. A subjective probability represents a) A measure of the historical frequency of an uncertain event. b) A measure of the frequency of a certain event. c) The degree of belief that an outcome will occur. d) an arbitrary or ad hoc assessment. e) The degree of variation around the mean. ANSWER: c SECTION: 1
6. An individual is uncertain whether to bet on a football game. He believes that the probability of his team winning is 40%. If his team wins, he will receive $180. If his team loses, he’ll pay $130. If the decision is made based exclusively on the expected value criterion then this person should a) Take the bet. b) Not take the bet. c) No clear-cut decision can be made. d) The expected value criterion cannot be applied in this situation. e) Be exactly indifferent to the bet. ANSWER: b SECTION: 1
7. A decision leading to a bad outcome or a loss a) Is always a bad decision. b) Is a bad decision if its underlying basis was purely subjective. c) Is a good decision plagued by bad luck. d) Is a good decision if the option chosen had the highest expected value. e) Should have never been taken. ANSWER: d SECTION: 2
8. When there are multiple risks, evaluating a decision tree involves a) First evaluating the most future risk. b) Averaging the risks in chronological order. c) Averaging only the most important risk. d) Listing the risks in chronological order on the decision tree. e) Answers a and d are both correct. ANSWER: e SECTION: 2 12-2
Chapter 12
9. The general rule for “solving” decision trees is to a) Work backward, averaging at circles and maximizing at squares. b) Work forward, averaging at both circles and squares. c) Work backward, averaging at squares and maximizing at circles. d) Work forward, averaging at circles and maximizing at squares. e) Work backward, maximizing at both circles and squares. ANSWER: a SECTION: 2
10. A firm must decide whether to launch a new product before knowing whether sales demand will be strong or weak. In addition, depending on how demand unfolds, the firm has the flexibility to set either a high price or a low price. The best order in which to draw the firm’s decision tree is a) Launch, Set Price, Observe Demand. b) Observe Demand, Launch, Set Price. c) Launch, Observe Demand, Set Price d) The expected value is the same regardless of the order. e) Both answers a and c are correct. ANSWER: c SECTION: 3
11. A firm might be liable for $10 million if a law suit is brought against it. The firm judges that the chance the suit will be brought is .6. In addition, it believes that its chance of winning such a suit (in which case it owes $0) is .7. The firm’s overall expected liability is a) $6 million. b) $4.2 million. c) $3 million. d) $1.8 million. e) $1.2 million. ANSWER: d SECTION: 3
.5
12. The expected profit associated with this decision tree is a) $10 b) $1 c) -$2 d) None of the answers is correct. e) There is not enough information to answer. ANSWER: d SECTION: 3
.6
$4
.4
13. A manager who chooses among options by applying the expected value criterion is a) Risk neutral. b) Risk averse. 12-3
.5
$10
-$20 -$5
$10
Decision Making Under Uncertainty c) Risk seeking. d) A risk minimizer. e) Answers a and d are both correct. ANSWER: a SECTION: 4
14. Risk aversion describes a person's tendency to a) Avoid risk at all cost. b) Be conservative in assessing a certainty equivalent. c) Select the safest option. d) Attach lower marginal utility to higher monetary outcomes. e) Always pay for 100% insurance against risks. ANSWER: d SECTION: 4
15. A manager who sets U($20,0000) = 20, U($40,000) = 40, U($60,000) = 70 is a) Indifferent toward risk. b) Risk loving. c) Risk neutral. d) Exhibiting decreasing marginal utility. e) Risk averse. ANSWER: b SECTION: 4
16. An individual is risk neutral if her utility curve for money is a) Linear. b) Concave. c) Convex. d) Decreasing. e) Increasing at an increasing rate. ANSWER: a SECTION: 1
17. An individual’s degree of risk aversion depends on a) Her attitude toward risk and her underlying assets. b) The extent of the risk. c) The standard deviation of the risky outcome. d) The branch structure of the decision tree. e) Her ability to insure against risk. ANSWER: a SECTION: 4
18. Given the opportunity, a rational decision-maker should always select the alternative with the 12-4
Chapter 12 a) Greatest expected return regardless of risk. b) Lowest risk. c) Greatest expected utility. d) Greatest value of the most likely scenario. e) Greatest marginal utility. ANSWER: c SECTION: 4
19. An investor estimates the expected return of option A to be $180,000 and its expected utility to be 400. The expected return of option B is $120,000, and its expected utility is 450. The investor should select a) Option A because it has the higher expected return. b) Option B because it has the higher expected utility. c) Option A because 180,000/120,000 > 450/400. d) Answers a and c are both correct. e) One cannot decide without additional information. ANSWER: b SECTION: 4
20. Consider the following risky prospect: Money $20,000 $30,000 $40,000
Utility 10 18 24
Probability .2 .2 .6
The expected utility is equal to a) $30,000 b) 18 c) 20 d) 24 e) $34,000 ANSWER: c SECTION: 4
SHORT ANSWER
21. A manufacturer of air-conditioning systems expects to sell 10,000 units next year if the economy recovers from the present recession. If the economy remains at its present state, the firm expects to sell 7,000 units, and if the recession worsens, sales will fall to 3,000 units. A survey of 40 economists reveals that 30 are forecasting recovery, 5 no change, and 5 a worse recession. Estimate the expected sales for next year. ANSWER: E(S) = (10,000)(.75) + (7,000)(.125) + (3,000)(.125) = 8,750 units. SECTION: 2
12-5
Decision Making Under Uncertainty
22. Apply the expected-value criterion to choose between these investments. Investment A has possible outcomes: $100,000 (50% chance), $40,000 (30% chance), and -$50,000 (20% chance). Investment B has possible outcomes: $150,000, $60,000, $20,000, and -$80,000 with each outcome equally likely. ANSWER: E(VA) = (.5)(100,000) + (.3)(40,000) + (.2)(-50,000) = $52,000. E(VB) = (.25)(150,000) + (.25)(60,000) + (.25)(20,000) – (.25)(-80,000) = $37,500. Select A because it has a significantly greater expected profit. SECTION: 2
23. A firm is thinking about introducing a new product. Marketing experts have determined that the product has a 10% chance of high success, a 60% chance of moderate success, and a 30% chance of failure. The gross profit from high success is $2.2 million and from moderate success $1.2 million. The estimated gross loss from failure is $500,000. Finally, the cost of introducing the product is $700,000. Should the firm introduce the product? ANSWER: No. With a launch, it’s expected net profit is: (.1)($2.2) + (.6)($1.2) + (.3)(-$.5) - $.7 = -$.26 million. Launching is a losing proposition. SECTION: 2
24. The following is the distribution of outcomes from two alternative advertising strategies: STRATEGY X PROBABILIITY REVENUE .2 $100,000 .4 $200,000 .4 $300,000 .2 $400,000
STRATEGY Y PROBABILITY REVENUE .1 $50,000 .2 $60,000 .4 $300,000 .2 $600,000 .1 $800,000
Which strategy is riskier? Explain. ANSWER: Strategy Y because its distribution appears much more dispersed. You may verify this by calculating the variances of both distributions. SECTION: 1
25. Based on the following utility schedule determine the decision maker’s attitude toward risk. Money (000's) 10 Utility Index 5
20 10
30 15
40 20
50 25
ANSWER: Since the utility schedule is linear, the individual is risk neutral. SECTION: 4
26. A manager reveals that she has a utility function U = 100M - 2M2, for M ≤ 25. Is this person risk averse, risk neutral, or risk seeking? ANSWER: The function is concave, that is, marginal utility = dU/dM = 100 - 4M declines as wealth M increases in the range, 0 ≤ M ≤ 25. Therefore, the manager is risk averse. 12-6
Chapter 12 SECTION: 4
27. Estimate the expected utility of two individuals, A and B, from the investment that has the following possible outcomes: Probability .3 .4 .2
Outcome $10,000 $30,000 $80,000
A’s Utility 10 30 80
B’s Utility 10 20 40
ANSWER: E(UA) = .3(10) + .4(30) + .3(80) = 39 and E(UB) = .3(10) + .4(20) + .3(40) = 23. Individual A is risk neutral and will always make the same decision regardless of whether expected value or expected utility are applied. Individual B, on the other hand, is risk averse and may choose a safer option with a lower expected monetary value. SECTION: 4
28. If a decision is made on the basis of expected utility, which of the two investments should the decision-maker buy?
Probability .2 .6 .2
Investment R Return ($) Utility 500 100 1200 200 1500 220
Investment C Probability Return ($) .4 500 .2 1200 .4 1800
Utility 100 200 235
ANSWER: E(UR) = .2(100) + .6(200) + .2(220) = 184. E(UC) = .4(100) + .2(200) + .4(220) = 168 Therefore, investment R should be selected. SECTION: 4
29. An individual has a utility of money function U = 20 + .5M and considers two options: (1) Invest $100,000 in a building lot, which could sell for $150,000 if interest rates decrease or $80,000 if they do not. (2) Invest the same $100,000 in bonds, which will be worth $135,000 if interest rates decrease, and $100,000 if they do not. The consensus among economic forecasters is that interest rates have an 80% probability of decreasing and 20% chance of remaining constant. Which investment option will this individual select? ANSWER: Since the marginal utility of money is constant, the individual is risk neutral. Thus, he selects the option with the greatest expected value. Option 1: E(V) = (.8)(150,000) + (.2)(80,000) = $136,000. Option 2: E(V) = (.8)(135,000) + (.2)(100,000) = $128,000. Therefore, select Option 1. SECTION: 2
30. Insurance has a negative expected value for the purchaser. (The premium paid exceeds the expected payout under the policy.) Is it rational to buy insurance? Explain why or why not. ANSWER: See section 4 of the chapter for more detail. In brief, insurance is a method of reducing the expected loss from an undesired event, such as accident, fire, and so on. Risk-averse persons will accept the small guaranteed loss in exchange for a limit on the size of the potential loss. 12-7
Decision Making Under Uncertainty SECTION: 4
31. How are certainty equivalent and attitude toward risk related? Give an example to illustrate your answer. ANSWER: The certainty equivalent is the amount of money for certain that makes an individual indifferent to a risky prospect. If a person's certainty equivalent is equal to the expected value of the risky prospect, then the person is risk neutral. If the certainty equivalent is less than the expected value, the person is risk averse. If the certainty equivalent is more than the expected value, the person is risk seeking. The example used in the text involved flipping coins. You can accept a sure $60, or you can risk a toss of a coin, where you would win $400 for heads and lose $200 for tails (implying an expected value of $100). A person who chooses the certain $60 is risk averse. SECTION: 4
ESSAY
32. Firm X is currently selling a consumer good and faces two related decisions. With respect to pricing, it can maintain its “standard” price or it can adopt a lower “discount” price. With respect to marketing, it can keep with its current advertising campaign or it can expand its advertising. The main risk facing the firm concerns the course of the economy in the near-term: whether the economy will continue healthy growth or whether it will experience a recession. The table below shows the firm’s possible profit results (in $ millions) depending on its price and advertising actions. Finally, the firm judges that there is an 80% chance of growth and a 20% chance of a recession.
Standard P + Level Ads Discount P + Level Ads Standard P + Increased Ads Discount P + Increased Ads
Growing Economy 25 15 30 20
Recession -20 0 -45 -10
a) Firm X must make its decision now (before knowing the future course of the economy). Which of the four alternatives maximizes its expected profit? b) Now suppose that Firm X can wait and decide its pricing decision after it knows the course of the economy. (It still must make its advertising decision immediately.) Draw a decision tree to find the firm’s best course of action. ANSWER: The respective expected profits are: Standard P + Level Ads: (.6)(25) + (.4)(-20) = $7 million, Discount P + Level Ads: (.6)(15) + (.4)(0) = $9 million, Standard P + Greater Ads: (.6)(30) + (.4)(-45) = $0 million, and Discount P + Greater Ads: (.6)(20) + (.4)(-10) = $8 million. A discount price and level advertising are the best decisions. b) The decision tree is:
12-8
Chapter 12
According to the decision tree, the firm should keep its advertising at its current level. Then, it should set standard prices in a growing economy, but cut prices in a recession. SECTION: 3
33. You are the chief appraiser for a large art dealer in a major American city. You are offered a chance to examine, and buy, a work of art. You have reason to believe that it is a piece from a famous artist of the 15th century that has been lost to the art world for hundreds of years. Such a painting would have an estimated market value of $1 million. However, you face two risks. First, the painting may be a forgery, a chance that you estimate to be .4. Second, even if the painting is authentic it may be stolen. Once you buy the painting, you bear all risk. If it is a fake, its value is $0. If it proves to be stolen (a .2 risk in your estimation), you must return the painting to its rightful owner and you cannot recover the purchase price. a) You have the chance to buy the painting for $500,000. As a risk-neutral decision maker, should you make the purchase? b) Suppose you can buy insurance against the risk od theft. You pay a premium of $20,000, and the insurance company compensates you according to your purchase price if the work proves to be stolen. Should you buy the painting for $500,000? ANSWER: a) According to your decision tree, you should not buy the painting. Buying means a loss of $20,000 on average. (In other words, the expected value of the painting is only $480,000.) b) The second decision tree is similar to the first – except that the outcome is $0 (the insurance company compensates you for the purchase price) if the painting is stolen. The expected value of the tree (before subtracting out the cost of the insurance premium!) is $40,000. Thus, your final expected profit is 40,000 – 20,000 = $20,000. You should elect the insurance and buy the painting. SECTION: 3
34. A financial analyst considers three funds. The funds’ estimated returns depend on future economic conditions – summarized by outcomes A, B, C, or D. The table lists the probabilities of these outcomes and each funds expected return for each outcome. Outcome & Probability A .10 B .30 C .40
Monetary Returns (% change) Fund M Fund N Fund P -10 -25 10 8 10 12 12 20 15 12-9
Decision Making Under Uncertainty D
.20
20
30
16
Which fund has the greatest expected monetary return? Comment on the appropriateness of the expected-value criterion. ANSWER: a) EV(A) = .1(-10) + .3(8) + .4(12) + .2(20) = 10.2%, EV(B) = .1(-25) + .3(10) + .4(20) + .2(30) = 14.5%, and EV(C) = .1(10) + .3(12) + .4(15) + .2(16) = 13.8%. Fund B has the greatest expected return. b) The selection of Fund B may not necessarily be the best choice. B has the highest expected return but also the greatest risk. Fund C, on the other hand, appears much safer because of the obvious smaller variation of returns. SECTION: 2
35. Consumer surveys indicate that 40% of newspaper readers read automobile ads and 5% of those who read the ads actually purchase automobiles. On the other hand, 50% of magazine readers read automobile ads but only 3% of those who read the ads actually buy a car. Among those who do not read either newspaper or magazine auto ads, 1% buy cars anyway. Sixty percent of the population reads newspapers, while 20 percent primarily read magazines. Compute the overall percentage of the population that purchase automobiles in a given year. (To aid your analysis, you might wish to draw a decision tree listing appropriate probabilities for the three aforementioned reading segments.) ANSWER: Newspaper readers buy cars at the rate of (.4)(.05) = .02, i.e. 2% of newspaper readers buy. Magazine readers buy cars at the rate of (.5)(.03) = .015, i.e. 1.5% buy. Finally, 1% of non-readers buy. Using the proportions for these 3 groups, we find the overall buying rate to be: (.6)(.02) + (.2)(.015) + (.2)(.01) = .017. Overall, 1.7% of the population buys cars each year. SECTION: 2
36. A manager’s utility of money schedule is (monetary amounts are in $000s): Money Utility
100 10
200 18
300 25
400 30
500 32
Two investment opportunities have the following net present values (again in $000s).: Investment K Prob NPV .2 100 .4 300 .2 400 .2 500
Investment L Prob NPV .1 100 .2 200 .2 300 .4 400 .1 500
a) Select the optimal investment based on the expected-value criterion. b) Make your selection using the expected-utility criterion. c) Comment on the difference in your answers in part (a) and (b). ANSWER: a) EV(K) = .2(100) + .4(300) + .2(400) + .2(500) = $320,000, and EV(L) = .1(100) + .2(200) + .2(300) + .4(400) + .1(500) = $320,000. b) EU(K) = .2(10) + .4(25) + .2(30) + .2(32) = 24.4, and EU(L) = .1(10) + .2(18) + .2(25) + .4(30) + .1(32) = 24.8 c) The expected values are equal but investment L appears safer than investment K. (Investment L has lower chances of the extreme outcomes.) Investment L’s higher expected utility reflects its lower risk. The right investment typically reflects both expected value and risk. Thus the expected utility criterion should be applied and investment L should be selected 12-10
Chapter 12 SECTION: 4
37. A chemical company is in the process of studying two long-term plans. The first plan involves expansion of their industrial division. The second plan emphasizes expansion in the business of consumer pharmaceuticals. Market research reveals the following (preliminary) results (returns are in $ millions): Industrial Expansion Prob Profits .3 10 .3 15 .4 20
Pharmaceuticals Prob Profits .2 0 .3 10 .3 20 .2 40 The planning committee has the (risk averse) utility function U = 10M -.05M2. Discuss the long-term planning decision based on the preliminary predictions and the given utility function: ANSWER: Expansion of the industrial division seems to involve less risk but also a lower expected profit, $15.5 million compared to $17 million. The key question is whether the riskier investment’s higher expected value is enough to offset the higher risk. To answer this question, you must estimate each program’s expected utility. Using the utility equation, calculate the utility for the various potential monetary returns. For the industrial expansion: E(U) = (.3)(95) + (.3)(138.75) + (.4)(180) = 142.125. For consumer pharmaceuticals: E(U) = (.2)(0) + (.3)(95) + (.3)(180) + (.2)(320) = 146.5. Though pharmaceutical expansion is riskier, it nonetheless generates the greater expected utility, and, therefore, is the better choice. SECTION NUMBER: 4
38. a) You are offered a choice between two lotteries, K and L: Lottery K: You win $1,000 with complete certainty. Lottery L: You win $5,000 with probability .10 You win $1,000 with probability .75 You win $0 with probability .15 Compute the expected value of both lotteries, and indicate which you would choose. Explain your choice, using the concept of certainty equivalent. b) You are offered a choice between two lotteries, R and S: Lottery R: You win $1,000 with probability .387, or you win $0 with probability .613 Lottery S: You win $5,000 with probability .12, or you win $0 with probability .88 Compute the expected value of the two lotteries, and indicate which you would choose. Is your choice consistent with part a.? Explain.
ANSWER: a) The expected value of K is $1,000. The expected value of L is: (.1)($5,000) + (.75)($1,000) = $1,250. Even though L has the greater expected value, a sufficiently risk-averse person will lean toward choosing Lottery K; the certain $1,000 is preferred to the risk of L (an appreciable chance of receiving nothing). b) The expected value of R = (.387)($1,000) = $387. The expected value of S = (.12)($5,000) = $600. Lottery R is less risky than S, and a risk-averse person will tend toward choosing R. The ratio of the expected value of R and S is actually the same as the ratio of K and L. For consistency, one should expect that a risk-averse person who chooses K will also choose R. SECTION NUMBER: 4
39. Mary runs her own small business, and has a utility function for assets of: 12-11
Decision Making Under Uncertainty U(A) = 22A - .07A2‚ for all 100 A 0 where A = total assets in thousands of dollars. a) Describe Mary's attitude toward risk. b) Assume that Mary's current asset holding are $20,000. Should she accept a business opportunity that has a probability of .55 of netting a profit of $15,000 and a probability of .45 of netting a loss of $15,000? c) Assume that Mary's assets are $85,000 instead. Should she now accept the same offer? d) Comment on the results of b. and c. ANSWER: a) Marginal utility = d[U(A)]/dA = 22 - .14A. Mary is risk averse. b) The utility of $20,000 = 412. The utility of the offer is: (.55)U($35,000) + (.45)U($5,000) = (.55)(684.25) + (.45)(108.25) = 425.1. Mary should accept the offer. c) The utility of $85,000 is 1,364.25. The utility of the offer is: (.55)U($100,000) + (.45)U($70,000) = (.55)(1,500) + (.45)(1,197) = 1,363.65. Mary is essentially indifferent between the options. d) Mary shows increasing risk aversion. As her assets increase, a given risky offer becomes relatively less attractive. In this case, the increase in utility from a gain is more than offset by the drop in utility from a loss. SECTION: 4
40. Suppose that you are fortunate enough to receive a gift from a family member of $5,000, which you may use as you see fit. You are then offered a chance to receive an additional $2,000 with certainty, or a 50-50 chance of either $5,000 or $0. a) Which would you accept? b) Suppose instead that you have $10,000 in a bank account. You must now choose between paying $3,000 with certainty or taking a 50-50 chance of loss of either $0 or $5,000. Which would you choose? c) Were your choices consistent? Explain why or why not. ANSWER: a) A risk-neutral person prefers the gamble. However, the size of the risk and prevailing risk aversion means that empirically about 65% of experimental subjects choose the sure $2,000. b) Most people accept the gamble, reasoning that they can afford the loss (still retain $5,000), and hope for no loss ($10,000), rather than settle for $7,000. c) It is inconsistent to take the sure thing in part a and to gamble in part b. In each case, the sure thing is $7,000, while gambling amounts to a 50-50 risk of $5,000 and $10,000. Though the risky choices in parts a and b are identical, the different “framing” of the risks can cause the decision maker to see them differently and make different, inconsistent decisions. SECTION: 4
12-12
File: Ch13; Chapter 13: The Value of Information
Each question contains a code showing the section of the chapter text from which it was taken. The codes for this chapter are: Code 1 2 3 4 5
Section The Value of Information Revising Probabilities Other Applications Optimal Search The Value of Additional Alternatives
MULTIPLE CHOICE
1. The expected value of test information is a) Zero if the new information does not change the firm’s decisions. b) The difference between the actual outcome with test information and without it. c) The difference between the expected value with the information and without it. d) The expected value of the decision using the test. e) Answers a and c are both correct. ANSWER: e SECTION: 1
2. A decision-maker should acquire new information a) Only if its cost is low. b) Only if its expected value is greater than its cost. c) Whenever the information will have an impact on the manager’s decision. d) Only when the information is highly reliable. e) None of the answers above is correct. ANSWER: b SECTION: 1
3. A “prior” probability refers to a) A probability before new information is obtained. b) A conditional probability. c) The past accuracy of a given information source. d) An assessment that combines both current and new information. e) Historical frequencies. ANSWER: a SECTION: 1
4. A firm's expected profit without information is $50,000, while its expected value with test information is $75,000. If the cost of the test is $40,000, then 13-1
The Value of Information a) The firm should undertake the test. b) The EVI is $35,000. c) The EVI is $25,000. d) The EVI is $10,000. e) Additional information is needed to determine the firm's best decision. ANSWER: c SECTION: 1
5. A price cut would increase the firm's profits by $2 million if demand is weak but would decrease profit by $3 million if demand proves to be strong. The firm’s best assessment is a .3 probability of strong demand. The expected value of perfect information about demand is: a) $0. b) $.5 million. c) $.9 million. d) $1.4 million. e) None of the answers above is correct. ANSWER: c SECTION: 1
6. You are offered a favorable bet on a coin toss, heads or tails. If you correctly call the result, you gain $20. If your call is incorrect, you lose $10. What is the EVI if you were clairvoyant and could perfectly predict the coin toss? a) $5. b) $10. c) $15. d) $20. e) None of the answers above is correct. ANSWER: c SECTION: 1
7. Revised probabilities depend on a) Purely subjective assessments. b) Prior probabilities. c) The accuracy of new information. d) Averaging the judgments of experts. e) Answers b and c are both correct. ANSWER: e SECTION: 2
8. Joint probability refers to a) The decision maker’s prior probability. b) The accuracy of new test information. c) A long-run frequency. d) The chance that one event occurs given that another has occurred. e) The chance that two events both occur.
13-2
Chapter 13 ANSWER: e SECTION: 2
9. Information is of no value if it a) Is too costly. b) Is imperfect. c) Does not change an individual's optimal decisions. d) Results in probability revisions. e) Is asymmetric. ANSWER: c SECTION: 2
10. Suppose that the chance of having both a “favorable” survey and an unsuccessful product launch is .2. In addition, the frequency of “favorable” market surveys for all new product launches is .5. Then the chance of a successful product launch given a favorable survey is a) .8. b) .5. c) .4. d) .6. e) There is insufficient information to determine the answer. ANSWER: d SECTION: 2
11. If Pr(a) = .5 and Pr(b) = .3, then Pr(a & b) is a) .8. b) .375. c) .15. d) .2. e) There is insufficient information to determine the answer. ANSWER: e SECTION: 2
12. If Pr(a) = .4, Pr(b) = .3, and Pr(ba) = .5, then Pr(a & b) is a) .35. b) .5. c) .2. d) .7. e) .14. ANSWER: c SECTION: 2
13. Pr(ab) can be expressed using Bayes Theorem as a) Pr(ba)/Pr(b). b) Pr(a & b)/Pr(b). 13-3
The Value of Information c) Pr(ba)/Pr(a). d) Pr(a & b)/Pr(a). e) Pr(ab)/Pr(a). ANSWER: b SECTION: 2
14. In a large metropolitan area, one out of ten drivers on the road on Saturday after midnight is intoxicated. Half of all accidents during this time period involve drunk drivers. Finally, the overall accident rate Saturday after midnight is 3 accidents per 100 cars on the road. For a drunk driver, the risk of accident is a) 1/10. b) 1/2. c) 3/100. d) 15/100. e) 30/100. ANSWER: d SECTION: 2
15. The test result B has no value in predicting outcome A if. a) Pr(AB) = 1 b) Pr(A & B) = Pr(A)Pr(B) c) Pr(AB) = Pr(BA) d) Pr(A) > Pr(AB) e) Pr(AB) = 0 ANSWER: b SECTION: 2
16. A bank has categorized its credit card accounts as high risk or low risk. The overall default rate on all the bank’s credit card accounts is .20. In the past, of the accounts that defaulted, 50 percent were correctly identified by the bank as high risk. Therefore, the default risk for a high-risk account is a) .50. b) .15. c) .40. d) .25. e) There is not enough information to determine the answer. ANSWER: e SECTION: 3
17. Intuitive prediction a) Puts the wrong weights on different kinds of information. b) Provides approximately correct decisions most of the time. c) Leads to overconfident forecasts. d) Answers a and c are both correct. e) Answers b and c are both correct.
13-4
Chapter 13 ANSWER: d SECTION: 3
18. In an optimal stopping problem with increasing probabilities of a successful venture, the firm should a) Invest until the total cost of its investment equals the potential profit. b) Invest once to “test the waters.” c) Invest until the venture is successful or not invest at all. d) Continue to invest in order to recover sunk costs. e) None of the answers above is correct. ANSWER: c SECTION: 4
19. With declining probabilities of success, the optimal stopping strategy is to a) Continue to invest until the venture is successful. b) Discontinue investing when accumulated costs exceed the potential profit from the project. c) Not invest at all. d) Discontinue investing when the expected profit from continuing becomes negative. e) Invest once to acquire information about the likelihood of success. ANSWER: d SECTION: 4
20. Given two methods for developing a new product, a firm should undertake a) Only the method with the greater chance of success. b) Only the method with the lower investment cost. c) Them in order of greatest probability-to-cost ratio. d) Only the method with the greater probability-to-cost ratio. e) Both methods simultaneously. ANSWER: c SECTION: 4
21. Assuming a uniform distribution of purchase offers between $100,000 and $200,000, the expected maximum offer from 9 potential buyers is a) $150,000. b) $160,000. c) $188,888. d) $180,000. e) $190,000. ANSWER: e SECTION: 5
22. Buyer A has offered $20,000 for a painting you are trying to sell. You are about to approach Buyer B whose best offer, you believe, might be any where between $16,000 and $24,000, with all values in between being equally likely. After hearing B’s price, you will pick the higher of the two offers. Your expected price is 13-5
The Value of Information a) $20,000. b) $21,000. c) $22,000. d) $22,500. e) None of these answers is correct. ANSWER: b SECTION: 5
SHORT ANSWER
23. Suppose that the firm’s expected profit without test information is $75,000. There exists a perfectly reliable test that produces a positive result with .75 probability and a negative result otherwise. In light of a positive result, the firm's expected profit is $120,000; after a negative result, its expected profit is $40,000. Find the expected value of information. ANSWER: With the information, expected profit is: (.75)(120) + (.25)(40) = $100,000. Thus, the EVI is 100,000 – 75,000 = $25,000. SECTION: 1
24. With respect to a decision-maker's optimal strategy, what is the difference between situations of perfect and imperfect information? ANSWER: Under perfect information, the manager is able to undertake an optimal decision under certainty. For each outcome that might occur, the manager selects the optimal contingent decision. By contrast, when information is imperfect, the manager faces the usual task of assessing probabilities for uncertain events and revising probabilities in light of new information. Given the imperfect information in his possession, he continues to select the decision that maximizes the firm’s expected profit. SECTION: 1
25. From the entries below, compute the joint probability table. Then calculate Pr(BY) and Pr(XB). X Y A 325 455 B 416 104 ANSWER: After dividing each entry by the total number of cases (1,300), the joint table is: X Y Total A .25 .35 .6 B .32 .08 .4 Total .57 .43 In turn, Pr(BY) = .08/.43 = .186, and Pr(XB)= .32/.40 = .8. SECTION: 2
26. Suppose that two independent geologists begin with different prior assessments concerning the chance of oil and natural gas at a particular site. They both observe the results of a seismic test. Will they agree concerning their revised probabilities? In what instance, would their revised probabilities be identical? 13-6
Chapter 13
ANSWER: Bayes theorem instructs us that different prior probabilities will induce different revised probabilities – even with the same test information. The one case in which revised probabilities will be the same (despite different prior probabilities) is if there is perfect test information. In this instance, the test information will reveal the actual outcome with complete certainty. SECTION: 2
27. Explain how Bayes Theorem is used to revise probabilities. ANSWER: Bayes Theorem offers a logical means for incorporating new information into a decisionmaker's probability assessment. Information is (generally) useful in determining a course of action. The usual formulation of Bayes theorem using test result t to predict uncertain event e is: Pr(e|t) = [Pr(tIe)/Pr(t)]Pr(e). SECTION: 2
28. Briefly describe the potential pitfalls associated with making intuitive predictions. ANSWER: See the discussion and examples in section 3 of the chapter. SECTION: 3
29. A firm is considering development of a new technology with a declining probability of success in each research stage. The firm’s researchers have estimated the probabilities at .35, .25, .15, .07, and .01 for the various stages. The profit the firm would receive for successful development is $100 million, while the cost of research in each period is $10 million. How many investment stages should the firm undertake before abandoning the project? ANSWER: The cut-off probability is: p* = c/ = 10/100 = .1. The firm should invest $30 million (three stages) if necessary before abandoning the project. SECTION: 4
30. A high-tech firm is pursuing R&D to commercialize the next generation of DVD players (using very high-definition DVDs). Two R&D approaches are available: laser technology and digital technology. Either way, the firm will receive the same expected profit if successful. Development costs are $100 million and $125 million, and probabilities of success are .3 and .5, for the respective approaches. Which R&D method should the firm pursue first? ANSWER: Digital’s profitability-to-cost ratio, pD/cD = .5/125 is greater than laser’s ratio, pL/cL = .3/100. Therefore, the digital approach should be pursued first. SECTION: 4
31. Explain how ascending and descending probabilities of success in research affect investment strategies. ANSWER: With ascending probabilities, once an initial investment is made, the firm should invest until successful. With descending probabilities, the firm should invest only as long as p > c/. SECTION: 4
13-7
The Value of Information
32. A real estate broker is attempting to sell a warehouse. She estimates that an offer from a typical potential buyer will be centered on $5.5 million plus or minus $.5 million and that any offers will be uniformly distributed within this range. The broker has located four potential buyers. What will be the “best” price, on average, that she can expect to receive? ANSWER: E(VMAX) = [1/(N + 1)]L + [N/(N + 1)]U = (1/5)(5) + (4/5)(6) = $5.8 million. SECTION: 5
ESSAY
33. A petrochemical company must decide whether to fill a specialty order for one of its customers. Its cost (and therefore profit) depends on the quality of the raw material it has on hand to make the chemical. The firm expects to earn $50,000 from the order if the material is high quality (H) but will lose $30,000 if it is low quality (L). The firm's engineers estimate these probabilities to be .32 and .68 respectively. Before making its decision, the firm can test the material with one of two outcomes, “favorable” or “unfavorable.” A favorable test increases the chance of H to .5, while an unfavorable result reduces it to .2. The likelihood of a favorable test is .4. Determine the expected value of this test. ANSWER: Without the test, the firm's expected value for filling the order is: (.32)(50,000) + (.68)(-30,000) = -$4,400. Thus, the firm should turn down the order. Suppose the firm tests the raw material. If the result is favorable, the firm should fill the order. In this case, the expected value is: (.5)(50,000) + (.5)(-30,000) = $10,000. If the result is unfavorable, the firm should definitely turn down the order. Thus, the overall expected value of the test is: (.4)(10,000) = $4,000. SECTION: 1
34. Describe how a decision-maker's attitude toward risk affects her strategy for acquiring information. ANSWER: Information is valuable whether the manager is risk neutral or risk averse (indeed, it is often of greater value to the risk-averse manager). Inclusion of the information in the decision tree (listing of test results and revised probabilities) is the same in either case. The only difference is that the risk-neutral manager averages back the tree using expected values, while the risk-averse manager uses expected utilities. SECTION: 2
35. In a medical study of 5,000 middle-aged men, it was found that (1) 10% suffered heart disease, (2) 20% got little or no exercise, and (3) Of those suffering from heart disease, 60% had a history of little or no exercise. Based on this information, determine the risk of heart disease for a middle-aged man who does not exercise. ANSWER: According to Bayes theorem, the probability of heart disease conditional on no exercise is: Pr(HDNE) = [Pr(NEHD)/Pr(NE)]Pr(HD). Therefore: Pr(HDNE) = [.6/.2][.1] = .3. Middle-aged men who do not exercise have a 30% chance of developing heart disease. SECTION: 2
36. Stake Gold Mines has the option to purchase a parcel of land adjacent to its current mining operations in a Western state. The seller’s best and final price is $3 million. If the land has commercial mineral deposits, Stake Gold estimates its value at $5 million. If there are no deposits, the estimated 13-8
Chapter 13 value is $2 million. A preliminary look at the land leads Stake Gold to believe that the chance of mineral deposits is 50-50. a) Given this information, should Stake Gold purchase the land? b) For a fee of $200,000, the seller has agreed to let Stake Gold collect extensive mineral samples on the site. Based on past experience, if there are minerals present, the samples will provide a favorable indication 80% of the time. If no minerals are present, the samples will (falsely) give a favorable reading 40% of the time. Determine Pr(M|F) and Pr(M|U). (Here, M denotes mineral deposits, F denotes favorable samples, and U denotes unfavorable samples.) c) Should stake Gold pay $200,000 for the right to collect samples? ANSWER: a) The expected value of the land is: (.5)(5) + (.5)(2) = $3.5 million. Thus, Stake Gold should buy the land for $3 million, making a net profit of $.5 million. b) The joint probability table is:
F U Total
Minerals .4 .1 .5
Not .2 .3 .5
Total .6 .4
Therefore, Pr(M|F) = .4/.6 = 2/3 and Pr(M|U) = .1/.4 = .25. c) Upon collecting the mineral samples, Stake Gold should purchase the land if the sample is favorable. In this case, the expected value of the land is: (2/3)(5) + (1/3)(2) = $4 million, and Stake Gold’s net profit is $1 million. If the sample is unfavorable, the land’s expected value is: (.25)(5) + (.75)(2) = $2.75 million, so there should not be a purchase. Thus, Stake Gold’s overall expected profit is: (.6)(1) + (.4)(0) = $.6 million. Thus, EVI = .6 - .5 = $.1 million. It is not worth paying $200,000 for the right to collect samples. SECTION: 2
37. A company is about to launch a new product and is considering one of two prices: high or low. However, the company is uncertain about the market response to the product -- whether demand will be strong or weak. The table below lists the firm's economic profit (in millions of dollars) at the two prices under strong and weak demand. According to the firm's marketing department, the probability of strong demand is .6 and of weak demand is .4. Demand for Product Strong (S) Weak (W) Low Price 16 -4 High Price 30 -20 No Launch 0 0 a) Suppose the company is risk neutral and must commit to a price before knowing what the market response will be. Should it launch the product? If so, at what price? b) The company is considering spending $10 million to test market the product on a national scale. In the process, it will learn exactly the market response (strong or weak demand) before having to decide on a final launch and pricing strategy. Should it go ahead with the market test? Explain carefully. c) Suppose instead that the company can hire a marketing consultant to undertake a limited market survey in the Midwest. The company anticipates that the consultant will come back with one of two possible demand forecasts: favorable (F) or unfavorable (U). In the past, the consultant's forecast accuracy has been as follows: Pr(F|S) = .8 and Pr(U|W) = .6. Compute the revised probabilities, Pr(S|F) and Pr(S|U). ANSWER: a) The expected profit at a low price is: (.6)(16) + (.4)(-4) = $8 million. The expected profit at a high price is: (.6)(30) + (.4)(-20) = $10 million. The high price is the best option. b) Making the price and launch decision after the national market test means that (1) if demand is strong, the firm should charge a high price ($30 > $16), and (2) if demand is weak, the firm should not launch ($0 > -$4 > -$20). Its overall expected profit is: (.6)(30) + (.4)(0) = $18 million. Therefore, its EVI is: 18 - 10 = $8 million. Because the cost of the national market test ($10 million) exceeds its expected benefit, the test should not be undertaken. c) From the joint table below, we calculate: Pr(S|F) = .48/.64 = .75, and Pr(S|U) = .12/.36 = 1/3. 13-9
The Value of Information Strong
Weak
Total
.48
.16
.64
Unfav .12 Total 0.6 SECTION: 2
.24 0.4
.36
Favor
38. Oliver undergoes a standard medical test while at his regular checkup. The test is 90% reliable in detecting a form of cancer (C) that is found in 2% of the population. In particular, Pr(+|C) = .90. The test is also 90% reliable in screening out cancer – that is, Pr(-|H) = .90. a) If Oliver tests positive, how likely is it that he actually has cancer? If he tests negative, what is his cancer risk? b) Persons who test negative, and who actually have cancer, are able to sue for malpractice. Plaintiffs in such legal suits are awarded $250,000 on average (to cover medical expenses, pain and suffering, and legal fees). What is the hospital’s expected monetary liability due to the risk of incorrect negative tests? ANSWER: a) Construct the following joint probability table. For instance, the upper-left entry is: Pr(H & -) = Pr(H)Pr(-|H) = (.98)(.9) = .882. Therefore, Pr(C|+) = .018/.116 = .155 or about 15.5%. In turn, Pr(C|-) = .002/.884 = .0023 or about .23%. Healthy Cancer Total Negative .882 .002 .884 Positive .098 .018 .116 Total .98 .02 b) The joint probability of a patient receiving a negative test result and having cancer is .002 (the upper middle table entry). Thus, the hospital’s expected monetary liability per patient tested is: (.002)(250,000) = $500. SECTION: 2
39. A company is trying to decide whether to build a large plant or a small plant to supply future sales of a new product. However, it is uncertain about the market response to the product -- whether demand will be strong or weak. According to the firm's marketing department, the probability of strong demand is .3 and of weak demand is .7. The table below lists the firm's profits (in millions of dollars) depending on plant capacity and the market response: Demand for New Product Strong Weak Small Plant 8 3 Large Plant 24 -6 a) The company must make its plant decision now, before it will know what the market response will be. Which plant size maximizes its expected profit? b) Now suppose the company has a third option: building a modular plant. This is the same size as the small plant but is built so it can be expanded to the size of the large plant at a later date. The modular plant costs $4 million more to build than the small plant, but it allows the company the flexibility to observe the market response to the new product and immediately expand its capacity if demand warrants it. (Note: If the modular plant is expanded, the firm’s total cost is also $4 million more than building a large plant in the first place.) Should the company choose to build the modular plant? c) Suppose that the firm can take a small-scale market survey that will help it forecast market demand. The test has two possible outcomes: positive or negative. In the past, products that went on to enjoy strong demand received positive test market scores in 4 of 6 cases: Pr(+|S) = 2/3. Products generating weak demand received negative test results in 5 of 7 cases: Pr(-|W) = 5/7. Compute the revised probabilities, Pr(S|+) and Pr(S|-). ANSWER: a) The expected profit of the small plant is: (.3)(8) + (.7)(3) = $4.5 million. The expected profit of the large plant is: (.3)(24) + (.7)(-6) = $3 million. Thus, the small plant is more profitable. 13-10
Chapter 13 b) Note that building the modular plant allows the firm to adjust capacity after it knows the state of demand. Thus, the firm makes its capacity decision with perfect information in hand. If demand turns out to be weak, it stays with a small capacity and makes net profit: 3 – 4 = -$1 million. If demand is strong, it expands and earns net profit: 24 – 4 = $20 million. Therefore, it’s overall expected profit is: (.7)(-1) + (.3)(20) = $5.3 million, making the modular plant the most profitable option. c) We compute the joint table as: Strong Weak Total + .2 .2 .4 .1 .5 .6 Total .3 .7 For instance, Pr(S & +) = (2/3)(.3) = .2 and Pr(W & -) = (5/7)(.7) = .5. Therefore, Pr(S|+) = .2/.4 = 1/2, and Pr(S|-) = .1/.6 = 1/6. SECTION: 2
40. Firm X is currently selling a consumer good at a “standard” price, but is also considering cutting its price. The main risk facing the firm concerns the course of the economy in the near-term: whether the economy will continue healthy growth (G) or whether it will experience a recession (R). The table below shows the firm’s possible profit results (in $ millions). Finally, the firm judges that there is a 70% chance of growth and a 30% chance of a recession. Growth Recession Standard Price 20 -10 Cut Price 15 0 a) Firm X must make its decision now (before knowing the future course of the economy). Which pricing policy maximizes its expected profit? b) Now suppose that Firm X can wait and decide its pricing decision after it knows the course of the economy. Determine its best pricing decisions and its overall expected profit. c) Firm X has hired a macroeconomic forecaster. The macro forecast is either positive (+) or negative (-). In the past, the forecaster has made positive forecasts prior to 4 of 7 periods of economic growth: Pr(+|G) = 4/7. In turn, he has made negative forecasts prior to 2 of 3 recessions: Pr(-|R) = 2/3. Compute Pr(G|+) and Pr(G|-). d) Suppose Firm X faces the decision setting in part a and can purchase the macro forecast (in part c) for $.2 million. Draw a decision tree to determine whether the firm should acquire this macro information. ANSWER: a) If it continues to set a standard price, the firm’s expected profit is: (.7)(20) + (.3)(-10) = $11 million. If it cuts price, its expected profit is: (.7)(15) + (.3)(0) = $10.5 million. Setting a standard price is the better option. b) Under perfect information, the firm should set standard prices in a growing economy ($20 million), but cut prices in a recession ($0 million). Thus, it’s overall expected profit is: (.7)(20) + (.3)(0) = $14 million. c) According to the completed joint probability table, Pr(G|+) = .4/.5 = .8, and Pr(G|-) = .3/.5 = .6. Growth Recession
Total
+
.4
.1
.5
Total
.3 .7
.2 .3
.5
d) The decision tree under imperfect information must consider two contingencies. After a positive macro forecast, setting a standard price generates the greater expected profit: (.8)(20) + (.2)(-10) = $14 million. However, after a negative forecast, cutting price is the more profitable strategy: (.6)(15) + (.4)(0) = $9 million. According to the joint probability table, Pr(+) = Pr(-) = .5. Therefore, Firm X’s expected profit from the macro forecast is: (.5)(14) + (.5)(9) = $11.5 million. Compared to the firm’s expected profit in part a, the expected value of this macro information is: 11.5 – 11 = $.5 million. The firm should acquire the macro forecast because its value is greater than its cost ($.2 million). SECTION: 2
13-11
The Value of Information
41. A middle manager is an avid runner and keeps an informal diary of her daily 5-mile training runs. Most of the time, she spends 10 minutes or more stretching before running, believing that this will help prevent minor muscle injuries. In fact, she estimates that 64% of days over the last year, she has stretched and avoided any muscle problems — that is, the relevant joint probability is Pr(Stretch & Healthy) = .64. a) Is she correct in concluding that there is a positive association between stretching and being injury free? b) Now suppose she does some additional thinking and recalls many days when she hadn’t bothered to stretch and fortunately still avoided any muscle pulls. Her guess is: Pr(No Stretch & Healthy) = .20. Determine Pr(Stretch|Healthy). Does this indicate that stretching reduces the risk of injury? c) Finally, the manager recalls a small number of instances when she neglected to stretch and, indeed, suffered muscle pulls, leading to the guestimate: Pr(No Stretch and Muscle Pull) = .02. Write down the appropriate two-by-two joint probability table. Does stretching reduce the risk of injury? ANSWER: a) The correct answer is, maybe yes, maybe no. In effect, she has filled in only one cell (the upper left one) of a two-by-two joint probability table. We need to fill in additional table cells to see what difference stretching (or not stretching) makes for the risk of injury. Many people intuitively judge association by the simple rule of whether two events frequently occur together. Unfortunately, this can lead to big mistakes in prediction. b) Notice that the overall frequency of healthy runs is Pr(H) = .64 + .20 = .84. As far as healthy runs are concerned, the vast majority of the time, she dutifully stretched before hand, Pr(Stretch|Healthy) = .64/.84 = .76. This is a positive indication that stretching probably reduces injuries, but based only on two cells of the joint table, we still do not know this for sure. c) The complete joint probability table is: Healthy Injury Total Stretch .64 .14 .78 No Stretch .20 .02 .22 Total .84 .16 The table shows that the runner is unusually injury prone; some 16 percent of her daily runs leave her with some type of minor muscle injury. More to the point, we compute the revised probabilities: Pr(Injury|Stretch) = .14/.78 = .18, and in turn, Pr(Injury|No Stretch) = .02/.22 = .09. For this particular runner, pre-workout stretching actually raises the risk of injury! Either she is stretching incorrectly (“bouncing” stretches can cause minute muscle tears that are exacerbated by her running) or inadequately (she begins her runs at too fast a pace thinking she is already sufficiently stretched). SECTION: 2
42. In making sequential risky investments, what is the firm’s optimal stopping rule? Provide a brief explanation as to why it makes sense. ANSWER: Regardless of how much has already been invested (sunk costs), the optimal stopping rule instructs the firm to stop investing when the revised probability of success falls sufficiently low so that the expected profitability of continuing becomes negative. Thus, the firm should assess the probability of success (p), and compare it to the additional investment cost (c) and the profit upon success (). In mathematical terms, the firm’s break-even condition is: p - c ≥ 0. Thus, the firm should profitably continue to invest as long as: p ≥ c/. Conversely, the firm should stop investing if p < c/. SECTION: 4
43. a) Suppose that buyers' offers are independently and uniformly distributed between $32 million and $56 million. Construct a table showing expected maximum prices with from 1 to 7 buyers. b) From the firm's point of view, what is the “best” number of buyers? Explain.
13-12
Chapter 13 c) Now suppose the search cost of finding each additional buyer is $1 million. What is the optimal number of buyers? Explain. ANSWER: a)
N E(VMAX) 1 44 2 48 3 50 4 51.2 5 52 6 52.6 7 53 The table uses the formula: E(VMAX) = [1/(N + 1)]L + [N/(N + 1)]U, where L = 32 and U = 56. b) Ideally, the firm would like to see an unlimited of buyers since E(VMAX) increases steadily with the number of bidders. c) Adding a fourth buyer raises the expected price by $1.2 million, which is worth the search cost. But adding a fifth buyer (MB = $.8 million) is not worthwhile. Thus, the optimal number of buyers is four. SECTION: 5
44. In the late 1990s, many local affiliates of the three TV networks left their current partner to join a rival network that was seeking new stations. (The networks pay their affiliates to carry programs, which is a major source of revenue for the stations.) Why would the affiliates leave their current partner for a new network? ANSWER: The affiliates (probably) have the goal of maximizing profit. Enlisting one or more competing networks to bid for the affiliate’s allegiance should increase the affiliate’s expected compensation. Most likely, the new networks offered more money than the current partners, and the stations made the switch to increase their net incomes. SECTION: 5
45. The Professional Beach Volleyball League is accepting bids for televising the national championship playoffs. Competition is stiff, and the league expects bids to be higher this year than last. League officials have estimated that the bid of a particular network might range between $10 million and $20 million, with all values in between considered equally likely. Furthermore, the values of network bids are considered to be (probabilistically) independent of each other. a) If the three major television networks bid, what is the expected value of the winning bid? b) If Fox decides to enter the bidding as well, what is the new expected value of the winning bid? c) Explain why the addition of a new bidder raises the expected value of the winning bid. ANSWER: a) Using Equation 13.6 from the text for three bidders: E(VMAX) = (1/4)(10) + (3/4)(20) = $17.5 million. b) The addition of Fox increases the expected value of the winning bid to: (1/5)(10) + (4/5)(20) = $18 million. c) As additional potential buyers enter the bidding, it is more likely that one of the buyers will have a monetary value near the upper bound of its probability distribution. This high-value buyer will place the high, winning bid. SECTION: 5
13-13
File: Ch14; CHAPTER 14: Asymmetric Information and Organizational Design
Each question contains a code showing the section of the chapter text from which it was taken. The codes for this chapter are: Code 1 2
Section Asymmetric Information Organizational Design
MULTIPLE CHOICE
1. Asymmetric information is a) Imperfect information. b) One factor leading to adverse selection. c) caused by delegated decisions. d) Information possessed by one agent but not by the other. e) Answers b and d are both correct. ANSWER: e SECTION: 1
2. The “lemons” model refers to a market a) That is unsustainable in the long run. b) That is regulated to control quality. c) Where different quality goods sell at different prices. d) Where asymmetric information leads to the sale of mostly low-quality goods. e) Where only the buyer has access to complete information. ANSWER: d SECTION: 1
3. Adverse selection usually occurs due to a) Signaling. b) Externalities. c) Agents’ shared uncertainty. d) Asymmetric information. e) Moral hazard. ANSWER: d SECTION: 1
4. When a used car salesperson offers a warranty on any car sold in the lot, it's referred to as a) Signaling. b) Risk aversion. c) Self-selection. d) Asymmetric information. 14-1
Asymmetric Information and Organizational Design e) Adverse selection. ANSWER: a SECTION: 1
5. Moral hazard occurs when a) The principal purposely misleads the agent to obtain higher profits. b) Limited information causes uncertainty for the agent. c) An agent has an incentive to pursue its own interests to the detriment of the principal. d) Self-selection is impossible. e) An agent has inferior information when taking an action on behalf of the principal. ANSWER: c SECTION: 1
6. Adverse selection occurs because a) One party has better information about the true risk than another party. b) Both parties have an incentive to cheat on a contract. c) One party has worse luck than another party. d) One party is unable to perform the contract as specified. e) Answers b and d are both correct. ANSWER: a SECTION: 1
7. One way to overcome the problem of asymmetric information is a) Word-of-mouth. b) Adverse selection. c) Self-selection. d) Signaling. e) Risk Sharing. ANSWER: d SECTION: 1
8. Employers that permit telecommuting (working at home and contacting the office by electronic methods) may face the problem of a) Asymmetric Information. b) Moral hazard. c) A lateral organizational structure. d) Annual performance review. e) Answers a and c are both correct. ANSWER: b SECTION: 1
9. One of the important features of large, modern firms is a) The dispersion of information among many decision makers. 14-2
Chapter 14 b) The inclusion of management and information in a single entity. c) The division of responsibility for profits between management and labor. d) The agreement between managers to increase profits at any cost. e) The employment of independent contractors rather than employees. ANSWER: a SECTION: 2
10. In a firm organized along functional lines, a) There is optimal coordination of information and decisions. b) There are usually decreasing returns to scale. c) Information required for decisions becomes more generic, and therefore easier to use. d) Functional managers may lose sight of the bigger picture with respect to decisions and objectives. e) Answers b and d are both correct. ANSWER: d SECTION: 2
11. Centralized decision making is favored over decentralized decision making a) When incentive problems are mild. b) When decisions need to be made on a case-by-case basis. c) When coordinated decisions are essential. d) When decision-relevant information is very dispersed. e) None of the answers above is correct. ANSWER: c SECTION: 2
12. The use of teams is an example of a) Defused responsibility. b) Centralized decision making. c) An incomplete specialization by firms with consequent adverse selection. d) A hybrid sharing of information and decision responsibilities e) One way of strengthening individual incentives. ANSWER: d SECTION: 2
13. If management wants to induce increased effort from its employees, it should a) Have them work in teams. b) Pay them fixed wages. c) Increase the workers’ profit shares. d) Monitor and reward effort (if this is possible and not excessively costly). e) Answers c and d are both correct. ANSWER: e SECTION: 2
14-3
Asymmetric Information and Organizational Design 14. A major problem of using team-based incentives is a) Some of the members may “free ride” on the work of the others. b) It is more difficult to measure team output than individual outputs. c) Team decision making is inevitably marked by interpersonal conflicts. d) Work by its nature is individual rather than done in teams. e) All of the answers are correct. ANSWER: a SECTION: 2
15. A major impediment to shareholder control of large corporations is that a) Top management controls the voting and proxy process. b) Shareholders who challenge management recover their costs only if they are successful. c) Shareholding is diffuse, that is, no one shareholder owns very much of the corporation. d) Most shareholders engage in “rational apathy.” e) All of the above answers are correct. ANSWER: e SECTION: 2
16. The major mechanisms to address the principal-agent issue in the management of large corporations include a) External enforcement of managerial duties. b) Shareholder empowerment. c) Corporate governance reforms. d) The market for corporate control. e) All of the above answers are correct. ANSWER: e SECTION: 2
SHORT ANSWER
17. According to the saleswoman, the used car you are thinking of buying was owned by an elderly lady who only drove it to church and always trades in for a new vehicle every two years. Is this car likely to be a good buy? ANSWER: Assuming the saleswoman is truthful, this car is likely to be of high quality. The elderly woman is unlikely to be unloading a car she knows to be a “lemon.” SECTION: 1
18. The Federal Reserve System has suggested that some very large banks in the US are “too big to fail.” If the Fed adopts such a policy stance, what problem will it probably face as it seeks to cope with troubled banks? ANSWER: The problem is one of moral hazard. Banks that are classified as “too big to fail” have little incentive to be careful in their lending operations, and may take on too much risk as they seek profits. The result may be many bank failures. 14-4
Chapter 14 SECTION: 1
19. Compare and contrast adverse selection and moral hazard. ANSWER: The phenomena are similar in that both stem from asymmetric information and both present potential problems to the principal. Adverse selection occurs when an agent (whose interests are at odds with the principal’s) holds unobservable or hidden information. Moral hazard occurs when an agent (whose interests are at odds with the principal’s) takes unobservable or hidden actions. SECTION: 1
20. Describe how reputation and warranties help alleviate the problem of adverse selection. ANSWER: The offer of a warranty is a credible way of distinguishing a high-quality producer from his lowquality counterpart. Reputation plays a similar role. Instead of a monetary payment, the high-quality producer stakes his reputation (which is important for future sales prospects) on quality products. Highquality producers have an incentive to maintain their high-quality reputations. SECTION: 1
21. In 2000, Amtrak discontinued its customer satisfaction guarantee program (a full price refund if the rail trip was not to the customer’s satisfaction). Instead of 1 passenger in 1,000 claiming the guarantee, the rate was 4 in 1,000 (many claims being due to delays caused by weather or due to congested tracks used by other freight rail companies). Critically assess the pros and cons of Amtrak’s guarantee program. ANSWER: The positive aim was to attract customers by using the guarantee to signal Amtrak’s improved efficiency, quality, and on-time performance. The obvious shortcoming was that the guarantee was much too broad; it covered problems – weather, track congestion – that were beyond Amtrak’s control. Thus, it exposed Amtrak to uncontrollable risks and costs. SECTION: 1
22. Which factors typically lead a firm to produce an item in-house? Which typically lead a firm to outsource production? ANSWER: See Table 14.1 for a complete answer. Factors favoring in-house production are: a firmspecific good or service; outside risks to quality or supply disruptions; and a high degree of coordination required for production. Factors favoring outsourcing are: standardized goods or services; a competitive market to supply the good or service; and a low degree of coordination required in production. SECTION: 2
23. What factors typically lead a firm to centralize decision making? Which lead it to decentralize? ANSWER: See Table 14.2 for a complete answer. Factors that favor centralization: (1) a high degree of coordination required, (2) concentration of decision-relevant information at the center; and (3) significant principal-agent problems. Factors that favor decentralization: (1) a low degree of coordination required, (2) dispersion of decision-relevant information, and (3) compatible interests and objectives between managers and employees. SECTION: 2
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Asymmetric Information and Organizational Design
24. Across its facilities, a financial firm pays its back-office clerical workers in two different ways: 1) a set wage per hours worked (hours are flexible and can vary between 40 hours and 50 hours per week) or 2) compensation according to the quantity (number of “job tasks”) and quality of work completed. Which method would you recommend? Explain briefly. ANSWER: Paying by the hour (according to inputs expended) provides the wrong incentive to expend additional hours (or report extra hours) – whether or not the extra hours benefit the task. Paying for performance (i.e., quantity and quality of jobs) aligns the incentives of worker and principal. Performance pay is preferred, provided that performance is relatively easy and not unduly costly to monitor and measure. SECTION: 2
ESSAY
25. The text cites numerous examples in which there exists a “lemons” market. Think of your own example and describe how the problem of asymmetric information might be overcome. ANSWER: Here is just one of many examples. In the 1990s, the wave of corporate takeovers was marked by numerous disasters. After the fact, it became clear that many acquiring companies paid much more than the acquired company proved to be worth. Particularly, in competitive tender offer contests, the "winning" company was often much too optimistic about the potential value of the target. Post acquisition, they often discovered numerous hidden "warts" (which may help to explain why the company was up for sale in the first place). Would-be acquirers can overcome this lemons problem in a number of ways: (1) by moderating the price they pay, (2) by acquiring better information about the target firm in the first place, and (3) by making the purchase price contingent in part on future performance. SECTION: 1
26. You have decided to purchase a new car and are making arrangements for payment. The salesperson suggests that you consider purchasing an extended warranty. In fact, it seems that the salesperson is even more eager to sell the extended warranty than to sell the new car. What economic issues should you consider before you buy the warranty? Explain. ANSWER: The eagerness of the salesperson implies that the warranty is very profitable for the company. Indeed, the warranty is most profitable to the manufacturer when the vehicle is very reliable (so the warranty won’t be needed). For the buyer, that’s good news. The bad news is that the warranty is probably overpriced. Therefore, not buying the warranty is probably the buyer’s best move. However, if you are very risk averse and cannot accept the risk that the car might, in fact, be a “lemon” or at least be at risk for greater than average repair bills, then you should buy the extended warranty. SECTION: 1
27. A strain of bird flu has broken out in a Southeast Asian country, killing flocks of chickens and sickening scores of rural dwellers. Raising and selling chickens (both live and butchered) to local townspeople is the main livelihood of many rural farmers. a) i) Does the chance of chicken flu in “healthy looking” chickens pose problems for transactions between farmers and local buyers? Explain. ii) What regulatory actions might the government take to improve the performance of the chicken market? b) A New Zealand poultry firm, Kiwi, Inc. traditionally has raised all of its produce in domestic facilities. Five years ago, it decided to outsource, i.e. obtain about 15 percent of its chickens (at reduced cost) from
14-6
Chapter 14 the largest food processor in the Southeast Asian country. What are the pros and cons of this strategy? How should Kiwi deal with the food processor to address the bird flu problem? ANSWER: a) i) Asymmetric information (the farmer knows more about the likelihood that his chickens are infected than buyers) is a likely problem. At first, unknowing buyers will get chickens that quickly die. In time, buyers will be wary and insist on lower prices. Sellers of healthy chickens (who cannot prove this to buyers) are also harmed. Because of these informational problems, the disease is likely to spread (to other chickens and possibly humans) and local chicken markets might dry up all together. Seller moral hazard (not taking hygienic measures to prevent disease in his chickens) may also be a problem. ii) If risks to chickens and humans are extreme, regulators might ban chicken sales altogether and even order the killing of all suspected chickens. Alternatively, regulators might inspect all (or some sample of) chickens brought to market to identify which farmers’ chickens are infected. The least intrusive action (and probably least effective) is to simply disseminate information about the disease risks to farmers and sellers. b) This example shows one “cost” of outsourcing (compared to in-house production): surrender of control over quality. In the extreme, the New Zealand firm might cease buying from the Asian source. Alternatively, the firm could insist on strong quality guarantees (with refunds and penalties) from the Asian company (with one or both sides or even a third party responsible for testing). SECTION: 1 and 2
28. A large health insurance plan pays for 90% of the cost of emergency room and other hospital visits but only 20% of the cost of an individual’s purchases of prescription drugs. How might this affect the individual’s health-care decisions? Why might the result lead to high health-care spending? ANSWER: The insurance plan is heavily weighted toward paying for remedies after the fact rather than preventive treatment in the first place. A low-income family on the plan is likely to skimp on necessary preventive medicines and rely on expensive emergency room visits. But this might be a very expensive and inefficient health-care strategy. Thus, the poorly constructed plan could lead to moral hazard – the patient taking actions (purely for financial reasons) that are not in any one’s best medical interests. SECTION: 1
29. What are the major mechanisms to address the principal-agent problems of large, publicly held corporations? How are they intended to correct the problems? How effective are they? ANSWER: See section 2 under the heading “Limiting the Power of Top Management” where four mechanisms are highlighted: external enforcement of managerial duties, the market for corporate control, shareholder empowerment, and corporate governance reforms. None of them is completely effective, although all of them are at least partially successful in correcting the costs of agency due to asymmetric information. SECTION: 2
30. The German electronics company Siemens has a two-tier system of corporate governance: a management board and a separate supervisory board. For major company decisions, management must build a consensus with the supervisory board. What are the advantages and disadvantages of this corporate structure? ANSWER: Siemens’ supervisory board exerts much greater power and control than a typical American board of directors. The advantage is that the structure helps prevent poor decisions (and even wrong doing) by dictatorial CEOs. The major disadvantage is greater decision making costs. Having to attain a consensus for major actions can impede firm functions (in the extreme can lead to paralysis). Siemens has been slow to revamp its lagging divisions and to expand aggressively into more lucrative international markets. 14-7
Asymmetric Information and Organizational Design SECTION: 2
14-8
File: Ch15; CHAPTER 15: Bargaining and Negotiation
Each question contains a code showing the section of the chapter text from which it was taken. The codes for this chapter are: Code 1 2 3
Section The Economic Sources of Beneficial Agreements Multiple-Issue Negotiations Negotiation Strategy
MULTIPLE CHOICE
1. The term “bilateral monopoly” refers to a) A monopolist that sells in two different markets. b) A duopoly marked by collusion. c) A single seller engaged in negotiations with a single buyer. d) A monopoly that requires only two inputs. e) A monopolist that sells a pair of products. ANSWER: c SECTION: 1
2. The maximum value a buyer sets for a transaction is its a) Aspiration level. b) Reservation price. c) Acceptable price. d) Sale price. e) Market price. ANSWER: b SECTION: 1
3. The size of the zone of agreement measures a) The difference between the seller’s and buyer’s profits. b) The average of the parties’ walk-away prices. c) The total trading profits. d) The difference between the buyer’s and seller’s walk-away values. e) Answers c and d are both correct. ANSWER: e SECTION: 1
4. Given buyer and seller reservation prices of $40,000 and $60,000, respectively, a) The total available profit to the two parties is $20,000. b) A price of $50,000 generates an equitable agreement. c) The size of the zone of agreement is $20,000. 15-1
Bargaining and Negotiation d) A zone of agreement does not exist. e) Answers a, b, and c are all correct. ANSWER: d SECTION: 1
5. The outcome of a negotiated agreement is deemed efficient if a) Neither the buyer nor the seller receives more than 60% of the profits. b) The sum of the buyer's and seller's profit shares is less than 100%. c) The agreement equitably balances both sides’ interests. d) Both parties benefit from the agreement (relative to their walk-away options). e) No other agreement exists which would make one party better off without making the other worse off. ANSWER: e SECTION: 1
6. The price at which an agreement occurs is a matter of a) Arbitration. b) Competition. c) Cooperation. d) Answers b and c are both correct. e) None of the above answers is correct. ANSWER: d SECTION: 1
7. A distributive bargain is one in which a) Bargaining occurs over each party's share of total profits. b) Total profits are distributed equally to the participating parties. c) Arbitration determines the distribution of total profits. d) Wage negotiations occur between management and labor. e) Multiple issues are at stake. ANSWER: a SECTION: 1
8. Total trading gains available in a negotiation are influenced by a) The negotiating skills of the bargainers. b) The parties’ walk-away options. c) Differences in the parties’ probability assessments. d) Differences in the parties' values. e) Answers b, c, and d are all correct. ANSWER: e SECTION: 1
9. An out-of-court settlement is mutually beneficial if the
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Chapter 15 a) Difference between the parties' court costs is greater than the difference between their expected values from litigation. b) Sum of the parties' court costs is smaller than the difference between their expected values from litigation. c) Sum of the parties' court costs is greater than the difference between their expected values from litigation. d) Sum of the parties' court costs is greater than the sum of their expected values from litigation. e) None of the above answers is correct. ANSWER: c SECTION: 1
10. The prospect for a mutually beneficial agreement is created by a) Litigation costs. b) Differences in probability assessments. c) Difference in values. d) Multiple issues. e) All of the above answers are correct. ANSWER: e SECTION: 1
11. If the expected litigation value for each firm is $275,000 and the court costs for the firms are $55,000 and $30,000 respectively, then the size of the zone of agreement is: a) $220,000. b) $85,000. c) $25,000. d) $75,000. e) No zone of agreement exists. ANSWER: b SECTION: 1
12. An agent is risk averse if a) An outcome’s certainty equivalent is greater than its expected value. b) He or she cannot afford to sustain large losses. c) An outcome’s expected value is equal to its certainty. d) An outcome’s certainty equivalent is less than its expected value. e) Either b or d. ANSWER: d SECTION: 1
13. An efficient quantity-price agreement is achieved by a) Finding a tangency between buyer and seller profit contours. b) Supplying the maximum quantity that the buyer can use. c) Finding the buyer’s value-maximizing quantity. d) Minimizing the supplier’s average cost per unit. e) Answers a and d are both correct.
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Bargaining and Negotiation ANSWER: a SECTION: 2
14. When each party makes a single offer to divide profits, the offers are incompatible if a) They add up to less than 100% of the total profit. b) The agreement is inequitable. c) They add up to more than 100% of the total profit. d) One of the negotiators makes a non-negotiable demand. e) They are not equal to one another. ANSWER: c SECTION: 3
15. Contractor A is negotiating to build a warehouse for Firm B to be completed in 75 days. Contractor A’s estimated cost is $200,000. Pushing back the completion date by 15 days would allow it to reduce its cost by $30,000. The value to Firm B of the warehouse is $250,000 if completed in 75 days and $235,000 if completed in 90 days. A mutually beneficial, value-maximizing deal a) Means completion in 90 days at a price greater than $235,000. b) Means completion in 90 days at a price between $170,000 and $235,000. c) Is not possible. There is no zone of agreement. d) Means completion in 75 days at a price between $200,000 and $250,000. e) Answers b and d are both correct. ANSWER: b SECTION: 2
16. If both sides have perfect information about all economic facts of the negotiation, a) The parties are sure to reach an efficient agreement. b) The parties are sure to reach an equitable agreement. c) Any mutually-beneficial profit split can be supported as an equilibrium outcome. d) A 50-50 profit split is the sole equilibrium outcome. e) Answers a and b are both correct. ANSWER: c SECTION: 3
17. Under imperfect information, bargainers a) May miss some efficient agreements due to self-interested strategic behavior. b) Can never reach an efficient agreement. c) Can typically reach efficient agreements. d) Will have an interest in revealing their true values at the outset of negotiations. e) None of the above answers is correct. ANSWER: a SECTION: 3
18. In multiple-issue negotiations where monetary compensation is available, a) There is less opportunity for mutual gain than when a single issue is at stake. 15-4
Chapter 15 b) A new issue should be adopted only if the benefit to one side exceeds the cost to the other. c) A new issue should be adopted only if both sides directly benefit. d) A new issue should be adopted only if it increases the total value of the deal. e) Answers b, and d are both correct. ANSWER: e SECTION: 2
SHORT ANSWER
19. In each case, determine the total possible trading gain (i.e., the sum of the agents' profits). a) The seller and buyer reservation prices are $275,000 and $375,000, respectively. b) The reservation prices are $800,000 and $545,000, respectively. ANSWER: a) The total gain is: 375,000 - 275,000 = $100,000. b) There is no zone of agreement. The seller's reservation price is greater than the buyer's, making an agreement impossible. SECTION: 1
20. “All agreements involve compromise, which means each party has to give up something. Therefore, there is no such thing as a mutually beneficial agreement since everyone loses something.” Comment. ANSWER: The quotation's conclusion is clearly incorrect. Since agreements are voluntary, any outcome achieved by compromise must be better than the alternative of no agreement. In short, any agreement must be mutually beneficial. SECTION: 1
21. Briefly summarize how bargaining can be simultaneously cooperative and competitive. ANSWER: Bargaining is cooperative due to the parties' mutual desire to “create value”, that is, make the total profit “pie” as big as possible. Multiple-issue negotiations under imperfect information and repeated negotiations provide fertile ground for such cooperation. Competition occurs due to the parties' efforts to "claim value"-- to secure a greater profit for oneself at the expense of the other side. SECTION: 1
22. What factors are responsible for buyers and sellers holding different walk-away prices? ANSWER: Differences in reservation prices stem from differences in preferences (monetary values), differences in probability assessments, and differences in attitudes toward risk. SECTION: 1
23. A faulty gasket on a piece of machinery supplied by Firm Z caused a fluid leak that damaged equipment in Factory X. Determine the range of out-of-court settlements when the expected value of litigation for the two firms is $65,000 in favor of Factory A. The court costs for Firm Z are $20,000; the costs for Firm X are $25,000. 15-5
Bargaining and Negotiation
ANSWER: The settlement range is between: $65,000 - $25,000 = $40,000 and $65,000 + 20,000 = $85,000. SECTION: 1
24. How do bargaining strategies differ between multiple-issue negotiations and single-issue negotiations? ANSWER: When multiple issues are at stake, the bargainers must conscientiously search for ways to make trades on the issues for their mutual benefit. Any trade that will increase the total value of the ‘pie’ should be sought. Notwithstanding, there is still a tension between truthfully revealing marginal benefits and marginal costs (to promote efficiency) versus misrepresenting them (for strategic purposes). SECTION: 2
25. Determine the value-maximizing order quantity when the buyer's total value from purchasing Q units of output is B = 30Q - Q‚ and the seller's cost of producing Q units is C = .5Q. ANSWER: To find the value-maximizing output, we maximize total net benefits (B - C) by setting MB = MC. We have MB = 30 - 2Q and MC = Q. Setting these equal implies that Q = 10. SECTION: 2
26. At her current per-day consulting charge, a free-lance marketing consultant finds herself with as many jobs as she can handle. In fact, over the past six months, she has been hired by nine of the ten clients who have made queries about her services. At her current charge, she finds herself indifferent between “taking or leaving” the extra work. Evaluate the consultant's pricing strategy. ANSWER: Though perhaps once appropriate, her pricing strategy now appears to be problematic. If almost all her clients readily accept her terms, then this indicates that her terms are much too low. She should mark up her per diem charge well above her cost (she is currently almost at the point of indifference) even if this means risking the loss of some work. At higher margins, she will still be ahead provided her “hit rate” for getting jobs does not fall too precipitously. SECTION: 3
27. Describe factors that might cause bargainers to fail to reach efficient agreements. ANSWER: Factors that might lead to bargaining failures include: conflicting (i.e., optimistic) value assessments, different concepts of what is equitable, strategic behavior under imperfect information, and misjudging the other side's intentions. SECTION: 3
28. Discuss the differences between one-shot bargaining situations and repeated situations. Will the situations produce different bargaining strategies? Explain why or why not. ANSWER: For a complete answer, refer to the discussion in Section 3 of the text. SECTION: 3
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Chapter 15 ESSAY
29. In recent years, the U.S. government has often negotiated cost-plus contracts (CPC) with defense firms developing new weapons systems. Under a CPC, the government reimburses the contractor for the total costs it incurs. Frequently, the result is cost overruns in development. Why might this occur? How might an alternative contract structure remedy this problem? Could this contract “solution” cause a new problem? ANSWER: As noted, under a CPC, the government reimburses the firm for all costs, while guaranteeing it a fixed profit. A CPC is an efficient means of risk sharing when the government buyer is risk neutral and the contractor is risk averse. However, under a CPC, the firm has little or no incentive to minimize costs (and indeed may attempt to overcharge the government). A fixed-price contract cures the problem of cost overruns by making the firm responsible for all costs. However, a fixed-price contract may be expensive or infeasible in a high-risk environment. (See the discussion in Section 1.) A better solution is to write an incentive contract in which the firm is responsible for a pre-specified fraction of any cost overruns. SECTION: 1
30. What determines whether or not a company will settle out of court when sued for a faulty product? How might the company react differently if other agents might sue it in the future? Explain. ANSWER: In a one-shot litigation episode, the defendant company's chief task is to assess the expected total cost it will incur in court (This cost includes its expected damage payments, legal costs, and perhaps “reputation” costs if it loses). This total cost (or its certainty equivalent if the firm is risk averse) determines the maximum settlement it will be willing to pay out of court. If future suits are expected, the firm might be much more reluctant to settle. Rather, it would seek to establish a reputation for resisting questionable law suits. In other words, it may go to court now specifically to deter future suits. SECTION: 3
31. Frequently, bargaining impasses lead to prolonged and costly strikes. If we assume that the negotiators are rational decision makers, how can this occur? ANSWER: A costly strike could have resulted from a number of factors: differing assessments by the parties as to the relative costs of a strike, misjudgment of the other's intentions, and reputation concerns, among other factors. SECTION: 3
32. a) Determine the range of out-of-court settlements for Firms A and B when the expected value of litigation for both is $300,000 in favor of Firm A. The court costs for A and B are $50,000 and $75,000, respectively. b) What does the range calculated in part a mean? c) How would the range be affected by introducing conflicting assessments? Specifically, suppose each side believes its own winning chance is 70%. d) When would an out-of-court settlement be impossible? ANSWER: a) The range is between $250,000 and $375,000. b) The range shows the set of possible out-of-court settlements that would be mutually beneficial. The length of the range, $125,000, measures the total gains from an agreement.
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Bargaining and Negotiation c) If each side sees its winning chance at 70%, Firm A's minimally acceptable price is (.7)(300,000) 50,000 = $160,000. The maximum amount Firm B is willing to pay is (.3)(300,000) + 75,000 = $165,000. The zone of agreement (and total gains) has shrunk to $5,000. d) A zone of agreement would fail to exist if the probability assessments were slightly more optimistic or if total court costs were slightly lower. SECTION: 1
33. Why might legislators often end up reversing their political position on an issue by voting in favor of a bill when previously they had spoken out against it? ANSWER: As noted in the text, vote swapping (or so-called logrolling) may be mutually beneficial for legislative members seeking to achieve winning voting coalitions on issues of greatest importance to them. SECTION: 2
34. Delays and failure to reach an agreement are often viewed as inefficient, based on irrational behavior, or mistakes. Is this always the case? Explain why or why not. ANSWER: No. The view that failure to reach an agreement is irrational implicitly assumes that information is perfect, and that there is initially a zone of agreement. This is generally not true for actual negotiations – information is limited and sometimes faulty, and there may be a very narrow or even no zone of agreement. In addition, it may be difficult to communicate with other parties to a transaction. Delay may be a method of communicating that a party is actually unable to pay a higher price, or accept a lower price. In this case, credibility is an important issue in a negotiation. It may be a method of establishing reputation. SECTION: 3
35. A would-be acquirer is preparing to make a first-and-final tender offer to acquire target Company T. The acquirer judges that Company T’s reservation value is somewhere between $60 and $90 per share, with all values in between equally likely. Under its own management, the acquirer predicts that the target will be worth $100 per share. Should the firm offer $90 per share to assure that Company T will sell out? Determine the offer that maximizes the acquirer’s expected profit. ANSWER: No. With a $90 offer, the acquirer’s profit is: 100 – 90 = $10 per share. An offer of $80 per share provides the maximum expected profit: (100 – 80)Pr(offer is accepted) = (20)[(80 – 60)/(90 - 60)] = $13.33 per share. SECTION: 3
36. A movie producer is negotiating with an up-and-coming director to direct its next summer action film. The director’s latest movie has been well-received and there is talk that he might be nominated for an academy award. The producer believes the director is currently worth a $500,000 fee but would be worth a $2 million fee if he is nominated for an Oscar. (These are the producer’s reservation prices.) For his part, the director’s current walk-away price is $300,000 but it would rise to $1.5 million with an Oscar nomination. The producer thinks the chance of a nomination is .3; the director thinks it is .6. a) Can the parties agree on a flat dollar fee? If so, what is the zone of agreement? b) Might the parties do better negotiating a contingent fee? Explain. ANSWER: a) The producer’s expected reservation price is: (.3)(2) + (.7)(.5) = $.95 million. In turn, the director’s expected reservation price is: (.6)(1.5) + (.4)(.3) = $1.2 million. There is no zone of agreement. 15-8
Chapter 15 b) A contingent fee arrangement makes obvious sense. For instance, the director’s subsequent fee might be $1.8 million if he is nominated, but only $.4 million if he is not. Whatever the nomination outcome, the fee in each case is mutually beneficial. The contingent fee also acts as a means of risk sharing. SECTION: 1
37. In winter 2000, Time Warner (TW) and Disney were engaged in lengthy negotiations to strike a deal so that TW’s cable television service would continue to carry Disney programming and Disney’s ABC network channels. Without an agreement, TW would lose ABC and Disney shows in 3.5 million homes across seven major markets. Disney was demanding as much as $300 million from TW for the right to carry the channels. It also wanted TW to feature its new channels (including Toon Disney) and for TW to make the Disney channel part of its basic cable package. If its demands were not met, Disney threatened to pull its programming immediately, during the crucial ratings sweeps period when audience levels are measured and future advertising rates are set. Losing ABC and Disney would anger TW’s cable customers who might decide to switch to rival satellite television to get the channels. TW wanted the current agreement extended for six months, by which time the AOL Time Warner merger would be completed (securing the company’s position as a multimedia giant). a) Describe the relevant factors that would influence the “balance of power” in the negotiation between Disney and TW. Is each side’s negotiation strategy utilizing what power it has? Explain briefly. b) Imagine that the negotiations were to end in failure. Provide at least two reasons (in general) why this kind of outcome could occur. c) Disney is worried that in the near future when interactive television is a reality, TW could hinder Disney and others from offering interactive programming over its cable lines while favoring its (TW’s) own programming. Disney is pressing TW to commit to treat others’ channels and programming the same as their own. TW says Disney’s demand is too broad for discussion and that it is impossible to negotiate the terms of businesses that don’t yet exist. What are the pros and cons of considering these issues in the current negotiations? ANSWER: a) The relative power of the parties depends on who has the most to lose from a disagreement. (The side with the most to lose is in the weaker bargaining position.) It’s obvious that both sides have a lot to lose. Most analysts contended that losing ABC would be a bigger financial blow to TW than losing TW would be for Disney. In the short-term, TW’s pulling ABC disaffected its cable customers (and brought cries of “monopoly” from some congressmen who vowed closer scrutiny of the AOL Time Warner merger). Another reason Disney might have less to lose is the alternative of broadcasting its ABC channel via satellite TV. Both sides, but especially Disney, would lose from an immediate impasse during the sweeps period. Finally, TW’s best position is to secure a six to eight month extension until after the merger; then it can negotiate from a position of strength. b) The general reasons for impasse include: 1. There is simply no zone of agreement. Disney deals with satellite TV and/or other cable operators are more lucrative than the best deal with TW. 2. There is a zone of agreement, but intransigence and miscalculations by the parties cause the impasse. (In part, this seems to be the case.) 3. There is a zone of agreement, but the self-interested strategic behavior of the parties causes an impasse. Disney’s $300 million demand may make strategic sense – submitting an aggressive demand that risks being rejected. Strategic behavior may also involve timing rather than price. Disney is pushing for a long-term agreement, while TW wants a “bridge” agreement until its merger is complete. Finally, strategic behavior might be based on each side trying to establish a “tough” reputation when it comes to future negotiations (either with each other or other networks, cable operators, and so on). c) Negotiating a deal on interactive programming. Pros: 1. Introduces a new issue that might be traded off in the current negotiations, thereby spurring an agreement. (Disney could drop its $300 million demand in exchange for TW concessions on this front.) 2. Establishes the ground rules for interactive TV making for an efficient transition in the future. 3. Flexible/contingent deal would be adaptable to uncertain (unforeseeable) outcomes in the future. Cons: 1. Will possibly complicate current negotiations. 2. Inflexible deal will be inefficient (will not respond to uncertain outcomes in the future). SECTION: 3
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File: Ch16; CHAPTER 16: Auctions and Competitive Bidding
Each question contains a code showing the section of the chapter text from which it was taken. The codes for this chapter are: Code 1 2 3
Section The Advantages of Auctions Bidder Strategies Optimal Auctions
MULTIPLE CHOICE 1. A manager recommends selling one of the firm’s divisions to a prospective buyer, rather than soliciting competitive bids from other firms. Does this strategy make sense? a) Yes, it is quicker, less expensive, and is likely to provide a better price than a bidding competition. b) No, soliciting competing bids is always superior than negotiating with a single buyer. c) No, competitive bids will provide a better price, provided there are 3 or more buyers. d) It depends. Multiple bids are likely to provide a better price, but are also costly and time consuming. e) Yes, negotiating a fixed sale price with the buyer in hand minimizes the firm’s risk. ANSWER: d SECTION: 1
2. Assuming a uniform distribution of offers between $100,000 and $175,000, what would be the maximum expected price from 9 potential buyers? a) $125,000 b) $137,500 c) $155,000 d) $167,500 e) $175,000 ANSWER: d SECTION: 3
3. In an English auction with private buyer values, a) There are higher and higher oral bids until the bidding stops. b) A typical buyer shades its bid below his true private value. c) Increasing the number of competitors causes each buyer to raise its bid. d) The final price is approximately equal to the second highest buyer value. e) Answers a and d are both correct. ANSWER: e SECTION: 2
4. Auctions are a viable method of selling an item a) Except when one-on-one negotiations with a buyer are possible.
16-1
Auctions and Competitive Bidding
b) But can be inferior to posted pricing when demand uncertainty is great. c) When a competitive market fails to exist. d) Only if the item at auction is unique. e) Answers b and c are both correct. ANSWER: c SECTION: 1
5. A buyer's reservation price a) Is equal to buyer's initial bid in an English auction. b) Is set at a level allowing the buyer an adequate profit in the auction. c) Is always equal to the buyer's optimal bid in a sealed-bid auction. d) Increases as the number of bidders increases. e) Is the buyer's value for the item, i.e., his walk-away price. ANSWER: e SECTION: 2
6. An auction characterized by descending bids is termed a(n) a) English auction. b) Dutch auction. c) French auction. d) Sealed-bid auction. e) Unsuccessful auction. ANSWER: b SECTION: 2
7. The following auctions are strategically equivalent for bidders holding private values: a) English = Dutch. b) Sealed-Bid = Second-Price. c) English = Second-Price. d) Sealed-Bid = Dutch. e) Answers c and d are both correct. ANSWER: e SECTION: 2
8. In a sealed-bid auction, a firm with a reservation price of $48,000 submits a bid of $40,000. If its probability of winning is .75, then its expected profit from the auction is a) $8,000. b) $2,000. c) $6,000. d) $4,000. e) There is insufficient information to answer. ANSWER: c SECTION: 2
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9. The BCB distribution curve (“Best Competing Bid) is most useful for a) Estimating the competitors’ reservation prices. b) Estimating the probability that the firm’s bid will win. c) Measuring the probability a competitor will follow a particular bid strategy. d) Computing the firm’s expected profit from a particular bid. e) Answers b and d are both correct. ANSWER: e SECTION: 2
10. Firm Z is one of 4 bidders, each with a value independently drawn from the range $20,000 to $60,000 with all values in between equally likely. In sealed bidding, Firm Z’s equilibrium bidding strategy is a) bi = (.25)(40,000) + .75vi. b) bi = (.5)(20,000) + .5vi. c) bi = (.5)(40,000) + .5vi. d) bi = (.25)(20,000) + .75vi. e) None of the above answers is correct. ANSWER: d SECTION: 2
10. The winner's curse occurs when a) The winning bidder could have won the item at a lower sealed bid. b) The winning bid exceeds the true value of a good. c) The winning contract bidder experiences cost overruns. d) The winning bid is drawn from the left tail of the bid distribution. e) The firm's bid discount exceeds its estimation error. ANSWER: b SECTION: 2
11. To avoid the winner’s curse, a buyer should reduce his bid a) As the number of bidders increases. b) If new information has caused him to increase his private estimate. c) If there is greater uncertainty about the item’s value. d) Answers a and b are both correct. e) Answers a and c are both correct. ANSWER: e SECTION: 2
12. The potential size of the winner’s curse increases a) As uncertainty about the value of the item increases. b) As the number of bidders declines. c) As the number of bidders increases.
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Auctions and Competitive Bidding
d) As bidders become more risk averse. e) Answers a and c are both correct. ANSWER: e SECTION: 2
12. When buyers have private values, the optimal strategy in a sealed-bid auction is a) To place a bid equal to the expected value of the next highest value (conditional on winning). b) To bid up to the buyer's reservation price if necessary. c) The same as under an English auction. d) The same as under a Dutch auction. e) Answers a and d are both correct. ANSWER: e SECTION: 2
13. Suppose that risk-neutral buyers with independent private values bid in an English auction. In equilibrium, the seller's expected revenue a) Is the same regardless of the number of bidders. b) Increases as the number of bidders falls. c) Equals the expected revenue in a sealed-bid auction. d) Exceeds the expected revenue in a sealed-bid auction. e) Is equal to the expectation of the highest buyer value. ANSWER: c SECTION: 3
14. There are five risk-neutral bidders, each of whom has a private value independently drawn from the range $60 thousand to $120 thousand with all values in between equally likely. The respective expected revenues from the English and sealed-bid auctions are: a. E(PE) = (2/6)(60) + (4/6)(120) = $100 and E(PS) = (1/6)(60) + (5/6)(120) = $110. b. E(PE) = E(PS) = (2/5)(60) + (3/5)(120) = $96 thousand. c. E(PE) = E(PS) = (2/6)(60) + (4/6)(120) = $100 thousand. d. E(PE) = (2/5)(60) + (3/5)(120) = $96 and E(PS) = (1/5)(60) + (4/5)(120) = $108. e. E(PE) = E(PS) = (1/6)(60) + (5/6)(120) = $110 thousand. ANSWER: c SECTION: 3
15. For the seller, the advantage of an auction vis-a-vis posted pricing is a) That both buyer and seller influence price. b) Greater price flexibility in the face of uncertain demand. c) A competitively determined price. d) That an auction attracts a greater number of buyers. e) None of the above answers is correct. ANSWER: b SECTION: 1
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16. In a competitive procurement, Firm 1 is one of three bidders, each with a cost independently drawn from the range $300,000 to $400,000 with all costs in between considered to be equally likely. In sealed bidding, Firm Z’s equilibrium strategy is: a) b1 = c1. b) b1 = (.5)(300,000) + .5c1. c) b1 = (.5)(400,000) + .5c1. d) b1 = (1/3)(300,000) + .(2/3)c1. e) b1 = (1/3)(400,000) + (2/3)c1. ANSWER: e SECTION: 3
17. If buyer private values are drawn from different distributions: a) Revenue equivalence continues to hold. b) Buyers will employ non-identical bidding strategies. c) There will be no effect on English auction bidding strategies. d) Answers a and c are both correct. e) Answers b and c are both correct. ANSWER: e SECTION: 3
SHORT ANSWER
18. Compare bidder strategies in an English auction versus a sealed-bid auction. ANSWER: In an English auction with private values, each buyer's dominant strategy is to bid up to its reservation price if necessary. In a sealed-bid auction, each buyer shades its bid below its reservation price. Specifically, a risk-neutral buyer submits an equilibrium bid equal to the expected value of the highest of the other buyers' values (conditional on these being below its own value). SECTION: 2
19. a) In a sealed-bid auction, find the firm's expected profit if its reservation price is $7.5 million, its bid is $7 million, and its probability of winning at this bid is 0.4. b) What if instead it bids $7.2 million and has a 0.6 chance of winning? ANSWER: The firm's expected profit is: E() = (7.5 - b)Pr(b wins) a) E() = (7.5 - 7)(.4) = $.2 million or $200,000. b) E() = (7.5 - 7.2)(.6) = $.18 million or $180,000. SECTION: 2
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Auctions and Competitive Bidding
20. In a sealed-bid auction, suppose there are three firms bidding. Each firm's bid lies between $25 million and $35 million, with all values in between equally likely. If the first firm were to bid $30 million, what is the probability its bid is the highest? If it were to bid $33 million? ANSWER: In general, the winning probability is: H(b) = [(b - 25)/10]n-1 a) H(b) = [(30 - 25)/10]2‚ = .25 b) H(b) = [(33 - 25)/10]2‚ = .64 SECTION: 2
21. Discuss the advantages of auctions as a type of transaction compared with posted prices and negotiated transactions. ANSWER: See the discussion in section 1 of the text. SECTION: 1
22. What economic conditions are necessary for auctions to be feasible? Explain. ANSWER: An auction is not feasible if there already exists a well-developed competitive market for the item in question. Thus, for auctions to flourish, such markets must be absent. In other words, the auctioned item must be differentiated or at least in limited supply. SECTION: 1
23. In the private-value model with risk-neutral buyers, compare the expected revenues generated by English and sealed-bid auctions. ANSWER: In equilibrium, revenue equivalence holds. The degree of shading by the highest bidder in a sealed-bid auction results in an expected price exactly equal to the expectation of the second-highest reservation price – exactly the result in an English auction. SECTION: 3
24. Suppose that an item with a common unknown value is being sold via an English auction. Should bidders still be concerned about the possibility of the winner’s curse? Explain. ANSWER: Like the sealed-bid auction, the English auction is susceptible to the winner’s curse. Even if a bidder has an unbiased estimate of the unknown item’s value, he should not be willing to bid this high in an English auction. If he does, he will win the item exactly when he is most overly optimistic about its value. The item will prove to be worth less than he thinks and he will fall prey to the winner’s curse. To avoid the winner’s curse, the highest he should bid in an English auction is below his “raw” estimate. SECTION: 2
25. In what circumstances might the sealed bid auction generate greater revenue on average than the sealed-bid auction? ANSWER: The auctions provide the same expected revenue if the buyers are risk neutral and have private values drawn from a common distribution. The sealed-bid auction provides greater expected
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Chapter 16
revenue if (1) bidders are risk averse, or (2) when one buyer has a value distribution that is greater than the others. SECTION: 3
ESSAY
26. What steps should a decision-maker go through when determining its bidding strategy in an auction? ANSWER: The first step is to determine one's reservation price, i.e. the item's value in an auction or the firm's cost of supply in competitive procurement. In a sealed-bid auction, the next step is to assess the likely number of competitors and the likely distribution of competing bids. Both factors influence the buyer’s optimal sealed bid. In an English auction, the strategy is simpler – bid up to one’s reservation price if necessary. SECTION: 2
27. Compare the strategies bidders employ when participating in the English, Dutch, and sealed-bid auctions. ANSWER: In an English auction with private values, each buyer’s dominant strategy is to bid up to its reservation price if necessary. In a sealed-bid auction, each buyer shades its bid below its reservation price. Specifically, a risk-neutral buyer submits an equilibrium bid equal to the expected value of the highest of the other buyers’ values (conditional on these being below its own value). As pointed out in the text, the equilibrium strategy in the Dutch auction is identical to that of the sealed-bid auction. (That is, the buyer should wait to bid until the price falls in the Dutch auction to the level of his optimal bid in the sealed-bid auction.) SECTION: 2
28. Almost every week, a dealer buys items at antique auctions. The dealer notices a consistent pattern in large antiques auctions. Items auctioned in the first 30 minutes and in the last 30 minutes tend to fetch lower than expected prices. Items in the middle of the auction claim relatively high prices. a) If the dealer’s observation is correct, are antique buyers behaving rationally? c) What strategy do you suggest in response to this pattern? ANSWER: a) Suppose the dealer has carefully checked that the higher prices in the middle of the auction do not simply reflect more valuable items positioned there. Then, the high prices on these items could be due to more numerous bidders or due to more overly-enthusiastic or overly optimistic bidders. The latter behavior could be called irrational. b) The dealer can exploit this pattern by being sure to bid early and late -- expending less bidding effort in the middle if rival bids mean few “winning deals” are available. SECTION: 2
29. Suppose four bidders compete in a sealed-bid auction with private values independently and uniformly distributed between $0 and $200. a) Compute the expected revenue in an English auction. b) Compute the expected revenue in a sealed-bid auction. c) Compare the results in parts a and b.
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Auctions and Competitive Bidding
ANSWER: a) E(Rev) = E(v2nd) = [2/(n + 1)]L + [(n - 1)/(n + 1)]U = (.6)(200) = $120. b) The equilibrium bidding strategy is: bi - [(n - 1)/n)]vi = .75vi. The expected value of the highest reservation price is: E(vmax) = [1/(n + 1)]L + [n/(n + 1)]U = (.8)(200) = $160. Therefore, E(bmax) = .75E(vmax) = (.75)(160) = $120. c) The expected revenues in parts a and b are the same. This confirms revenue equivalence. SECTION: 3
30. The U.S. Beanbag Federation is accepting bids for televising the national championship playoffs. Competition is stiff, and the Federation expects bids to be higher this year than last. Officials of the Federation have estimated that the advertising revenue that a network might receive ranges from $500 million to $700 million (with all values in between equally likely). a) If the three major networks bid, what is the expected value of the winning bid? b) Fox Network has expressed an interest in televising the playoffs. If Fox enters the bidding, what is the new expected value of the winning bid? c) Explain why the addition of a new bidder raises the value of the expected winning bid. d) How does an increase in the number of bidders affect the likelihood of the winning bidder suffering the winner's curse? ANSWER: a) For three bidders: E(V2ND) = [2/(n + 1)]L + [(n – 1)/(n + 1)]U = (2/4)(500) + (2/4)(700) = $700 million. This is the expected price at an English auction and also the expected price at a sealed-bid auction. b) The addition of Fox increases the expected value of the winning bid to: (2/5)(500) + (3/5)(700) = $720 million. c) As new bidders enter, the likelihood that one firm will perceive the benefits differently from the others increases, which increases the spread of the bids and this raises the expected value of the highest bid. d) There is a common, unknown value component to the potential advertising revenue from televising the playoffs. Thus, increasing the number of bidders increases the chance of the winner’s curse (unless all bidders are savvy enough to bid well below their advertising estimates). SECTION: 3
31. Under what conditions should a seller use an auction? Explain. ANSWER: An auction occupies a kind of middle ground between posted prices and negotiated prices. Auctions are viable when competitive markets do not exist. This is likely to be the case when goods are unique or rare. Auctions ensure that competition among buyers sets the final price, which is the highest that the market will bear. It is also a less time-consuming method than one-on-one negotiations, while preserving the seller's monopoly position. Finally, auctions are more flexible than selling at posted prices. If these conditions are met, an auction will tend to increase the expected payoff from the sale. SECTION: 1
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File: Ch17; CHAPTER 17: Linear Programming
Each question contains a code showing the section of the chapter text from which it was taken. The codes for this chapter are: Code 1 2 3
Section Linear Programs Shadow Prices and Sensitivity Analysis Formulation and Computer Solution for Larger LP Problems
MULTIPLE CHOICE
1. Linear programming is useful for solving optimization problems involving a) Both linear and nonlinear constraints. b) Linear constraints. c) Bounded and unbounded feasible regions. d) A small number of optimal solutions. e) Optimization using conventional calculus. ANSWER: b SECTION: 1
2. In a linear programming problem, the objective function a) expresses the objective in terms of the relevant decision variables. b) Is the expression to be maximized or minimized. c) Shows the feasible region and its corners. d) Defines each resource constraint. e) Answers a and b are both correct. ANSWER: e SECTION: 1
3. The feasible region contains values of the decision variable that a) Optimize the value of the objective function. b) Are non-negative and finite in magnitude. c) Satisfy all relevant constraints. d) Satisfy only nonbinding constraints. e) Answers a and c are both correct. ANSWER: c SECTION: 1
4. The optimal solution in a linear programming problem a) Is determined by solving all constraints as equalities.
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Linear Programming
b) Always exists. c) Typically occurs in the interior of the feasible region. d) Occurs at a corner solution. e) Answers a and b are both correct. ANSWER: d SECTION: 1
5. A small machine shop produces steel shafts and metal plates. The production process uses labor, milling machine hours, and lathe machine hours. The firm tries to identify how many metal shafts and plates to produce per week in order to maximize profit. The decision variables in the problem are the a) Profit contributions of shafts and plates. b) Maximum weekly labor hours available. c) Milling and lathe machine hours available per week. d) Quantities of shafts and plates produced per week. e) The total profit earned by the shop. ANSWER: d SECTION: 1
6. In order to identify the feasible region, one must a) Graph all constraints. b) Plot the objective function contours. c) Identify and graph all nonbinding constraints. d) Solve simultaneously a number of binding equations. e) Determine the optimal corners of the region. ANSWER: a SECTION: 1
7. The profit contribution of product Y is $2 per unit and of X is $4 per unit. The firm wishes to maximize total profit under certain constraints. Each contour of the objective function has slope, Y/X = a) -4. b) -2. c) 8. d) -.5. e) There is insufficient information to determine the answer. ANSWER: b SECTION: 1
8. In an LP problem, the inequalities, X + 2Y ≤ 12 and 3X + 4Y 28, hold as binding constraints. The problem’s optimal solution is a) X = 0, Y = 6. b) Y = 0, X = 12. c) X = 4, and Y = 4. d) X = 0, and Y = 7. e) There is insufficient information to determine the answer.
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ANSWER: c SECTION: 1
9. In an LP problem, there are 3 binding constraints. Constraint A has slope –1.5, Constraint B has slope -.5, and slope C has slope -.2. The objective function’s slope is -1.2. The optimal solution is a) At the intersection of Constraints A and B. b) At the intersection of Constraints B and C. c) At the intersection of Constraint A and the horizontal axis. d) At the intersection of Constraint C and the vertical axis. e) Anywhere along Constraint A. ANSWER: a SECTION: 1
10. A shadow price measures a) The impact of a change in one of the constraints on the objective function. b) The market price of the resource in question. c) Implied revenue from the possible sale of goods. d) Profit tradeoffs among goods produced by a multiproduct firm. e) The slope of the objective function. ANSWER: a SECTION: 2
11. The shadow price of a nonbinding constraint is a) Negative in value. b) Zero. c) The positive cost (the reduction in the firm’s objective) of tightening the constraint. d) The positive benefit associated with relaxing the constraint. e) Answers c and d are both correct. ANSWER: b SECTION: 2
12. In a linear programming problem, sensitivity analysis involves a) Changing one or more coefficients in the objective function. b) Changing the amount of an available resource. c) Finding the solution using the Simplex method. d) Assuming the binding constraints have changed. e) Answers a and b are both correct. ANSWER: e SECTION: 2
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Linear Programming
13. In a linear programming problem involving two goods, a change in the profit contribution of one of the goods will a) Always change the optimal solution. b) Typically change the feasible region. c) Never change the optimal solution. d) Change the optimal solution only if the slope of the profit contours changes significantly. e) Not affect any shadow prices because the constraints are not affected. ANSWER: d SECTION: 2
14. The change in the objective function associated with a unit change in a resource measures the a) Total product of the resource. b) Average product of the resource. c) Slope of the isoprofit lines. d) Slope of that resource constraint. e) Shadow price of the resource. ANSWER: e SECTION: 2
15. In a linear programming problem, multiple optimal solutions are possible if a) The objective function is minimized rather than maximized. b) There are more than two nonbinding constraints. c) The objective function is quadratic. d) The slope of the objective function equals the slope of a binding constraint. e) The feasible region is unbounded. ANSWER: d SECTION: 2
16. If a given constraint takes the form X + 2Y 700 and the optimal solution is X = 300 and Y = 200, then the shadow price of this constraint is a) Zero. b) Negative. c) Positive. d) 700. e) Answers c and d are both correct. ANSWER: c SECTION: 2
17. If the shadow price of a given resource is $100 and the cost of expanding the capacity of that resource is $80 per unit, then a) Capacity should not be expanded. b) The shadow price calculation is in error. The shadow price reflects the cost of expanding capacity. c) The constraint is nonbinding. d) Capacity should be expanded.
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Chapter 17
e) None of the answers above is correct. ANSWER: d SECTION: 2
18. A new product should be introduced if its profit contribution a) Exceeds the shadow price of each resource needed to produce it. b) Is less than the opportunity cost of producing it. c) Exceeds the total value of the resources used, valued at their respective shadow prices. d) Is greater than zero. e) Is greater than the profit contributions of the other goods produced by the firm. ANSWER: c SECTION: 2
19. In a linear programming problem, the objective is to maximize: 2S + 3T, subject to the binding constraints S + T 700 and S + 2T 1,000. The optimal solution is S = 400 and T = 300. The shadow price of the second constraint is a) 1.0. b) 2.0 c) .5. d) 2/3. e) None of the above answers is correct. ANSWER: a SECTION: 2
20. A firm is pondering the introduction of a new good with a profit contribution of $70 per unit. Each unit of the good uses 2 units of input A and 3 units of input B. The shadow price of A is $10, and the shadow price of input B is $15. a) The firm should produce the new good. b) Producing the new good implies an opportunity cost of $75. c) The firm should not produce the new good. d) Answers b and c are both correct. e) There is not enough information to determine the answer. ANSWER: a SECTION: 2
21. The optimal solution of an LP problem is x = 1,000 and y = 2,000. A given resource constraint takes the form, 5x + 2y 9,500. The shadow price of this constraint is a) 9,000. b) 7. c) Zero. d) 500. e) There is not enough information to determine the shadow price. ANSWER: c
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Linear Programming
SECTION: 2
22. Most large-scale linear programs are solved using a) The graphical approach. b) Standard computer programs. c) Standard differential calculus techniques. d) A combination of algebraic and geometric techniques. e) Matrix algebra. ANSWER: b SECTION: 3
SHORT ANSWER
20. A manufacturer of leather goods produces two models of briefcases, the Executive and the Student. Each unit of the Executive (E) requires 1 square yard of leather, 2.5 hours of labor, and 1 hour of machine time. The Student (S) requires .75 square yards of leather, 2 hours of labor, and .5 hours of machine time. Each unit of E contributes $8 of profit while S contributes $5. The manufacturer has 500 yards of leather available per week, 400 labor hours, and 180 machine hours. Formulate as a linear programming problem. The basic objective is to maximize profit. ANSWER: Maximize: Profit = 8E + 5S subject to: E + .75S 500 2.5E + 2S 400 E + .5S 180; x, y 0 SECTION: 1
21. Determine the feasible region for the following linear programming problem: Maximize Z = 10x + 8y subject to: 2x + 3y 11 5x + 2y 11; x, y 0 ANSWER: The two constraints (as binding equalities) intersect at x = 1, y = 3. The feasible region is a triangle in the positive quadrant lying above the second constraint and below the first. SECTION: 1
22. A furniture manufacturer produces three types of chairs. Model A requires 1.2 hours of labor and .25 hours of machine time. Model B requires 1 hour of labor and .2 hours of machine time. Model C requires .8 hours of labor and .15 hours of machine time. There are 600 labor hours and 200 machine hours available per period. The manufacturer seeks to maximize profit and has determined that profit contributions of each unit of A, B, and C are $20, $15, and $12 respectively. Formulate as a linear program. ANSWER: Maximize Profit = 20A + 15B + 12C
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Chapter 17
subject to: 1.2A + B + .8C 600 .25A + .2B + .15C 200; A, B, C 0 SECTION: 1
23. An investor wishes to maximize the return on her portfolio and also maintain certain liquidity and risk standards. The alternatives and their corresponding returns are: Alternative Municipal Bonds (M) Certificates of Deposit (S) Treasury Bills (T) AA Bonds (B)
Return 6.2% 5.1% 6.9% 10.5%
The investor wishes to have at least 25% of the portfolio in Treasury Bills, no more than 20% in AA bonds; no more than 15% in Certificates of Deposit, and no more than 10% in municipal bonds. Determine the LP formulation for an investor seeking to maximize the expected return of a $200,000 portfolio. ANSWER: Maximize: Z = .062M + .051S + .069T + .105B subject to: T 50,000, B 40,000; S 30,000, M 20,000; T + B + S + M = 200,000 SECTION: 1
24. A firm is mulling over its optimal mix of print advertising. Magazine ads (M) cost $2,500 each, reach an estimated 20,000 consumers, and generate about $7,500 in revenue. Newspaper ads (N) cost $1,500 each, reach an estimated 15,000 consumers, and generate about $6,000 in revenue. The advertising budget is $75,000 and management wishes to reach at least 600,000 consumers in total. Finally, the firm wants to have at least twice as many magazine ads as newspaper ads. Formulate the firm’s linear programming problem. ANSWER: Maximize: Z = (7,500 - 2,500)M + (6,000 - 1,500)N subject to: 2,500M + 1,500N 75,000 20,000M + 15,000N 600,000 M 2N SECTION: 1
25. Determine the feasible region given the following constraints: 4x + 3y 120 x 20 y 10 x, y 0 ANSWER: The feasible region is a trapezoid in the positive quadrant, below the first constraint, to the left of the second constraint, and above the third constraint. SECTION: 1
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Linear Programming
26. A manufacturer of nutritional products is formulating a new liquid vitamin supplement. A bottle of the new product must contain at least 30 units of vitamin B and 50 units of vitamin C. A unit of vegetable extract contains 1.2 units of vitamin B and .8 units of vitamin C. A unit of fruit extract contains .25 units of vitamin B and 1.8 units of vitamin C. The cost of vegetable extract is $.05 per unit and fruit extract costs $.06 per unit. The firm's goal is to minimize its cost per bottle. Formulate the LP problem. ANSWER: Minimize: Cost = .05V + .06F subject to: 1.2V + .25F 30 .8V + 1.8F 50 SECTION: 1
27. Determine the feasible region and the optimal corner of the following linear programming problem: Minimize: Z = 3x + 5y subject to: 2x + 5y 21 x+y6 x 2 and y 0 ANSWER: The feasible region lies above the first two constraints and to the right of the vertical line x = 2. The slope of the objective function (-3/5) lies between the slopes of the first two constraints (-2/5 and -1), so that the optimal corner satisfies the two constraints: 2x + 5y = 21 and x + y = 6. The solution is x = 3 and y = 3. The minimum value of Z is 24. SECTION: 1
28. A firm is maximizing profit by producing goods X and Y, using resources A and B. The firm is fully utilizing its supply of resource A, while a surplus of resource B is available. Its profit contribution is $5 per unit of X and $4 per unit of Y. The firm is considering expanding its supply of resource A (at a cost of $8 per unit). Increasing A by one unit would allow the firm to produce 3 additional units of X, while producing 1 fewer units of Y. Should the firm expand its supply of A? Explain. ANSWER: The marginal cost of expanding is $8 (per unit of A). The marginal profit from expansion is: (5)(3) + (4)(-1) = $11. Yes, the firm should expand its supply of A. Its profit increases by $3 for each additional unit of A. (Note that there is plenty of resource B to produce the extra output.) SECTION: 2
29. A discount appliance company is planning to advertise extensively before opening a new store. The firm allocates $240,000 for advertising. The objective is to maximize the total number of customers exposed to the firm’s ads. Formulate and solve the appropriate linear programming problem. TYPE OF ADVERTISING
COST PER AD ($1000s)
Radio (R) Television (T) Direct Mail (M) Newspaper (N)
6 16 1 5
CUSTOMERS (1000s) EXPOSED TO EACH AD 20 40 5 10
ANSWER: Maximize: Z = 20R + 40T + 5M + 10N subject to: 6R + 16T + M + 5N 240 R 20, T 15, M 40, and N 10
17-8
MAXIMUM NUMBER OF ADS 20 15 40 10
Chapter 17
Ad spending should be based on the ratio of customers per dollar spent. By this criterion, direct mail has the greatest “bang for the buck” followed by radio, television and newspaper. Because of constraints on the maximum number of ads in each category, the optimal solution is: M = 40, R = 20, and T = 5. Note that the number of television ads is limited because this mix exhausts the total $240,000 budget. SECTION: 3
ESSAY
30. Graph and solve the following linear programming problem: Maximize Z = 100x + 50y subject to: 10x + 10y 50 y 3, x, y 0 ANSWER: The feasible region is a trapezoid in the positive quadrant bounded by the two constraints. The slope of the objective function is –2 and the slopes of the two constraints are -1 and 0, respectively. Therefore the optimal corner is at the intersection of the first constraint and the x axis. Therefore, the solution is x = 5 and y = 0. The maximum value of the objective function is: Z = (100)(5) + (50)(0) = 500. SECTION: 1
31. A furniture manufacturer produces two types of tables. Table A sells for $430 and Table B for $300 per unit. Table A requires 10 hours of labor and $120 of hardwood per table. Table B requires 10 hours of labor and $60 of hardwood per table. The cost of labor is $10 an hour, and 400 labor hours are available per week. In turn, the firm’s available supply is $3,600 of hardwood per week. Formulate, graph and solve the firm’s LP problem. ANSWER: The profit contribution for Table A is: 430 - 100 - 120 = $210 per unit. The contribution for B is: 300 - 100 - 60 = $140 per unit. Therefore, the formulation is: Maximize: Profit = 210A + 140B subject to: 10A + 10B 400 120A + 60B 3,600; A, B 0 The feasible region is the quadrilateral bounded by the two listed constraints. In addition, the slope of the objective function (-1.5) lies between the constraint slopes (-1 and –2, respectively). Thus, both constraints are binding. The solution of 10A + 10B = 400 and 120A + 60B = 3,600 is: A = B = 20. Maximum weekly profit from producing 20 of each table type is: (60)(20) + (40)(20) = $2,000. SECTION: 1
32. The manager of an appliance store wishes to obtain survey responses from a sample of at least 900 households regarding their future purchasing plans. The cost of mail surveys (M) is $1.00 each, while the cost of telephone surveys (T) is $3 per call. Response rates are 60% for telephone calls and 30% for mail questionnaires. To assure sufficient response accuracy, the manager insists on gathering at least three times as many actual telephone responses as mail responses. The manager’s objective is to minimize the cost of the survey while meeting the stipulated goals. Formulate and solve the firm’s linear programming problem. ANSWER: Television responses (.6T) should be at least three times as great as magazine responses (.3M) implying: .6T (3)(.3M), or equivalently, T 1.5M. Therefore, the formulation is: Minimize: C = M + 3T
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Linear Programming
subject to: .3M + .6T 900 T 1.5M; T, M 0 The two constraints establish the feasible region. In addition both constraints are binding. This is because the slope of the objective function (-1/3) lies between the constraint slopes (-.5 and 1.5 respectively). Solving 3M + .6T = 900 and T = 1.5M implies M = 750 mailings and T = 1,125 calls. The minimum total survey cost is: 750 + (3)(1,125) = $4,125. SECTION: 1
33. A producer of two types of fine chocolate bars utilizes four basic ingredients: milk, sugar, cocoa, and almonds. The milk bar (M) requires 8 ounces of milk, 2 ounces of sugar, and 3 ounces of cocoa. The Almond Bar (A) requires 5 ounces of milk, 1 ounce of sugar, 2.5 ounces of cocoa, and 2 ounces of almonds. The profit contribution of each bar is $.50. The daily availability of the ingredients is limited to 5,000 ounces of milk, 1,200 ounces of sugar, 2,000 ounces of cocoa, and 1,000 ounces of almonds. a) Formulate and solve the producer’s LP problem. b) What can one conclude about the shadow prices of milk and sugar? ANSWER: a) Maximize Profit = .5M + .5A subject to: 8M + 5A 5,000 2M + 1.5A 1,200 3M + 2.5A 2,000 2A 1,000; A, B 0 b) A suitable graph shows that the feasible region lies inside all 4 of the (binding) constraints listed above. The slope of the objective function (-1) lies between the slopes of the last two constraints (slopes –2 and 0, respectively). Thus, only the constraints 3M + 2.5A = 2,000 and 2A = 1,000 are binding. The optimal solution is: M = 250 bars and A = 500 bars. The firm’s maximum daily profit is $375. b) There is more than enough daily supplies of milk and sugar to produce the optimal production plan. In other words, neither of the first two constraints is binding. Thus, the milk and sugar shadow prices are both zero. SECTION: 2
34 What are shadow prices and why are they important? Explain. ANSWER: A shadow price measures the change in the objective function from a unit change in the amount of that resource, assuming that all other resources are held constant. Shadow prices measure implicit values for the decision-maker's limited resources. In the short run, resource constraints may be fixed. In the long run, however, decision-makers can usually expand or contract resources, usually at some cost. The shadow price permits decision-makers the chance to compare the cost of changing the constraint and the increase in the objective function from doing so. In addition, shadow prices play a crucial role in evaluating new activities. A new activity can be profitably introduced if, and only if, its direct benefit exceeds its opportunity cost, where opportunity cost is the sum of the resources used, valued at their respective shadow prices. SECTION: 2
35. An investor seeks to create a portfolio from three types of securities: Treasury Bills (T), Corporate Paper (C), and Junk Bonds (J). The table lists the expected rates of returns for the asset types and their average risk (on a 1 to 5 scale, where 5 is most risky). The investor seeks portfolio allocations (T + C + J
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Chapter 17
= 1) that will maximize the expected return on her portfolio, while maintaining an overall risk of no more than 3. Security Return(%) Risk Treasury Bill 2.5 2.0 Corporate Paper 5.0 2.5 Junk Bond 8.0 5.0 a) Formulate the investor’s linear programming problem. b) Explain why the investor’s portfolio should contain only two assets. Determine the investor’s optimal portfolio. If the investor is willing to increase her portfolio risk by 1.0, how much does her return increase? c) Find the optimal portfolio if treasury bills and junk bonds are the only available assets. ANSWER: a) Maximize: R = 2.5T + 5.0C + 8.0J subject to: 2.0T + 2.5C + 5.0J 3.0 T + C + J = 1; T, C, J 0 b) Because there are only two binding constraints, only two assets will be part of the optimal portfolio. The included assets are those with the greatest ratio of return to risk: Corporate paper (5/2.5) and Junk bonds (8.0/5.0). Thus, one solves: 2.5C + 5J = 3 and C + J = 1 to find: C = .8 and J = .2. The maximum expected return is: R = (5)(.8) + (8)(.2) = 5.6%. If portfolio risk is increased from 3 to 4, the new solution is C = .4 and J = .6. The portfolio return increases by 1.2% (from 5.6 to 6.8). c) In determining the optimal proportions T and J, we know that both constraints are binding: 2T + 5J = 3 and T + J = 1, implying T = .667 and J = .333. The maximum return is now 4.33%. SECTION: 3
36. A beverage producer produces cola at two bottling plants and distributes it to 4 major cities in the Southeast. The table shows the bottling plant capacities, the number of cases to be shipped to each city, and the transport costs ($ per case) between plants and cities. The producer’s objective is to meet its delivery requirements while minimizing its total transport costs.
City A (1,000) City B (1,400) City C (2,100) City D (1,800)
Plant X (3,000) .37 .30 .25 .10
Plant Y (3,500) .10 .20 .35 .40
a) Formulate the firm’s linear programming problem. b) The optimal solution is: XC = 1,200, XD = 1,800, YA = 1,000, YB = 1,400, and YC = 900. What is the shadow price associated with Plant Y capacity? Confirm that the shadow price associated with delivering an additional case to City D is $.20. ANSWER: a) Minimize: Cost = .37XA + .30XB + … .35YC + .40YD subject to: XA + XB + XC + XD 3,000 YA + YB + YC + YD 3,500 XA + YA 1,000 XB + YB 1,400 XC + YC 2,100 XD + YD 1,800 All variables are non-negative. b) Total production at Plant Y is 3,300 cases. This is less than the plant’s capacity indicating that this shadow price is zero. Increasing City D’s requirement to 1,801 cases implies increasing XD to 1,801 at an added transport cost of $.10. But with Plant X at full capacity XC must be reduced to 1,199 cases. In turn
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Linear Programming
with XC reduced by 1 case (a $.25 cost saving), YC must be increased by 1 case (at an additional cost of $.35) to meet City C’s requirement. Thus, the total cost increase is .10 - .25 + .35 = $.20. SECTION: 3
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