Economics of managerial decisions 1st edition blair solutions manual by robyn.gordon139

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Chapter 7 Cartels and Oligopoly Chapter Summary and Learning Objectives 7.1 Explain why cartels are potentially profitable but unstable and difficult to sustain. The best-case scenario for an oligopoly, cartels work to achieve the same collective profits as a monopolist would. However, the incentive for each firm to earn higher profits at the expense of the other firms makes cartels inherently unstable. 7.2 Describe how managers can engage in and sustain tacit collusion to boost their prices and economic profit. In this section, we highlight four conditions that are conducive to tacit collusion, then describe four practices used by firms to increase cartel profit. 7.3 Compare the assumptions and equilibrium outcomes of Cournot, Chamberlin, Stackelberg, and Bertrand oligopolies. This section examines four different oligopoly models, clarifying the assumptions for each, examining firm behavior, and finally summarizing the differences in outcomes (price, output, profit, etc.) 7.4 Apply the economic theory of cartels and the different types of oligopolies to help make more profitable managerial decisions. With what has been learned about cartels, we highlight a few practices firms often engage in that may be a sign of the desire to form a cartel. The models also illustrate the importance of two concepts: product differentiation and considering how your competitors will respond to any action you may take.

Chapter Outline Introduction

A. Summary: The last market structure to examine is an oligopoly, marked by a small number of mutually interdependent firms. Barriers to entry exist but are not insurmountable. There are many different models of oligopoly, each appropriate in different circumstances. B. Key Terms i. Oligopoly: A market structure in which a small number of mutually interdependent firms compete.

Chapter 7: Cartels and Oligopoly

C. Teaching Tip: Interdependence means that any action taken by one firm will have consequences for other firms, which will likely react. One good example involves Walmart and Target. On September 21, 2006, Walmart announced it would cut the price for a 30-day supply of 291 generic drugs to $4. This was likely done as a way of convincing customers to move their prescriptions to Walmart instead of their current pharmacy. The next day, Target matched this policy. In 2006, Walmart announced it would offer 90-day prescriptions for $10, an even better deal than $4/month. This time, within hours, Target announced it intended to match the policy.

7.1 Cartels

Learning Objective 7.1: Explain why cartels are potentially profitable but unstable and difficult to sustain. A. Summary: Unlike competitive markets, monopolies can earn long-run profits due to barriers to entry. A cartel works to achieve such profits by choosing not to compete on price, quantity, and other aspects of their product. The potential negative consequences to consumers from cartels are the reason for antitrust laws. A profit-maximizing cartel chooses the level of industry output that would equate industry MR and MC, and each firm charges the equivalent monopoly price. Cartels are unstable for three reasons: bargaining amongst cartel members, self-interest of each member, and entry by new firms. A variety of methods have been used to sustain a successful cartel: price-fixing, trade associations, and using government to solidify entry barriers against potential outside competition. B. Key Terms: i. Cartel: A group of producers who agree not to compete on price, quantity, quality, and promotional activity. C. Teaching Tip: The idea that some firms in a market might work together is not a foreign idea to most students. However, they may associate it with particular industries like oil or pharmaceuticals. Ask students to work in groups to identify a few industries that are reasonably characterized as oligopolies, and make arguments for each as to how the firms in the market might actually be colluding together to keep prices high. Many students have no trouble thinking that oil companies are colluding, but have never considered the possibility that Coca-Cola and Pepsi are not really competing with each other, the result being that these soft drink brands often charge more than twice the price of generic soda brands.

7.2 Tacit Collusion

Learning Objective 7.2: Describe how managers can engage in and sustain tacit collusion to boost their prices and economic profit. A. Summary: There are four conditions that help make a cartel more successful: few firms in the market, high entry barriers, firms have similar costs and product characteristics, and small price elasticity of demand. How do firms in a cartel coordinate their activities? Overt, or tacit, acts of collusion include price visibility, preannouncements, precommitment strategies, and price leadership.

Rush Managerial Economics, 1e

B. Key Terms: i. Tacit collusion: An informal, unstated agreement on price and quantity among the managers of different firms. ii. Precommitment strategy: A strategy in which managers voluntarily take actions that increase the cost of an action they have not yet taken, thereby making that action nonoptimal. iii. Price leadership: A pattern of pricing in which the managers of one oligopoly firm understood to be the price leader consistently change price before their rivals, after which rivals make similar price changes. C. Teaching Tip: When firms in a market all have the same price, the result is either perfect competition or perfect collusion. Whether firms are actually colluding to try to establish or maintain a cartel depends on their behaviors, as well as the prices they charge. Identifying and dismantling cartels is the job of the antitrust authorities, who must analyze behaviors and outcomes (price, output, profit, and other evidence) to determine whether firms are violating antitrust laws.

7.3 Four Types of Oligopolies

Learning Objective 7.3: Compare the assumptions and equilibrium outcomes of Cournot, Chamberlin, Stackelberg, and Bertrand oligopolies. A. Summary: There are many models of competitive oligopoly, based on different assumptions about firm behavior. The first three entail firms choosing how much output to produce, while the last (Bertrand) has firms deciding on price. Key to the quantitysetting models is the idea of a best-response curve, which is similar to the residual demand concept from the dominant firm model. Once the best-response curve is determined, it can be used to find Cournot, Chamberline, and Stackelberg equilibria. Profit in Cournot and Stackelberg models is less than in a successful cartel, which illustrates why firms may try to form a cartel in the first place. In each of these models, if a firm can reduce its costs, it will increase its output and profits at the expense of its competitor. In Bertrand competition, intense price competition exists, despite the fact that there may be as few as two firms in the market. The result is low prices and only a competitive return for firms. If product variety is of importance to consumers, prices will be a bit higher and firms may earn some economic profit. The chapter concludes with Table 7.3, which compares all four oligopoly models, as well as competitive and monopoly models, in terms of characteristics, equilibrium price and output, and economic profit for each firm. B. Key Terms: i. Cournot oligopoly: A market with two firms in which the managers do not collude and believe that once the rival managers have chosen their quantity, they will not change it. ii. Best-response curve: A curve that shows how a firm’s profit-maximizing output depends on its competitor’s output. iii. Cournot equilibrium: The situation in which each set of managers maximizes its firm’s profit, taking as given the other firm’s production and assuming that the other firm’s production will not change. iv. Chamberlin oligopoly: A market with two firms that produce identical products, have identical and constant average total costs and marginal costs, and in which rivals respond to one another’s actions.

Chapter 7: Cartels and Oligopoly

v. Stackelberg Oligopoly: A market in which one firm (the leader) makes its production decision first, knowing that the second firm (the follower) will make its production decision taking the leader’s production as given. vi. Bertrand oligopoly: A market with two firms, each producing an identical product, and in which the managers do not collude and believe that once the rival managers have chosen their price, they will not change it. C. Teaching Tip: The idea that firms would first decide how much output to produce may seem foreign to students, who are used to simply seeing the prices firms charge. Explain that many oligopoly industries are in raw minerals and commodities (oil, for example). The ADM cartel which served as the backdrop for The Informant movie was about lysine, an amino acid used largely in animal feed. Many of the products they buy might not be modeled well by Cournot or Bertrand, but the components that go into their food, or into their cell phone, likely are. D. Teaching Tip: As farmers markets have been experiencing a bit of a revival, a quantitysetting model may seem more realistic. Suppose two bakers each sell loaves of bread at the farmers market on Saturdays. The more they bring, the lower the price must be if they are to sell all of their bread. In a situation like this, a quantity-setting model may be an appropriate way of thinking about each baker’s decision.

7.4 Cartels and Oligopoly

Learning Objective 7.4: Apply the economic theory of cartels and the different types of oligopolies to help make more profitable managerial decisions. A. Summary: There are three main actions firms can take to signal they may be willing to establish a cartel, which are important to understand as either a manager or a consumer of a good. One should also note that these actions may be deemed antitrust violations, with violators subject to both private lawsuits seeking damages as well as federal penalties and even jail time. As a manager, the competitive models illustrate the importance of product differentiation, especially if you manage a firm in a price-setting industry. Overall, the most important takeaway from the chapter is the importance of understanding how firms in an oligopoly are interdependent, so a wise manager must consider how competitors might respond to a change in price, output, or quality.

Extra Example: Suppose you live in a sizeable, but somewhat remote city. Residents can buy most goods they need either inside city limits or have them shipped in from an online retailer. But services, like haircuts, oil changes, and spa treatments, must be purchased in the city, as they are not expensive enough to justify a long drive or flight to another city. A. Choose a service, either from the three provided or another one whose price is roughly $20–$60. Suppose there are only three such providers in your city and you manage one of them. Which of the oligopoly models discussed in the chapter most closely resembles the kind of competitive environment you face? B. Suppose one of your competitors announces that, due to increases in wages, rent, and other input prices, it is going to increase the price it charges by 10% at the start of the next month. Could this potentially be a sign of collusion? If you do not have the same input price increases, what would you do? Might you be violating antitrust laws?

Rush Managerial Economics, 1e

C. DISCUSSION QUESTION: Alone or in groups, brainstorm and come up with a half dozen or so different industries that could reasonable be categorized as oligopolies. For each, determine which model best approximates the behavior of firms (cartel or one of the four oligopoly models).

Solution to Extra Example: A. One could argue that a quantity-setting model could be applied here. Most service providers are open during “regular” business hours, so “setting output” would be done by choosing how much labor to hire. A salon may choose how many hair stylists to employ, for example. However, these firms are likely best described by the price-setting model of Bertrand competition. For oil changes, consumers may see the product as homogenous, while hair salons and spa treatments are likely seen as a differentiated product. B. This might be a sign of an intent to collude – unless it is verifiably due to an increase in costs. If you also have the same costs, you would want to do the same and raise your price. You may be tempted to leave your price the same and have your competitor’s clients come to you instead, but if your costs are higher, you will probably suffer a loss as a result. If, however, you do not have an increase in costs, you might raise your price a bit but still undercut your competitor and take some of its customers. Given that these industries do not exhibit entry barriers and anyone could open up a new hair salon if prices in the market were artificially high, it is unlikely that this action would be a violation of antitrust laws. C. Answers will vary.

Answer Key Here are the solutions to the Questions and Problems that appear at the end of the chapter.

7.1

CARTELS

1.1

In a competitive market, the intersection of the supply and demand curves determines the equilibrium price and quantity by. From the figure, we can see the equilibrium occurs at 300 million CPU chips with a price of $80. If the firms form a cartel, they maximize the cartel’s profits by producing the output where MR = MC. Once again from the figure, this quantity is 200 million CPU chips. The cartel sets the highest price that enables them to sell this amount, which from the demand curve is $120.

1.2

a. Each firm maximize its profits by producing the quantity that sets MR = MC. When the market is competitive, each firm faces a horizontal demand curve at the equilibrium price, so P = MR. Combining these two conditions, shows that the price of the product is given by P = MC = $40. Substitute this price into the demand equation and solve for the quantity: 800 – 2Q = 40 2Q = 760 Q = 380 Each firm makes zero economic profit because P = ATC = $40, so the combined economic profit of all the firms is also zero.

Chapter 7: Cartels and Oligopoly

b. When the firms form a price-fixing cartel that maximizes the cartel’s profit, they produce the quantity that sets MR = MC: 800 – 4Q = 40 4Q = 760 Q = 190 Substitute this quantity into the demand equation and solve for the price: P = 800 – (2 × 190) = $420. The cartel’s total economic profit equals (P – ATC) × Q, or: Economic Profit = (P – ATC) × Q = ($420 – $40) × 190 = $72,200. c. The firm makes $420 of additional revenue from selling one additional unit. The cost of producing this additional unit is $40. The cheate makes an additional $380 in economic profit. 1.3

a. A cheating firm lowers its price from the agreed upon level and produces more output than the agreed upon amount. b. Yes, cheating is profitable in the short run. The cheating firm will continue to profit from cheating until the other firms in the cartel take notice and the cartel agreement collapses.

1.4

The trade association might be helping to sustain the cartel by reporting their members’ prices. Reporting prices would facilitate collusion by reassuring all cartel members that no one is cheating on their agreement.

1.5

Cartel profits come at a cost to society. Higher prices transfer surplus from consumers to cartel members and create a deadweight loss. Accordingly, consumers and society are both worse off, which leads nations to make cartels illegal.

7.2

TACIT COLLUSION

2.1

Tacit collusion refers to non-competitive solutions that are reached without overt agreements. In a cartel, the firms explicitly agree on the price to charge and the amount of output to produce. In a tacit collusion, the firms agree upon price and amount of output to produce but they do so without an explicit agreement. Unlike an explicit cartel agreement, tacit collusion is not illegal, which can enable mangers to earn the cartel economic profit without the risk of antitrust action against their firms.

2.2

By preannouncing their prices, these firms are able to signal other managers about any price changes in advance. This action promotes collusion by reducing uncertainty among managers about the tacitly agreed-on price. Making prices public also helps to detect cheating on any tacit (or, illegal explicit) agreement about what price to charge.

2.3

a. Each firm’s economic profit is equals (P − ATC) × Q = ($150 − $130) × 200 = $4,000. b. Yes, the new contract is profitable for the firm. The marginal cost of cleaning the new office is $130 while the price is $140, so the firm profits from the new contract. If the other firms discover this lower price, the tacit agreement could break down. The other firms could respond by lowering their prices and increasing their output. Copyright © 2019 Pearson Education, Inc. 97

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c. Due to the most-favored customer clauses with existing companies, the janitorial firm would have to offer the reduced price of $140 per week price to all its existing customers. With this change, the firm’s new economic profit would be: Economic Profit = (P − ATC) × Q = ($140 − $130) × 201 = $2,010 This amount of economic profit is less than the economic profit from cleaning the original 200 offices at the old price of $150 per week. This fact makes It unlikely for the firm to take on the new client. If, nonetheless, the company agrees to this contract, the other firms could respond by lowering their price to $140. The tacit agreement could break down. 2.4

7.3

3.1

A firm is more likely to be the price leader if it can use either its size or cost advantage to credibly threaten a price war. Saudi Arabia is both one of the largest and the lowest-cost producer in OPEC, so they are very likely to be the price leader.

FOUR TYPES OF OLIGOPOLY

a. If there is only 1 airline in the market, it will choose the quantity of seats that sets MR = MC. The figure shows that this quantity is 300,000 seats per year. The firm sets the highest price that enables it to sell this quantity of seats, which the demand curve shows to be $150. The firm’s economic profit is (P − ATC) × Q = ($150 − $50) × 300,000 = $30,000,000. b. The following figure shows the two best response curves. The equations for these best response curves are: 

Global Air best response: QGA = 300 – QWA/2;



World Air best response: QWA = 300 – QGA/2;

Chapter 7: Cartels and Oligopoly

c. In the Cournot equilibrium, the intersection of the best response curves give both firms’ choice of quantity. These curves intersect at QGA = QWA = 200,000 seats, so each firm sells 200,000 seats per year. To determine the price, we first need to calculate the total industry output: QGA + QWA = 400,000. The demand curve from the figure in the questions shows that when 400,000 seats are produced, the price will be $116.67 per seat. Use this price to determine each firm’s economic profit: Economic Profit = (P − ATC) × Q, Economic Profit = ($116.67 − $50.00) × 200,000, Economic Profit = $13,334,000. Both firms are identical, produce the same quantity, and face the same price, so both firms earn the same economic profit. d. In the Chamberlin equilibrium, both firms produce half of the monopoly output. In part (a) we found this quantity was 300,000 seats per year, so each firm produces 150,000 seats per year. Both firms charge $150, the monopoly price. Each firm’s economic profit is (P − ATC) × Q = ($150 − $50) × 150,000 = $15,000,000, half of the monopoly profit. e. In the Bertrand model, the rival firms undercut each other on price until they make zero economic profit. Consequently both firms will set a price of P = ATC = $50. The total market demand at this price is 600,000. Because both firms sell an identical product so they will split the market demand evenly. Each firm sells 300,000 seats per year and each earns zero profit (because P = ATC). f. Yes, both firms have an incentive to form a cartel. Notice that profits for both firms is highest in the Chamberlin equilibrium in part (d). This equilibrium is equivalent to a price-fixing cartel. Therefore, collusion maximizes profits for both firms. 3.2

a. As a monopoly, Gamer Great will produce the quantity at which MR = MC. The figure in the problem shows that this quantity is 6 million game consoles per year. The demand curve shows that the highest price which enables this quantity to be sold is $500. Consequently, Gamer Great’s economic profit is (P − ATC) × Q = ($500 − $300) × 6,000,000 = $1,200,000,000. b. You can construct the best-response similarly to the procedure used in the chapter. Start by supposing that Gamer Great is the only firm in the market so that Player produces 0. Determine Gamer Great’s production. (As you saw above, it is 6 million consoles.) Next suppose that Player enters and produces 100 million consoles. Determine Gamer Great’s new demand and marginal revenue curves and its profit-maximizing production. You now have two points on Gamer Great’s best response curve: The best response when Player produces 0 and when Player produces 100 million. Gamer Great’s best-response curve will be linear, so use these two points to determine the best-response curve for Gamer Great. Follow a similar procedure for Player. The figure shows the two best-response curves. The equations for these best response curves are  Gamer Great best response: QGG = 6 – (QP/2);  Player best response: QP = 6 – (QGG/2);

Rush Managerial Economics, 1e

c. When Player enters the market, Gamer Great is producing the monopoly output of 6 million consoles per year. From Player’s best-response curve, we can see their best response is to produce 3 million consoles per year. d. Now Player is producing 3 million consoles per year. Gamer Great will react by lowering its output to 4.5 million consoles per year, found using Gamer Great’s best response curve. e. In the Cournot equilibrium, the intersection of the best-response curves give both firms’ choice of quantity. These curves intersect where QGG = QP = 4 million. The total economic profit is less than when the market was a monopoly because the total quantity produced (8 million) exceeds the quantity a monopoly produces (6 million). More precisely, the total industry output is QGG + QP = 8 million per year. Using the demand curve from the problem to solve for price as a function of the quantity shows that P = 700 – 0.000033Q. Consequently the price of 8 million consoles per year is $436 per console. With this price, each firm’s economic profit is Economic Profit = (P − ATC) × Q = ($436 − $300) × 4,000,000 = $544,000,000. Both firms are identical, produce the same quantity, and face the same price, so both firms earn the same economic profit. 3.3

As other firms enter the market, the total industry output increases and the market price decreases. In the long run, entry by new firms will drive the market price down to marginal cost and the economic profit will approach zero.

Chapter 7: Cartels and Oligopoly

3.4

a. If your products are identical to your rival’s, you will sell zero units if you raise the price above the equilibrium price. All the demand for the product will shift to your rival. Your economic profit is zero or, if you have fixed costs, you will incur an economic loss equal to your fixed costs. b. The quantity demanded of your product will fall but not to zero because the products are not perfect substitutes.

3.5

No, B’s best response to Firm A will be to produce fewer than 300 planes. We can see this result by using Firm B’s best-response curve given in Figure 7.4 in the chapter. (More precisely, the best-response curve shows that Firm B cuts its production to 225 planes.) If Firm A can then change its production, it will raise it. This response is apparent from A’s best response curves given in Figure 7.5 in the chapter. (Once again, using the best-response curve shows that Firm A boosts its production to 187.5 planes). If Firm B is unable to commit to its initial quantity, it ends up producing fewer planes and making a smaller economic profit.

3.6

a. The firm will produce the quantity that sets MR = MC: 100 − 0.2Q = 40,0.2Q=-60 Q = 300. Find the profit-maximizing price by substituting the quantity produced into the market demand equation: P = 100 − 0.1Q = 100 − (0.1 × 300) = $70 The economic profit equals (P – ATC) x Q, or ($70 - $40) x 300 = $9000. b. First, construct the best-response curves for the two firms (call them Firm 1 and Firm 2). You can calculate these curves similarly to the method used in the chapter: First, suppose that Firm 1 is the only firm in the market so that Firm 2 produces 0. Determine Firm 1’s production. (As you saw above, it is 300.) Next suppose that Firm 2 enters and produces 100 dinners. Determine Firm 1’s new demand and marginal revenue curves and its profit-maximizing production. You now have two points on Firm 1’s best response curve: The best response when Firm 2 produces 0 and when Firm 2 produces 100. Firm 1’s best-response curve will be linear, so use these two points to determine the best-response curve for Firm 1. Follow a similar procedure for Firm 2. The equations for these curves are: Q1 = 300 – Q2/2, Q2 = 300 – Q1/2. These curves intersect at Q1 = Q2 = 200. Consequently the total industry output is equal to Q1 + Q2 = 400. Substitute this quantity into the market demand function to get the equilibrium price: P = 100 − 0.1Q = 100 − (0.1 × 400) = $60

Rush Managerial Economics, 1e

Next find each firm’s economic profit: Economic Profit = (P − ATC) × Q, = ($60 − $40) × 200, = $4,000. Both firms are identical, produce the same quantity, and face the same price, so both firms earn the same economic profit. c. In the Bertrand model, the rival firms undercut each other on price until they earn zero economic profit. Both firms will set their price so that P = ATC = $40. The total market demand at this price is: P = 100 − 0.1Q, 40 = 100 − 0.1Q, 60 = 0.1Q, Q = 600. Both firms sell an identical product so they will split the market demand evenly. Each firm sells 300 steak dinners and makes zero economic profit because P = ATC.

7.4 4.1 4.2

4.3

MANAGERIAL APPLICATION: CARTELS AND OLIGOPOLIES If you choose to engage in tacit collusion with Coca-Cola, you can match the new price that has been pre-announced. You could also choose to remain at your current price or lower your price to undercut Coca-Cola and capture more sales. By matching your price, the new company may be signaling its willingness to tacitly collude with you as the price leader. The company is producing half of the monopoly profit-maximizing quantity. You could signal your tacit agreement to cooperate by cutting your output to 30,000. In this way, you and the new company will share the monopoly economic profit, which is larger than any other profit available. Amazon’s managers could offer an exclusive partnership with one of the publishing houses for a lower price. Apple’s contract contained a most-favored customer clause, so the publisher would then have to set the lower price in Apple’s bookstore as well. However, given Amazon’s volume of book sales, an exclusive agreement could well provide sufficient incentive to cheat on the cartel.

CHAPTER 7 APPENDIX

A7.1

Suppose that you are the manager of Matt’s Prime Steakhouse, one of only two premium steakhouses in Gainesville, Georgia. The nightly demand for steak dinners in town is given by: Qd = 80 – 2P, where Qd is the market quantity of steak dinners demanded, and P is the price of a steak dinner. Matt’s Prime Steakhouse produces qM dinners, and Matt’s only competitor in the premium steak market, Emberwood Grill, produces qE dinners. Each firm’s total cost of producing and selling q dinners is: TC(q) = 400 + 10q.

Chapter 7: Cartels and Oligopoly

a. What is Matt’s best-response function to the quantity produced by Emberwood? To begin, construct the inverse demand function by rearranging the demand function to show price as a function of the quantity demanded: P = 40 – 0.5Q. Next, Matt’s profit function is: Profit = (40 – 0.5qM – 0.5qE) × qM – (400 + 10qM), in which (40 – 0.5qM – 0.5qE) × qM is the total revenue and (400 + 10qM) the total cost. Take the derivative of Matt’s profit function with respect to its own quantity: dPro it dqM

= 30 − qM − 0.5qE.

Matt’s Prime Steakhouse produces the profit-maximizing quantity of steaks dPro it = 0, or: when it produces the quantity qM that sets dqM

30 − qM − 0.5qE = 0. Rearrange this equation to give Matt’s best-response function: qM = 30 − 0.5qE. b. How many steaks does each firm produce? Begin by determining Emberwood’s best-response function. Using the approach outlined in part (a), Emberwood’s best-response function is: 30 − qE − 0.5qM = 0, or: qE = 30 − 0.5qM. To solve for each firm’s quantity in equilibrium, determine the combination of qM and qE that satisfies both best response functions. To do so, substitute Emberwood’s best-response function, qE = (30 − 0.5qM), for qE in Matt’s bestresponse function, qM = 30 − 0.5qE, which gives: qM = 30 − [0.5 × (30 − 0.5qM)]  qM = 15 + 0.25qM  qM = 20 dinners. Then use qM = 20 in Emberwood’s best-response function to obtain Emberwood’s production, qE = 20 dinners. c. What is the price of a dinner when each restaurant sells its equilibrium quantity of steaks? The total market quantity is Q = qM + qE=40 dinners. From the inverse demand function, P = 40 – 0.5Q, so that P = 40 – (0.5 × 40) = $20. A7.2

The market for management consulting services is a Stackelberg duopoly. Alvarez Inc acts as the Stackelberg leader, and The Beaulieu Group as the Stackelberg follower. An independent research group has estimated that the daily demand for consulting services is: Q = 25 – 0.25P, where Q is the quantity of consulting hours and P is the hourly price of consulting services. The total quantity Q of consulting hours is equal to: Q = qA +qB,

Rush Managerial Economics, 1e

where qA is the quantity of consulting hours sold by Alvarez Inc. and qB is the quantity of consulting hours sold by The Beaulieu Group. The demand function can be solved for the price as a function of the quantity, which is the daily inverse demand: P = 100 – 4(qA + qB). Each firm’s cost of supplying an hour of consulting services is $36. a. How many hours of consulting services does each consulting firm provide? We begin by determining the best-response function for The Beaulieu Group. We do this by constructing the firm’s profit, then maximizing the profit by taking the derivative of it with respect to The Beaulieu Group’s quantity and setting it equal to zero, and finally solving for qB. The first step is the profit function: Profit(qB) = [(100 – 4qA – 4qB) × qB] – 36qB where (100 – 4qA – 4qB) × qB is the total revenue and (36qB) is the total cost. Next, taking the derivative with respect to qB, we obtain 64 – 4qA – 8qB = 0. Thus, The Beaulieu Group’s best-response function is given by: qB = 8 – 0.5qA. Next, determine Alvarez Inc.’s profit function: Profit(qA) = (100 – 4qA – 4qB) × qA − 36qA Because Alvarez Inc. is a Stackelberg leader, Alvarez’s managers take account of The Beaulieu Group’s best-response function. So use The Beaulieu Group’s bestresponse function in Alvarez Inc.’s profit function: (100 – 4qA − 4 × [8 − 0.5qA]) × qA − 36qA = 32qA – 2q2A Now, to maximize Alvarez’s profit, take the derivative with respect to qA, and set it equal to zero: 32 – 4qA = 0  qA = 8. Thus, Alvarez Inc. will produce 8 hours of consulting services daily. Using this result in The Beaulieu Group’s best-response function shows that The Beaulieu Group’s will produce 4 hours of consulting services daily. b. How much economic profit does each consulting firm make? The total quantity of consulting services is qA + qB = 4 + 8 = 12. Then, using this quantity in the inverse demand function, P = 100 – [4 × (qA + qB)], gives the price of an hour of consulting services as: P = 100 – (4 × 12) = $52. Alvarez Inc. makes an economic profit of Profit = ($52 − $36) × 8 = 16 × 8 = $128 daily and The Beaulieu Group makes an economic profit of Profit = ($52 – $36) × 4 = 16 × 4 = $64 daily.

Chapter 7: Cartels and Oligopoly

A7.3

You are the manager of Billy’s Burritos, one of only two suppliers of tasty fish tacos in town. Billy’s Burritos and its competitor, Ellen’s Enchiladas, compete in a Cournot duopoly. The weekly demand for fish tacos is: Q = 187.5 – 12.5P, where Q is the quantity of fish tacos and P is the price of a fish taco. The total quantity Q of fish tacos is equal to: Q = qB +qE, where qB is the quantity of fish tacos produced by Billy’s Burritos and qE is the quantity of fish tacos produced by Ellen’s Enchiladas. The demand function can be solved for the price as a function of the quantity, which is the inverse demand: P = 15 – (0.08Q). Each firm incurs a total cost of producing and selling qi fish tacos of: TC(qi) = 120 + 3qi. a. Determine the Cournot quantity of fish tacos that each firm produces each week. To begin, the total quantity produced is Q = qB + qE. Use this result in the inverse market demand function to yield P = 15 – 0.08 × (qB + qE) = 15 − 0.08qB − 0.08qE. Finally, use this expression for P to construct Billy’s Burritos’ profit function: Profit = (15 − 0.08qB − 0.08qE) × qB – (120 + 3qB), in which (15 − 0.08qB − 0.08qE) × qB is the total revenue and (120 + 3qB) is the total cost. Next take the derivative of Billy’s Burritos’ profit function with respect to its own quantity, qB: dPro it dqB

= (15 − 0.08qB − 0.08qE) − 0.08qB – 3

= 12 – 0.16qB – 0.08qE Set this derivative equal to zero to give Billy’s Burritos’ first order condition for profit maximization: 12 – 0.16qB – 0.08qE = 0. Because Billy’s Burritos and Ellen’s Enchiladas have the same costs and share the same demand, each company will produce the same quantity. That means that qB = qE. Substitute qB for qE in the first order condition and then solve for qB: 12 – 0.16qB – 0.08qB = 0  12 – 0.24qB = 0  qB = 50 tacos Because the quantity of tacos produced by Billy’s Burritos is the same as that produced by Ellen’s Enchiladas qB = 50 tacos means that qE = 50 tacos. b. When each firm produces its Cournot quantity, what is the resulting market price of a fish taco? Each firm produces 50 fish tacos, so the total market quantity is 100 fish tacos. Use this quantity in the inverse market demand function, P = 15 – 0.08Q, to determine that the price of a taco is: P = 15 – (0.08 × 100) = $7 per taco.

Rush Managerial Economics, 1e

A7.4

You are the top student in your economics class, and you decide that you will make some extra money by tutoring college freshmen in the Introduction to Economics course. Your only competitor is your classmate, Bernardo. You and Bernardo engage in Cournot competition, and you both know that the monthly demand for economics tutoring services is: Q = 160 – 2P where Q is the total monthly number of hours of economics tutoring services demanded, and P is the hourly price of economics tutoring services. Solving for P from the market demand gives the inverse market demand: P = 80 – 0.5Q, You supply qA hours of economics tutoring services, and Bernardo supplies qB hours of economics tutoring services. Each of you incurs a total cost of supplying qi hours of economics tutoring services equal to: TC(qi) = 240 + 0.25q2i . a. Determine the number of economics tutoring hours that each tutor supplies. To begin, the total quantity of tutoring services is Q = qA + qB. Use this result in the inverse market demand function to yield P = 80 – [0.5 × (qA + qB) = (80 − 0.5qA − 0.5qB) Next use this expression for P to construct the profit function: Profit = [(80 − 0.5qA − 0.5qB) × qA] – (240 + 0.25q2A ) where (80 − 0.5qA − 0.5qB) × qA is the total revenue and (240 + 0.25q2A ) is the total cost. Take the derivative of the profit function with respect to the quantity, qA: dPro it dqA

= (80 − 0.5qA − 0.5qB) − 0.5qA – 0.5qA,

= 80 – 1.5qA – 0.5qB. Set this derivative equal to zero to give the first order condition for profit maximization: 80 – 1.5qA – 0.5qB = 0. Because you and Bernardo have the same costs and share the same demand, each of you will have the same quantity of tutoring services. That means that qA = qB. Substitute qA for qB in the first order condition and then solve for qA: 80 – 1.5qA – 0.5qA = 0  80 – 2.0qA = 0  qA = 40 hours Because you and Bernardo both offer the same quantity of tutoring services, qA = 40 hours means that Bernardo also offers 40 hours of tutoring services, qB = 40 hours. b. When Bernardo and you supply your equilibrium quantities, what is the resulting market price of an hour of economics tutoring services? Because each of you provides 40 hours of tutoring services, the total market quantity is 80 hours. Use this quantity in the inverse market demand function, P = 80 – 0.5Q, to determine that the price of an hour of tutoring service: P = 80 – (0.5 × 80) = $40 per hour.

Chapter 7: Cartels and Oligopoly

A7.5

The market for knitted scarves at a local, weekend farmer’s market is a Stackelberg duopoly. Sammy’s Scarves acts as the Stackelberg leader and Knitting Nancy as the Stackelberg follower. Both Sammy and Nancy know that the market demand for knitted scarves at the farmer’s market is: Q = 160 – 4P, where Q is the quantity of knitted scarves demanded and P is the price of a knitted scarf. Solving the market demand for P as a function of Q gives the inverse market demand: P = 40 – 0.25Q, Sammy produces qS knitted scarves and Nancy produces qN knitted scarves. Each incurs a total cost of producing qi knitted scarves of: TC(qi) = 20 + 10qi. a. How many scarves does each supplier sell at the local, weekend farmer’s market? Start by determining Nancy’s best response function. To do so, construct Nancy’s profit function and then take the derivative with respect to her quantity. The first step in calculating Nancy’s profit function is note that Q = qS + qN. Use this result in the inverse demand function to give: P = 40 – 0.25qS – 0.25qN Consequently, using the total cost function in the question, Nancy’s profit function is: Profit = (40 − 0.25qS − 0.25qN) × qN− (20 + 10qN), in which (40 − 0.25qS − 0.25qN) × qN is the total revenue and (20 + 10qN) is the total cost. Next, taking the derivative with respect to qN gives: dPro it dqN

= (40 − 0.25qS − 0.25qN) − 0.25qN – 10,

= 30 – 0.25qS – 0.5qN. Setting this equal to zero and solving for qN gives Nancy’s best-response function: qN = 60 – 0.5qS. Because Sammy is the Stackelberg leader, Sammy’s profit function will take account of Nancy’s best response function. Therefore, (1) start with Sammy’s profit function, (2) substitute Nancy’s best response function for qN, and then (3) simplify: Profit = (40 − 0.25qS − 0.25qN) × qS− 20 – 10qS = (40 − 0.25qS − 0.25 × [60 – 0.5qS]) × qS− 20 – 10qS = (25 − 0.125qS) × qS− 20 – 10qS = (25qS − 0.125q2S ) − 20 – 10qS = − 0.125q2S + 15qS – 20. Finally, to maximize profit take the derivative of Sammy’s profit-function with respect to qS and set it equal to zero to get the first order condition: − 0.25qS + 15 = 0

Rush Managerial Economics, 1e

Solving for qS shows that Sammy produces 60 knitted scarves, that is, qS = 60. Use this value for qS in Nancy best-response function, which then yields qN = 30, that is, Nancy produces30 knitted scarves. b. How much economic profit does each supplier earn? Part a shows that a total of 60 + 30 = 90 scarves are produced, which, using the inverse demand function, means the price of a knitted scarf is P = 40 – 0.25 × 90 = $17.50. Sammy produces 60 scarves, so his total revenue is $17.50 × 60 = $1,050. Using the cost function TC(qS) = 20 + 10qS, Sammy’s total cost is $620. Therefore Sammy’s economic profit is $1,050 − $620 = $430. Nancy produces 30 scarves, so her total revenue is $17.50 × 30 = $525. Using the cost function TC(qS) = 20 + 10qS, Nancy’s total cost is $320. Therefore Nancy’s economic profit is $525 − $320 = $205.