Chapter 1 Introduction
Overview Economics and managerial decision making Economics of a business Review of economic terms
Learning objectives define managerial economics cite important types of resource allocation decisions illustrate how economic changes affect a firm’s ability to earn an acceptable return apply to an individual firm the three basic questions faced by a country
Economics and managerial decision making
• Economics
The study of the behavior of human beings in producing, distributing and consuming material goods and services in a world of scarce resources
Economics and managerial decision making
• Management
The science of organizing and allocating a firm’s scarce resources to achieve its desired objectives
Economics and managerial decision making • Managerial economics
The use of economic analysis to make business decisions involving the best use (allocation) of an organization’s scarce resources
Economics and managerial decision making • Douglas - “Managerial economics is .. the application of economic principles and methodologies to the decision-making process within the firm or organization.” • Pappas & Hirschey - “Managerial economics applies economic theory and methods to business and administrative decisionmaking.” • Salvatore - “Managerial economics refers to the application of economic theory and the tools of analysis of decision science to examine how an organisation can achieve its objectives most effectively.”
Examples • How to use economic theory to set prices that maximize profits. • How to use economic theory to choose the cost-minimizing production technique for a given scale of output. • How to use economic theory to select the “optimal” location for a new restaurant, grocery store, etc. • How to use economic theory to forecast near-term demand for goods and services.
Examples of Management Decisions 1.
What rates should Cingular charge for its wireless telephone service?
2.
How many iPods should Apple manufacture in the current quarter?
3.
Should Red Lobster locate a restaurant in Jonesboro?
4.
Should Time-Warner leave the cable TV business?
5.
Should Minneapolis build a new baseball facility for the Twins?
6.
Should Ohio Edison scrap its coal-fired power plants in favor of oil fired plants to comply with regulatory controls on sulfur emissions? Or should it install expensive “scrubbing� equipment to its existing plants?
7.
Should ASU charge differential tuition for business, nursing, and engineering courses?
8.
Should the City of Jonesboro offer bus service?
9.
Should H & R Block outsource tax preparation to India?
Six Steps to Decision Making 1. Defining the Problem 2.
Determining the
Objective
3.
Exploring the Alternatives
4.
Predicting the consequences
5.
Making a choice
6.
Performing sensitivity analysis
Defining the problem “I have a flat tire.�
Defining the objective The spare won’t last long I gotta get this tire replaced!
Exploring the alternatives • Go to Sears • Go to Wal-Mart
Predicting the consequences • Wal-Mart is closer and cheaper. • Sears has a sale on Michelin radials.
Making a choice I’m going to Wal-Mart
How can managerial economics assist decision-makings by firms? • Adopt a general perspective, not a sample of one • Simple models provide stepping stone to more complexity and realism • Thinking logically has value itself and can expose sloppy thinking
Why Managerial Economics? • A powerful “analytical engine”. • A broader perspective on the firm. • what is a firm? • what are the firm’s overall objectives? • what pressures drive the firm towards profit and away from profit
• The basis for some of the more rigourous analysis of issues in Marketing and Strategic Management.
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Economics and managerial decision making • Relationship to other business disciplines
Marketing: demand, price elasticity Finance: capital budgeting, breakeven analysis, opportunity cost, value added Management science: linear programming, regression analysis, forecasting
Economics and managerial decision making • Relationship to other business disciplines
Strategy: types of competition, structure-conduct-performance analysis Managerial accounting: relevant cost, breakeven analysis, incremental cost analysis, opportunity cost
Economics and managerial decision making • Questions that managers must answer: – What are the economic conditions in our particular market?
• market structure? • supply and demand? • technology?
Economics and managerial decision making • Questions that managers must answer:
– What are the economic conditions in our particular market? • government regulations? • international dimensions? • future conditions? • macroeconomic factors?
Economics and managerial decision making • Questions that managers must answer: – Should our firm be in this business?
• if so, at what price? • and at what output level?
Economics and managerial decision making • Questions that managers must answer:
– How can we maintain a competitive advantage over other firms? • cost-leader? • product differentiation? • market niche? • outsourcing, alliances, mergers? • international perspective?
Economics and managerial decision making • Questions that managers must answer:
– What are the risks involved? • shifts in demand/supply conditions? • technological changes? • the effect of competition? • changing interest rates and inflation rates?
Economics and managerial decision making • Questions that managers must answer:
– What are the risks involved? • exchange rates (for companies in international trade)? • political risk (for firms with foreign operations)? Risk is the chance that actual future outcomes will differ from those expected
Economics of a business • The economics of a business refers to the key factors that affect the firm’s ability to earn an acceptable rate of return on its owners’ investment The most important of these factors are
– competition – technology – customers
Economics of a business • Change: the four-stage model
– Stage I (the ‘good old days’) • market dominance • high profit margin • cost plus pricing
… changes in technology, competition, customers force firm into Stage II ..
Economics of a business • Change: the four-stage model
– Stage II (crisis) • cost management • downsizing • restructuring
… ‘re-engineering’ to deal with changes and move firm into Stage III ..
Economics of a business • Change: the four-stage model – Stage III (reform)
• revenue management • cost cutting has limited benefit … focus on ‘top-line’ growth ..
Economics of a business • Change: the four-stage model – Stage IV (recovery)
• revenue plus … revenue grows profitably
Economics of a business • Example: Avon
• well established company, in stage I until late 1970s • found itself in Stage II during 1980s • since mid 1990s, entered stage III • expanded into emerging markets and updated its image
Economics of a business • Example: Sears, Kmart • Wal-Mart effect • Sears pushed down to number three in late 1980s … repositioned itself as a clothing store • Kmart filed for bankruptcy in 2002 … plan to acquire Sears
Economics of a business • Example: Kodak • struggled to transition from chemical-based film to digital imaging • responded by developing strong cash flows in new product range
Review of economic terms • Microeconomics is the study of individual consumers and producers in specific markets, especially: • supply and demand • pricing of output • production process • cost structure • distribution of income
Review of economic terms • Macroeconomics is the study of the aggregate economy, especially: • national output (GDP) • unemployment • inflation • fiscal and monetary policies • trade and finance among nations
Review of economic terms • Resources are inputs (factors) of production, notably: • land • labor • capital • entrepreneurship (management skills)
Review of economic terms • Scarcity is the condition in which resources are not available to satisfy all the needs and wants of a specified group of people • Opportunity cost is the amount (or subjective value) that must be sacrificed in choosing one activity over the next best alternative
Review of economic terms • Allocation decisions must be made because of scarcity. Three choices: What should be produced? How should it be produced? For whom should be produced?
Review of economic terms • Economic decisions of the Firm What - begin or stop providing goods/services (production) How - hiring, staffing, capital budgeting (resourcing) For whom – target the customers most likely to purchase (marketing)
Review of economic terms • Entrepreneurship is the willingness to take certain risks in the pursuit of goals • Management is the ability to organize resources and administer tasks to achieve objectives
Global application • Example: Western Union • began over 100 years ago • huge changes in technology • to survive, the company branched out
Chapter 2 The Firm and Its Goals
The Firm and Its Goals • • • • • •
The Firm Economic Goal of the Firm Goals Other Than Profit Do Companies Maximize Profits? Maximizing the Wealth of Stockholders Economic Profits
Learning Objectives • Understand reasons for existence of firms and meaning of transaction costs • Explain economic goals and optimal decision making • Describe meaning of “principal-agent” problem • Distinguish between “profit maximization” and “shareholder wealth maximization” • Demonstrate usefulness of Market Value Added and Economic Value Added
Theory of Firm •
Why do firms exist? – Coase (1937) • Transaction costs (Market vs. Firm): company compares costs of organizing an activity internally with the cost of using the market system for its transaction.
– Alchian & Demsetz (1972) • Team production costs & monitoring • The firm emerges because extra output is provided by team production, but that the success of this depends on being able to manage the team so that metering problems (it is costly to measure the marginal outputs of the co-operating inputs for reward purposes) and attendant shirking (the moral hazard problem) can be overcome, by estimating marginal productivity by observing or specifying input behavior.
– Schumpeter (1938) • Entrepreneur (lower opportunity costs) Common Concern: Costs!!! Common Issue: Scarcity (Efficiency)
Coase (1937)
Transaction Costs
Why do Firms exist? • Why is all economic activity not coordinated through markets? • Firms exist because they offer cost advantages over market transactions - Transactions costs - Monitoring - Economies of scale or scope - Economies of team production
Why not Markets? • Why is all economic activity not coordinated through organized firms (or just one giant firm)? • Principal-agent and incentive problems • Problems of information and management provide limits to firm size
The Firm’s Constraints Available technology Prices of inputs Fixed capital in the short run Degree of competition in the output market Given these constraints the firm needs to choose the method of production and output level that will maximize profit • Maximizing profit implies minimizing the cost of production • • • • •
The Firm • A firm is a collection of resources that is transformed into products demanded by consumers. • Profit is the difference between revenue received and costs incurred.
The Firm • Transaction costs are incurred when entering into a contract. – Types of transaction costs • Investigation • Negotiation • Enforcing contract and coordinating transactions – Influences • Uncertainty • Frequency of recurrence • Asset specificity
The Firm • Examples Kodak – uses offshoring to source cameras IBM – manufacturing computers overseas Exult – third party services used in human resources
The Firm • Limits to Firm Size – tradeoff between external transactions and the cost of internal operations – Company chooses to allocate resources so total cost is minimum – Outsourcing of peripheral, non-core activities
The Firm • Illustration: Coase and the Internet • Ronald Coase wrote in 1937, pre-internet • but his ideas are still relevant today • tradeoff between internal costs and external transactions • search costs
Economic Goal of the Firm • Primary objective of the firm (to economists) is to maximize profits. – Profit maximization hypothesis – Other goals include market share, revenue growth, and shareholder value
• Optimal decision is the one that brings the firm closest to its goal.
Economic Goal of the Firm • Short-run vs. Long-run – Nothing to do directly with calendar time – Short-run: firm can vary amount of some resources but not others (e.g. Labor, but not capital) – Long-run: firm can vary amount of all resources – At times short-run profitability will be sacrificed for long-run purposes
Goals Other Than Profit • Economic Goals – Market share, Growth rate – Profit margin – Return on investment, Return on assets – Technological advancement – Customer satisfaction – Shareholder value
Goals Other Than Profit • Non-economic Objectives – Good work environment – Quality products and services – Corporate citizenship, social responsibility
Do Companies Maximize Profit? • Criticism: Companies do not maximize profits but instead their aim is to “satisfice.” – “Satisfice” is to achieve a set goal, even though that goal may not require the firm to “do its best.” – Two components to “satisficing”: • Position and power of stockholders • Position and power of professional management
Do Companies Maximize Profit? • Position and power of stockholders – Medium-sized or large corporations are owned by thousands of shareholders – Shareholders own only minute interests in the firm – Shareholders diversify holdings in many firms – Shareholders are concerned with performance of entire portfolio and not individual stocks.
Do Companies Maximize Profit? • Position and power of stockholders – Most stockholders are not well informed on how well a corporation can do and thus are not capable of determining the effectiveness of management. – Not likely to take any action as long as they are earning a “satisfactory” return on their investment.
Do Companies Maximize Profit? • Position and power of professional management – High-level managers who are responsible for major decision making may own very little of the company’s stock. – Managers tend to be more conservative because jobs will likely be safe if performance is steady, not spectacular.
Do Companies Maximize Profit? • Position and power of professional management – Management incentives may be misaligned • E.g. incentive for revenue growth, not profits • Managers may be more interested in maximizing own income and perks
– Divergence of objectives is known as “principalagent” problem or “agency problem”
Maximizing the Wealth of Stockholders • Counter-arguments which support the profit maximization hypothesis. – Large number of shares is owned by institutions (mutual funds, banks, etc.) utilizing analysts to judge the prospects of a company. – Stock prices are a reflection of a company’s profitability. If managers do not seek to maximize profits, stock prices fall and firms are subject to takeover bids and proxy fights.
– The compensation of many executives is tied to stock price.
Maximizing the Wealth of Stockholders • Views the firm from the perspective of a stream of earnings over time, i.e., a cash flow. • Must include the concept of the time value of money. – Dollars earned in the future are worth less than dollars earned today.
Maximizing the Wealth of Stockholders • Future cash flows must be discounted to the present (time value of money). • The discount rate (minimum required rate of return on investment) is affected by risk. • Two major types of risk: – Business Risk – Financial Risk
Maximizing the Wealth of Stockholders • Business risk involves variation in returns due to the ups and downs of the economy, the industry, and the firm (economy is cyclical). • All firms face business risk to varying degrees.
Maximizing the Wealth of Stockholders • Financial Risk concerns the variation in returns that is induced by leverage. • Leverage is the proportion of a company financed by debt (debt to equity ratio). • The higher the leverage, the greater the potential fluctuations in stockholder earnings. • Financial risk is directly related to the degree of leverage.
Maximizing the Wealth of Stockholders • The present price of a firm’s stock should reflect the discounted value of the expected future cash flows to shareholders (dividends).
P • • • •
D1 (1 k )
D2
D3
Dn
(1 k ) 2 (1 k )3 (1 k ) n
P = present price of the stock D = dividends received per year K = discount rate N = life of firm in years
Maximizing the Wealth of Stockholders • If the firm is assumed to have an infinitely long life, the price of a share of stock which earns a dividend D per year is determined by the equation: P = D/k
Maximizing the Wealth of Stockholders • Given an infinitely lived firm whose dividends grow at a constant rate (g) each year, the equation for the stock price becomes: P = D1/(k-g) where D1 is the dividend to be paid during the coming year. • Multiplying P by the number of shares outstanding gives total value of firm’s common equity (market capitalization).
Maximizing the Wealth of Stockholders • A simple example Assumption: Dividend PMT1=$4 Dividend Growth Rate=5% Stockholder’s minimum required rate of return=12%
What is the value of the company’s stock? P=4/(0.12-0.05)=4/0.7=$57.14
Maximizing the Wealth of Stockholders • Company tries to manage its business in such a way that the dividends over time paid from its earnings and the risk incurred to bring about the stream of dividends always create the highest price for the company’s stock. • When stock options are substantial part of executive compensation, management objectives tend to be more aligned with stockholder objectives.
Maximizing the Wealth of Stockholders • Another measure of the wealth of stockholders is called Market Value Added (MVA)®. • MVA represents the difference between the market value of the company and the capital that the investors have paid into the company.
Maximizing the Wealth of Stockholders • Market value includes value of both equity and debt. • Capital includes book value of equity and debt as well as certain adjustments. – E.g. Accumulated R&D and goodwill.
• While the market value of the company will always be positive, MVA may be positive or negative.
Maximizing the Wealth of Stockholders • Another measure of the wealth of stockholders is called Economic Value Added (EVA)®. – EVA=(Return on Total Capital – Cost of Capital) x Total Capital if EVA > 0 shareholder wealth rising if EVA < 0 shareholder wealth falling
Economic Profits • Economic profits and accounting profits are typically different. – Accounting treatments allowed by GAAP (Generally Accepted Accounting principles)
– Accountants report cost on historical basis. – Economists are more concerned with opportunity costs or alternative costs.
Economic Profits • Historical costs vs. replacement costs • Implicit costs and normal profits – Return required by scarce resources to remain committed to a particular firm
• An economist includes costs that would be excluded by an accountant. • Economic costs include historical and explicit costs (accounting) as well as replacement and implicit costs (normal profits) • Economic profits is total revenue minus all economic costs
Economic Profits • Explicit Costs – Actual payments made to factors of production and other suppliers
• Implicit Costs – All the opportunity costs of the resources supplied by the firm’s owners • Eg: opportunity cost of owner’s time • Eg: opportunity cost of owner-invested funds
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Three Types of Profit • Accounting Profit – Total Revenue – Explicit Costs
• Economic Profit – Total Revenue – Explicit Costs – Implicit Costs
• Normal Profit – The difference between accounting profit and economic profit – The opportunity cost of the resources – How much accounting profit is needed for econ profit to be exactly = 0?
• Economic Loss – An economic profit less than zero
The Difference Between Accounting Profit and Economic Profit
The Difference Between Accounting Profit and Economic Profit • Revenue – Acct Costs = Acct Profit • Revenue – Econ Costs = Econ Profit • Revenue – Explicit Costs = Acct Profit • Revenue – (Explicit + Implicit costs) = Econ Profit • Acct Profit – Implicit Costs = Econ Profit • If Acct Profit exactly = Implicit Costs => Econ Profit = 0, and the firm is said to be earning a “normal profit”
Econ vs. Acct Profits • True or False: Economic profits are always less than or equal to accounting profits. TRUE • If some implicit costs exist economic cost > accounting cost Economic profit < accounting profit (ie: we are subtracting more costs from the same revenue)
Example • After graduation from the UNVA with a degree in MBA, you face the following job choice: • Option 1: IBM in RTP Salary = $50K/year • Option 2: Suntan shop in Key Largo Salary = $15K/year • If you choose option 2, you have to drain your $10,000 savings to start the business. Assume that you could have earned 10% on that money.
Example continued • Suppose you choose option 2… 1st year analysis: Revenue = $50,000 Costs of inventory = $8,000 Labor expenses = $15,000 Rent = $12,000 • acounting - inventory - rent - wages for worker
economic - inventory - rent - wages for worker - opp cost of Labor ($50k) - opp cost of funds = $1,000 the normal rate of return on capital. 86
Example continued • Accounting profit = 50 – 8 – 15 – 12 = 15 • Economic profit = 50 – 8 – 15 – 12 – 50 – 1 -36 • Earning less than a normal profit – How much is a normal profit for this firm?
=
Global application • Other countries, other cultures • • • • •
foreign currencies legal differences language attitudes role of government
Chapter 3 Supply and Demand
Supply and Demand • • • •
Market Demand Market Supply Market Equilibrium Comparative Statics Analysis – Short-run Analysis – Long-run Analysis
• Supply, Demand, and Price
Learning Objectives • Define supply, demand, and equilibrium price. • List and provide specific examples of nonprice determinants of supply and demand. • Distinguish between short-run rationing function and long-run guiding function of price • Illustrate how concepts of supply and demand can be used to analyze market conditions in which management decisions about price and allocations must be made. • Use supply and demand diagrams to show how determinants of supply and demand interact to determine price in the short and long run
Market Demand â&#x20AC;˘ Demand for a good or service is defined as quantities of a good or service that people are ready (willing and able) to buy at various prices within some given time period, other factors besides price held constant.
Market Demand Market demand is the sum of all the individual demands. Example demand for pizza:
Market Demand The inverse relationship between price and the quantity demanded of a good or service is called the Law of Demand.
Market Demand • Changes in price result in changes in the quantity demanded. – This is shown as movement along the demand curve.
• Changes in nonprice determinants result in changes in demand. – This is shown as a shift in the demand curve.
Market Demand • Nonprice determinants of demand – Tastes and preferences – Income – Prices of related products – Future expectations – Number of buyers
Market Supply â&#x20AC;˘ The supply of a good or service is defined as quantities of a good or service that people are ready to sell at various prices within some given time period, other factors besides price held constant.
Market Supply • Changes in price result in changes in the quantity supplied. – This is shown as movement along the supply curve.
• Changes in nonprice determinants result in changes in supply. – This is shown as a shift in the supply curve.
Market Supply • Nonprice determinants of supply – Costs and technology – Prices of other goods or services offered by the seller – Future expectations – Number of sellers – Weather conditions
Market Equilibrium â&#x20AC;˘ Equilibrium price: The price that equates the quantity demanded with the quantity supplied. â&#x20AC;˘ Equilibrium quantity: The amount that people are willing to buy and sellers are willing to offer at the equilibrium price level.
Market Equilibrium • Shortage: A market situation in which the quantity demanded exceeds the quantity supplied. – A shortage occurs at a price below the equilibrium level.
• Surplus: A market situation in which the quantity supplied exceeds the quantity demanded. – A surplus occurs at a price above the equilibrium level.
Market Equilibrium
Comparative Statics Analysis • A commonly used method in economic analysis: a form of sensitivity, or what-if analysis • Process of comparative statics analysis – State all the assumptions needed to construct the model. – Begin by assuming that the model is in equilibrium. – Introduce a change in the model. In so doing, a condition of disequilibrium is created. – Find the new point at which equilibrium is restored. – Compare the new equilibrium point with the original one.
Comparative Statics: Example Step 2 â&#x20AC;˘ Begin the analysis in equilibrium as shown by Q1 and P1.
Comparative Statics: Example Step 2 â&#x20AC;˘ Begin the analysis in equilibrium as shown by Q1 and P1.
Comparative Statics: Example Step 3 â&#x20AC;˘ Assume that a new study shows pizza to be the most nutritious of all fast foods. â&#x20AC;˘ Consumers increase their demand for pizza as a result.
Comparative Statics: Example Step 4 â&#x20AC;˘ The shift in demand results in a new equilibrium price, P2 , and quantity, Q2.
Comparative Statics: Example Step 5 â&#x20AC;˘ Comparing the new equilibrium point with the original one we see that both equilibrium price and quantity have increased.
Comparative Statics Analysis • The short run is the period of time in which: – Sellers already in the market respond to a change in equilibrium price by adjusting variable inputs. – Buyers already in the market respond to changes in equilibrium price by adjusting the quantity demanded for the good or service.
Comparative Statics Analysis â&#x20AC;˘ The rationing function of price is the change in market price to eliminate the imbalance between quantities supplied and demanded.
Short-run Analysis â&#x20AC;˘ An increase in demand causes equilibrium price and quantity to rise.
Short-run Analysis â&#x20AC;˘ A decrease in demand causes equilibrium price and quantity to fall.
Short-run Analysis â&#x20AC;˘ An increase in supply causes equilibrium price to fall and equilibrium quantity to rise.
Short-run Analysis â&#x20AC;˘ A decrease in supply causes equilibrium price to rise and equilibrium quantity to fall.
Comparative Statics Analysis • The long run is the period of time in which: – New sellers may enter a market – Existing sellers may exit from a market – Existing sellers may adjust fixed factors of production – Buyers may react to a change in equilibrium price by changing their tastes and preferences or buying preferences
Comparative Statics Analysis â&#x20AC;˘ The guiding or allocating function of price is the movement of resources into or out of markets in response to a change in the equilibrium price.
Long-run Analysis • Initial change: decrease in demand from D1 to D2 • Result: reduction in equilibrium price and quantity, now P2,Q2 • Follow-on adjustment: – movement of resources out of the market – leftward shift in the supply curve to S2 – Equilibrium price and quantity now P3,Q3
Long-run Analysis • Initial change: increase in demand from D1 to D2 • Result: increase in equilibrium price and quantity, now P2,Q2 • Follow-on adjustment: – movement of resources into the market – rightward shift in the supply curve to S2 – Equilibrium price and quantity now P3,Q3
Supply, Demand, and Price: The Managerial Challenge • In the extreme case, the forces of supply and demand are the sole determinants of the market price. – This type of market is “perfect competition”
• In other markets, individual firms can exert market power over their price because of their: – dominant size. – ability to differentiate their product through advertising, brand name, features, or services
Supply, demand, and price: the managerial challenge • Example: coffee • • • •
‘buy low, sell high’ 2000: overproduction led to price falls 2004: prices moved up again Starbucks effects
Supply, demand, and price: the managerial challenge • Example: air travel • • • •
‘buy high, sell low’ industry deregulated in late 1970s tight competition post 9/11, a low-cost structure is needed
Global application • Example: the market for cobalt • • • •
rare metal produced as a by-product strategic item prices rising
Chapter 4 Demand Elasticity
Demand Elasticity • • • • • •
The Economic Concept of Elasticity The Price Elasticity of Demand The Cross-Elasticity of Demand Income Elasticity Other Elasticity Measures Elasticity of Supply
Learning Objectives • Define and measure elasticity • Apply concepts of price elasticity, crosselasticity, and income elasticity • Understand determinants of elasticity • Show how elasticity affects revenue
The Economic Concept of Elasticity â&#x20AC;˘ The demand curve sloped downward to the right (the lowered the price, the greater the quantity demanded) â&#x20AC;˘ Elasticity: the percentage change in one variable relative to a percentage change in another. percent change in A Coefficient of Elasticity ď&#x20AC;˝ percent change in B
The Price Elasticity of Demand • A firm contemplating lowering its price to counteract new competition • Price elasticity of demand: The percentage change in quantity demanded caused by a 1 percent change in price.
% Quantity Ep % Price
Measurement of Price Elasticity • Arc elasticity: Elasticity which is measured over a discrete interval of a demand (or a supply) curve.
• • • • •
Q2 Q1 P2 P1 Ep Q1price Qelasticity ( P1 P2 ) / 2 Ep = Coefficient of(arc 2) / 2 Q1 = Original quantity demanded Q2 = New quantity demanded P1 = Original price P2 = New price
Example â&#x20AC;˘ P1=11 P2=12 Q1=7 Q2=6 Then what is EP ?
The Price Elasticity of Demand â&#x20AC;˘ Point elasticity: Elasticity measured at a given point of a demand (or a supply) curve.
dQ P1 ÎľP = x dP Q1
The Price Elasticity of Demand The point elasticity of a linear demand function can be expressed as:
Q P1 p P Q1
Example • Q=18-P at when P=$12 and Q=6 then what is EP ? • Q=100-P2 when P1=5, then Q=75 then what is EP ?
The Price Elasticity of Demand • Some demand curves have constant elasticity over the relevant range • Such a curve would look like: Q = aP-b
where –b is the elasticity coefficient • This equation can be converted to linear by expressing it in logarithms: log Q = log a – b(log P)
The Price Elasticity of Demand â&#x20AC;˘ Elasticity differs along a linear demand curve
The Price Elasticity of Demand • Categories of Elasticity – Relative elasticity of demand: EP > 1 – Relative inelasticity of demand: 0 < EP < 1 – Unitary elasticity of demand: EP = 1 – Perfect elasticity: EP = ∞ – Perfect inelasticity: EP = 0
Special Cases P D
D
0
Q Infinitely (price) elastic
0 Infinitely price inelastic
Q
The Price Elasticity of Demand • Factors affecting demand elasticity – Ease of substitution – Proportion of total expenditures – Durability of product • Possibility of postponing purchase • Possibility of repair • Used product market
– Length of time period
The Price Elasticity of Demand â&#x20AC;˘ Derived demand: The demand for products or factors that are not directly consumed, but go into the production of a final product. â&#x20AC;˘ The demand for such a product or factor exists because there is demand for the final product.
The Price Elasticity of Demand • The derived demand curve will be more inelastic: – the more essential is the component in question. – the more inelastic is the demand curve for the final product. – the smaller is the fraction of total cost going to this component. – the more inelastic is the supply curve of cooperating factors.
Example â&#x20AC;˘ Consider demand for residential housing (the final product) and the derived demand for one class of labor employed in construction , electricians ( the demand for electricians does not exist for its own sake) â&#x20AC;&#x201C; Assumptions: 1. can not build a house without electricians 2. the cost of electricians is a relatively small percentage of the entire cost of the house
The Price Elasticity of Demand â&#x20AC;˘ A long-run demand curve will generally be more elastic than a short-run curve. â&#x20AC;˘ As the time period lengthens consumers find way to adjust to the price change, via substitution or shifting consumption
The Price Elasticity of Demand • There is a relationship between the price elasticity of demand and revenue received. – Because a demand curve is downward sloping, a decrease in price will increase the quantity demanded – If elasticity is greater than 1, the quantity effect is stronger than the price effect, and total revenue will increase
The Price Elasticity of Demand • As price decreases – Revenue rises when demand is elastic. – Revenue falls when it is inelastic. – Revenue reaches it peak when elasticity of demand equals 1.
The Price Elasticity of Demand • Marginal Revenue: The change in total revenue resulting from changing quantity by one unit.
Total Revenue MR Quantity
The Price Elasticity of Demand â&#x20AC;˘ For a straight-line demand curve the marginal revenue curve is twice as steep as the demand
The Price Elasticity of Demand â&#x20AC;˘ At the point where marginal revenue crosses the X-axis, the demand curve is unitary elastic and total revenue reaches a maximum.
The Price Elasticity of Demand • Some sample elasticities – Coffee: short run -0.2, long run -0.33 – Kitchen and household appliances: -0.63 – Meals at restaurants: -2.27 – Airline travel in U.S.: -1.98 – Beer: -0.84, Wine: -0.55
The Cross-Elasticity of Demand • Cross-elasticity of demand: The percentage change in quantity consumed of one product as a result of a 1 percent change in the price of a related product.
%QA EX %PB
The Cross-Elasticity of Demand • Arc Elasticity
Q2 A Q1 A P2 B P1B Ex (Q1 A Q2 A ) / 2 ( P1B P2 B ) / 2
The Cross-Elasticity of Demand • Point Elasticity
QA PB EX QA PB
The Cross-Elasticity of Demand â&#x20AC;˘ The sign of cross-elasticity for substitutes is positive. â&#x20AC;˘ The sign of cross-elasticity for complements is negative. â&#x20AC;˘ Two products are considered good substitutes or complements when the coefficient is larger than 0.5.
Income Elasticity • Income Elasticity of Demand: The percentage change in quantity demanded caused by a 1 percent change in income. • Y is shorthand for Income
%Q EY %Y
Income Elasticity • Arc Elasticity
Q2 Q1 Y2 Y1 EY (Q1 Q2 ) / 2 (Y1 Y2 ) / 2
Other Elasticity Measures • Categories of income elasticity – Superior goods: EY > 1 – Normal goods: 0 >EY >1 – Inferior goods – demand decreases as income increases: EY < 0
Elasticity of Supply • Elasticity is encountered every time a change in some variable affects quantities. – Advertising expenditure – Interest rates – Population size
Elasticity of Supply • Price Elasticity of Supply: The percentage change in quantity supplied as a result of a 1 percent change in price.
% Quantity Supplied ES % Price • If the supply curve slopes upward and to the right, the coefficient of supply elasticity is a positive number.
Elasticity of Supply • Arc elasticity
Q2 Q1 P2 P1 Es (Q1 Q2 ) / 2 ( P1 P2 ) / 2
Demand Elasticity â&#x20AC;˘ When the supply curve is more elastic, the effect of a change in demand will be greater on quantity than on the price of the product. â&#x20AC;˘ With a supply curve of low elasticity, a change in demand will have a greater effect on price than on quantity.
Global application • Example: price elasticities in Asia – imports almost always price inelastic – if exports price inelastic, export earnings will rise as prices rise – if exports price elastic, export earnings will rise with world incomes
Optimization using Calculus We will review some rules of differential calculus that are especially useful for management decision making
The profit function Suppose that a business firm has estimated its profit () function (based on marketing and production studies) as follows: 2
2Q 0.1Q 3.6 Where is profit (in thousands of dollars) and Q is quantity (in thousands of units). Thus the problem for management is to set its quantity(Q) at the level that maximizes profits ().
What is an objective function?
The profit function shows the relationship between the manager’s decision variable (Q) and her objective (). That is why we call it the objective function.
The Profit Function 8.0 6.0
P ro fit
4.0 2.0 0.0 -2.0 -4.0
0.0
2.0
4.0
6.0
8.0 10.0 12.0 14.0 16.0 18.0 20.0
Marginal profit at a particular output is given by the slope of a line tangent to the profit function
-6.0 Quantity
The profit function again
Computing profit at various output levels using a spreadsheet • • • • •
Recall our profit function is given by: = 2Q - .1Q2 – 3.6 Fill in the “quantity” column with 0, 2, 4, . . . Assume that you typed zero in column cell a3 of your spreadsheet Place your cursor in the the cell b3 (it now contains the bolded number –3.6)—just to the right of cell a3. Type the following in the formula bar:
=(2*a3)-(.1*a3^2)-3.6
•
and click on the check mark to the left of the formula bar. Now move your cursor to the southeast corner of cell b3 until you see a small cross (+).Now move your cursor down through cells b4, b5, b6 . . . to compute profit at various levels of output.
Quantity (000s) 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0
Profit (000s) -3.6 0.0 2.8 4.8 6.0 6.4 6.0 4.8 2.8 0.0 -3.6
Rules of calculus
Rule 1: The derivative of a constant is zero. Example:
y
Let Y = 7 Thus:
7
dy/dx = 0 0 X
Rule 2: The derivative of a constant times a variable is simply the constant.
y Example: Let y = 13x
26
Thus: dy/dx = 13
Rule 2
13
0
1
2
x
Rule 3: A power function has the form y = axn, where a and n are constants. The derivative of a power function is:
dy n ax dx
n 1
Example: Let y = 4x3 Thus:
dy / dx 12 x 2 Rule 3
Special cases of the power function Note the following: y =1/x2 is equivalently written as y = x-2 and
y ď&#x20AC;˝ x can be written y = x1/2 Hence by rule 3 (or the power rule), the respective derivatives are given by: dy/dx = -2x-3 And dy/dx = .5x-1/2 = .5 / x
Power functions
Rule 4: Suppose the product of two functions : y = f(x)g(x). Then we have: dy df dg ( g ) ( f ) dx dx dx
Example: Let y = (4x)(3x2) Thus: dy/dx = (4)(3x2) + (6x)(4x) = 36x2 Rule 4
Rule 5 Rule 5: The derivative of the sum of functions is equal to the sum of the derivatives. If y = f(x) + g(x), then: dy/dx = df/dx + dg/dx Example: Let: y = .1x2 – 2x3 Thus: dy/dx = .2x – 6x2
Rule 6: Suppose y is a quotient: y = f(x)/g(x). Then we have:
dy (df / dx)(g) (dg / dx)( f ) dx g2 Example Suppose we have: y = x/(8 + x) Thus: dy/dx = [1 • (8 + x) – 1 • (x)]/ (8 + x)2 = 8/(8 + x)2
Rule 6
The marginal profit (M) function Let the profit function be given by: = 2Q - .1Q2 – 3.6 To obtain the marginal profit function, we take the first derivative of profit with respect to output (Q): M = d/dQ = 2 - .2Q To solve for the output level that maximizes profits, set M =0. 2 - .2Q = 0 Thus: Q = 10
The second derivative We know that the slope of the profit function is zero at its maximum point. So the first derivative of the profit function with respect to Q will be zero at that output. Problem is, how do we know we have a maximum instead of a minimum?
Notice this function has a slope of zero at two levels of output
A more complicated profit function
15
1.8Q 2 .1Q 3 6Q 10
P rofit (Thousands)
10 5 0 -5
0
2
4
6
8
-10 -15 -20 Ouput (Thousands)
10
12
14
Taking the second derivative
Our profit function () is given by:
1.8Q 2 .1Q 3 6Q 10 Now let’s derive the marginal profit (M )function
d / dQ 3.6Q .3Q 2 6 We can verify that M = 0 when Q = 2 and Q = 10.
Maximum or minimum?
Notice at the minimum point of the function, the slope is turning from zero to positive. Notice also at the maximum point, the slope is changing from zero to negative
To insure a maximum, check to see that the second derivative is negative To take the second derivative of the profit function: d 2 d (d / dQ) dM 2 dQ dQ dQ Thus we have: d 2 d (3.6Q .3Q 2 ) 3.6 .6Q 2 dQ dQ Hence, when Q = 2, we find that d2/dQ2 = 3.6 - .6(2) = 2.4 When Q = 10, we find that d2/dQ2 = 3.6 - .6(10) = -2.4
Marginal Revenue and Marginal Cost
Marginal profit (Mď °) is zero when marginal revenue (MR) is equal to marginal cost (MC), or alternatively, when MR â&#x20AC;&#x201C; MC = 0.
Hence to find the profit maximizing output, set the first derivative of the revenue function equal to the first derivative of the cost functions
Solving for the profit maximizing output Let (Q) = R(Q) – C(Q), where R is sales revenue and C is cost Thus we have d dR dC MR MC 0 dQ dQ dQ
Multivariable functions Suppose we have a multivariate function such as the following: = f(P, A), where P is market price and A is the advertising budget. Our function has been estimated as follows:
20 2P 2P2 4 A A2 2PA We would like to know: •How sensitive are profits to a change in price, other things being equal (or ceteris paribus)? •How sensitive are profits to a change in the advertising budget, ceteris paribus?
We get the answer to question 1 by taking the first partial derivative of with respect to P.
Partial derivatives
2 4p 2A P
We can find the answer to question 2 by taking the first partial derivative of with respect to A: 4 2A 2P A
Solving for the P and A that maximize ď ° We know that profits will be maximized when the first partial derivatives are equal to zero. Hence, we set them equal to zero and obtain a linear equation system with 2 unknowns (P and A)
2 â&#x20AC;&#x201C; 4P + 2A= 0 4 - 2A + 2P = 0
The solution is: P = 3 and A = 5
Constrained optimization So far we have looked at problems in which the decision maker maximizes some variable () but faces no constraints. We call this “unconstrained optimization.” Often, however, we seek to maximize (or minimize) some variable subject to one or more constraints.
Examples: •Maximize profits subject to the constraint that output is equal to or greater than some minimum level. •Maximize output subject to the constraint that cost must be equal to or less than some maximum value.
Example 1 Suppose we are seeking to maximize the following profit function subject to the constraint that Q 7.
40 Q 4 Q 2 What happens if we take the first derivative, set equal to zero, and solve for Q? d 40 8Q dQ
Solving to maximize , we get Q = 5. But that violates our constraint.
Another example A firm has a limited amount of output and must decide what quantities (Q1 and Q2) to sell in two different market segments. Suppose its profit () function is given by: ( 20 Q 1 . 5 Q `1 2 ) ( 40 Q 2 Q 2 ) 2
The firm’s output cannot exceed 25—that is, it seeks to maximize subject to Q 25. If we set the marginal profit functions equal to zero and solved for Q1 and Q2, we would get: Q1 = 20 and Q2 = 20, so that Q1 + Q2 =40. Again, this violates the constraint that total output cannot exceed 25.
Method of Lagrange Multipliers
This technique entails creating a new variable (the Lagrange multiplier) for each constraint. We then determine optimal values for each decision variable and the Lagrange multiplier.
Lagrange technique: Example 1
Recall example 1 . Our constraint was given by Q = 7. We can restate this constraint as: 7–Q=0 Our new variable will be denoted by z. Our Lagrange (L) function can be written:
L z (7 Q) 40Q 4Q 2 z (7 Q)
Taking the partials of L with respect to Q and z Now we just take the first partial derivative of L with respect to Q and z, set them equal to zero, and solve.
L 40 8 Q z 0 Q L 7Q 0 z Solving for Q and z simultaneously, we obtain: Q = 7 and z = -16
Interpretation of the Lagrange multiplier (z)
You may interpret the result that z = -16 as follows: marginal profit (M) at the constrained optimum output is –16 — that is, the last unit produced subtracted $16 for our profit
Lagrange technique: Example 2
Recall example 2 . Our constraint was given by: Q1 + Q2 = 25 Our Lagrange (L) function can be written as :
L (20Q1 .5Q12 ) (40Q 2 Q 2 2 ) z (25 Q1 Q 2)
Taking the partials of L with respect to Q1, Q2 and z This time we take the first partial derivative of L with respect to Q1, Q2, and z, set them equal to zero, and solve.
L 20 Q 1 z 0 Q 1 L 40 2 Q 2 z 0 Q 2 L 25 Q 1 Q 2 0 z
The solutions are: Q1 = 10 Q2 = 15 z = 10
8
Profit (000s)
6 4 2 0 -2
0
2
4
6
8
10
12
14
-4 -6 Output (000s Units)
16
18
20
Chapter 5 Demand Estimation and Forecasting
Demand Estimation and Forecasting • • • • •
Regression Analysis Problems in Use of Regression Analysis Subjects of Forecasts Prerequisites of a Good Forecast Forecasting Techniques
Learning Objectives • Specify components of a regression model that can be used to estimate a demand equation • Interpret regression results • Explain meaning of R2 • Evaluate statistical significance of regression coefficients using t-test and statistical significance of R2 using F-test
Learning Objectives â&#x20AC;˘ Recognize challenges of obtaining reliable cross-sectional and time series data on consumer behavior that can be used in regression models of demand â&#x20AC;˘ Understand importance of forecasting in business â&#x20AC;˘ Describe six different forecasting techniques
Learning Objectives â&#x20AC;˘ Show how to carry out least squares projections and decompose them into trends, seasonal, cyclical, and irregular movements â&#x20AC;˘ Explain basic smoothing methods of forecasting, such as moving average and exponential smoothing
The Scientific Method 1. Identify the Question and Define Relevant Variables 2. Specify Assumptions Modify Approach
3. Formulate a hypothesis 4. Test the hypothesis or
Reject the hypothesis
Use the hypothesis until a better one shows up
198
Estimation • Estimation: an attempt to quantify the links between the level of demand for a product (dependant variable) and the variables (independent variables) which determine it • E.g., the demand for a hotel room depending upon – Their price – Household incomes – The weather
• Objective: Learn how to estimate a demand Estimation of Demand function using regression analysis, and interpret the results • A chief uncertainty for managers - what will happen to their product. – forecasting, prediction & estimation – need for data
Data Collection • Data for studies pertaining to countries, regions, or industries are readily available and reliable. • Data for analysis of specific product categories may be more difficult to obtain. – – – –
Buy from data providers (e.g. ACNielsen, IRI) Perform a consumer survey Focus groups Technology: Point-of-sale, bar codes, RFID(radio frequency identification)
Regression Analysis • Regression Analysis: A procedure commonly used by economists to estimate consumer demand with available data. – Cross-Sectional Data: provide information on variables for a given period of time. – Time Series Data: give information about variables over a number of periods of time.
Regression Analysis • Regression equation: linear, additive – Y = a + b1X1 + b2X2 + b3X3 + b4X4 • Y: dependent variable, amount to be determined • a: constant value, y-intercept • Xn: independent, explanatory variables, used to explain the variation in the dependent variable • bn: regression coefficients (measure impact of independent variables)
Regression Analysis • Regression Results – Negative coefficient shows that as the independent variable (Xn) changes, the quantity demanded changes in the opposite direction. – Positive coefficient shows that as the independent variable (Xn) changes, the quantity demanded changes in the same direction. – Magnitude of regression coefficients is measured by elasticity of each variable.
Simple Linear Regression • Qt = a + b Pt + t
Q
OLS -ordinary least squares
• time subscripts & error term • Find “best fitting” line
t = Qt - a - b Pt t 2= [Qt - a - b Pt] 2
_ Q
• min t 2= [Qt - a - b Pt]2 • Solution: b = Cov(Q,P)/Var(P) and a = mean(Q) - b•mean(P) _ P
Statistical Estimation of the a Demand Function • Steps to take: – Specify the variables -- formulate the demand model, select a Functional Form
• Linear Q = a + b•P + c•I • double log ln Q = a + b•ln P + c•ln I • quadratic Q = a + b•P + c•I+ d•P2 – Estimate the parameters -• determine which are statistically significant • try other variables & other functional forms
– Develop forecasts from the model
Estimation Process
Regression Model y = 0 + 1x + Regression Equation E(y) = 0 + 1x Unknown Parameters 0, 1
b0 and b1 provide estimates of 0 and 1
Sample Data: x y x1 . . xn
y1 . . yn
Estimated Regression Equation yˆ b 0 b 1 x
Sample Statistics b0, b1
Regression Analysis • Statistical evaluation of regression results – t-test: test of statistical significance of each estimated regression coefficient bˆ t SE
bˆ
– b: estimated coefficient – SEb: standard error of the estimated coefficient – Rule of 2: if absolute value of t is greater than 2, estimated coefficient is significant at the 5% level – If coefficient passes t-test, the variable has a true impact on demand
T-tests • Different samples would yield different coefficients
• Test the hypothesis that coefficient equals zero – Ho: b = 0 – Ha: b 0
• RULE: If absolute value of the estimated t > Critical-t, then REJECT Ho. – It’s significant.
• estimated t = (b - 0) / b • critical t – Large Samples, critical t 2 • N > 30
– Small Samples, critical t is on Student’s t-table • D.F. = # observations, minus number of independent variables, minus one. • N < 30
Regression Analysis • Statistical evaluation of regression results – Coefficient of determination (R2): percentage of variation in the dependent variable (Y) accounted for by variation in all explanatory variables (Xn) • Value ranges from 0.0 to 1.0 • Closer to 1.0, the greater the explanatory power of the regression equation – F-test: measures statistical significance of the entire regression as a whole (not each coefficient)
2 Coefficients of Determination: R • R-square -- % of variation in dependent variable that is explained
Q Qt
^
• Ratio of Qt] 2
[Qt -Qt] 2 to [Qt - _
• As more variables are included, R-square rises • Adjusted R-square, however, can decline
Q
_ P
Regression Analysis • Steps for analyzing regression results – Check signs and magnitudes – Compute elasticity coefficients – Determine statistical significance
Regression Problems â&#x20AC;˘ Identification Problem: The estimation of demand may produce biased results due to simultaneous shifting of supply and demand curves. â&#x20AC;˘ Advanced estimation techniques, such as twostage least squares and indirect least squares, are used to correct this problem.
Plot Historical Data Price
• Look at the relationship of price and quantity over time • Plot it
– Is it a demand curve or a supply curve? – Problem -- not held other things equal
D? or S? 92
98 93 97
96 94
95
quantity
Identification Problem P
• Q = a + b P can appear upward or downward sloping. • Suppose supply varies and demand is FIXED. • All points lie on the demand curve
S1 S2
S3
Demand
quantity
Suppose SUPPLY is Fixed • Let DEMAND shift and supply be FIXED. • All points are on the SUPPLY curve. • We say that the SUPPLY curve is identified.
P
Supply
D3 D2 D1 quantity
When both Supply and Demand Vary • Often both supply and demand vary. • Equilibrium points are in shaded region. • A regression of Q = a + b P will be neither a demand nor a supply curve.
P
S2 S1 D2
D1 quantity
Regression results • Example: estimating demand for pizza – demand for pizza affected by 1. price of pizza 2. price of complement (soda) – managers can expect price decreases to lead to lower revenue – tuition and location are not significant
Regression Problems • Multicollinearity: two or more independent variables are highly correlated, thus it is difficult to separate the effect each has on the dependent variable. • Passing the F-test as a whole, but failing the t-test for each coefficient is a sign that multicollinearity exists. • A standard remedy is to drop one of the closely related independent variables from the regression. • E.g., If current income changes in the same way as inflation over time, then we will not be able to separate their impact on current consumption
Problems • Autocorrelation: also known as serial correlation, occurs when the dependent variable relates to the independent variable according to a certain pattern. • Possible causes: – Effects on dependent variable exist that are not accounted for by the independent variables. – The relationship may be non-linear
• The Durbin-Watson statistic is used to identify the presence of autocorrelation. • To correct autocorrelation consider: – Transforming the data into a different order of magnitude – Introducing leading or lagging data
Forecasting • Forecasting: an attempt to predict the level of sales at some future date • Plan for future scenarios • Can be quantitative or qualitative
Subjects of Forecasts • Gross Domestic Product (GDP) • Components of GDP – E.g. consumption expenditure, producer durable equipment expenditure, residential construction
• Industry Forecasts – Sales of products across an industry
• Sales of a specific product
Prerequisites of a Good Forecast • A good forecast should: – be consistent with other parts of the business – be based on knowledge of the relevant past – consider the economic and political environment as well as changes – be timely
Forecasting Techniques • Factors in choosing the right forecasting technique: – Item to be forecast – Interaction of the situation with the characteristics of available forecasting methods – Amount of historical data available – Time allowed to prepare forecast
Forecasting Techniques • • • • • •
Expert opinion Opinion polls and market research Surveys of spending plans Economic indicators Projections Econometric models
Forecasting Techniques • Qualitative forecasting is based on judgments of individuals or groups. • Quantitative forecasting utilizes significant amounts of prior data as a basis for prediction. • Naïve forecasting projects past data without explaining future trends. • Causal (or explanatory) forecasting attempts to explain the functional relationships between the dependent variable and the independent variables.
Forecasting Techniques • Expert opinion techniques – Jury of executive opinion: Forecasts generated by a group of corporate executives assembled together. The major drawback is that persons with strong personalities may exercise disproportionate influence. – The Delphi Method: A form of expert opinion forecasting that uses a series of questions and answers to obtain a consensus forecast, where experts do not meet.
Forecasting Techniques • Opinion polls: Sample populations are surveyed to determine consumption trends. – may identify changes in trends – choice of sample is important – questions must be simple and clear
• Market research is closely related to opinion polling. – Market research will indicate “not only why the consumer is or is not buying, but also who the consumer is, how he or she is using the product, and what characteristics the consumer thinks are most important in the purchasing decision.”
Forecasting Techniques •
Surveys of spending plans: seek information about “macro-type” data relating to the economy. 1. Consumer intentions – Survey of Consumers, Survey Research Center, University of Michigan – Consumer Confidence Survey, The Conference Board 2. Inventories and sales expectations – A monthly survey published by the National Association of Purchasing Agents with a large sample of purchasing executives
Forecasting Techniques â&#x20AC;˘ Economic Indicators: A barometric method of forecasting designed to alert business to changes in economic conditions. â&#x20AC;&#x201C; Leading, coincident, and lagging indicators â&#x20AC;&#x201C; One indicator may not be very reliable, but a composite of leading indicators may be used for prediction.
Forecasting Techniques • Leading Indicators predict changes in future economic activity – – – – – – – – – –
Average hours, manufacturing Initial claims for unemployment insurance Manufacturers’ new orders for consumer goods and materials Vendor performance, slower deliveries diffusion index Manufacturers’ new orders, nondefense capital goods Building permits, new private housing units Stock prices, 500 common stocks Money supply, M2 Interest rate spread, 10-year Treasury bonds minus federal funds Index of consumer expectations
Forecasting Techniques •
Coincident Indicators identify trends in current economic activities – – – –
•
Employees on nonagricultural payrolls Personal income less transfer payments Industrial production Manufacturing and trade sales
Lagging Indicators confirm swings in past economic activities – – – – – – –
Average duration of unemployment, weeks Ratio, manufacturing and trade inventories to sales Change in labor cost per unit of output, manufacturing (%) Average prime rate charged by banks Commercial and industrial loans outstanding Ratio, consumer installment credit outstanding to personal income Change in consumer price index for services
Forecasting Techniques â&#x20AC;˘ General rule of thumb: if, after a period of increases, the leading indicator index sustains three consecutive declines, a recession (or a slowing) will follow. â&#x20AC;˘ Economic indicators have predicted each recession since 1948.
Forecasting Techniques • Economic Indicators Drawbacks – Leading indicator index has forecast a recession when none ensued. – A change in the index does not indicate the precise size of the decline or increase. – The data are subject to revision in the ensuing months.
Forecasting Techniques • Trend projections: A form of naïve forecasting that projects trends from past data without taking into consideration reasons for the change. – Compound growth rate – Visual time series projections – Least squares time series projection
Forecasting Techniques • Compound growth rate: Forecasting by projecting the average growth rate of the past into the future. – Calculate the constant growth rate using available data, then project this constant growth rate into the future. – Provides a relatively simple and timely forecast – Appropriate when the variable to be predicted increases at a constant percentage
Forecasting Techniques • General compound growth rate formula: E = B(1+i)n • • • •
E = final value n = years in the series B = beginning value i = constant growth rate
Forecasting Techniques â&#x20AC;˘ Visual Time Series Projections: plotting observations on a graph and viewing the shape of the data and any trends.
Forecasting Techniques • Time series analysis: A naïve method of forecasting from past data by using least squares statistical methods. • Data collected of a number of periods usually exhibit certain characteristics: – Trends – Cyclical fluctuations – Seasonal fluctuations – Irregular movements
Forecasting Techniques – Trends: direction of movement of the data over relatively long period of time, either upward or downward – Cyclical fluctuations: deviation from the trend due to general economic conditions – Seasonal fluctuations: a pattern that repeats annually, e.g., Christmas – Irregular movements: random occurrence of an event
Forecasting Techniques • Time Series Analysis Advantages – easy to calculate – does not require much judgment or analytical skill – describes the best possible fit for past data – usually reasonably reliable in the short run
Forecasting Techniques Yt = f(Tt, Ct, St, Rt) • Yt = Actual value of the data at time t • Tt = Trend component at t • Ct = Cyclical component at t • St = Seasonal component at t • Rt = Random component at t • Additive form: Yt = Tt + Ct + St + Rt • Multiplicative form: Yt = (Tt)(Ct)(St)(Rt)
Forecasting Techniques • Must decompose the time series into its four components – Remove seasonality – Compute trend – Isolate cycle – Cannot do anything with random component
Forecasting Techniques â&#x20AC;˘ Seasonality: need to identify and remove seasonal factors, using moving averages to isolate those factors. â&#x20AC;˘ Remove seasonality by dividing data by seasonal factor
Forecasting Techniques • Trend Line: use least squares method • Possible best-fit line styles: – Straight Line: Y = a + b(t) – Exponential Line: Y = abt – Quadratic Line: Y = a + b(t) + c(t)2
• Choose style with a balance of high R2 and high t-statistics
Forecasting Techniques • Cycle and Random Elements – Random factors cannot be predicted and should be ignored – Isolate cycle by smoothing with a moving average
Forecasting Techniques • Smoothing Techniques – Moving Average – Exponential Smoothing
• Work best when: – No strong trend in series (random variation) – Infrequent changes in direction of series – Fluctuations are random rather than seasonal or cyclical
Forecasting Techniques • Moving Average: average of actual past results used to forecast one period ahead Et+1 = (Xt + Xt-1 + … + Xt-N+1)/N
• • • •
Et+1 : forecast for next period Xt, Xt-1 : actual values at their respective times N: number of observations included in average E.g., twelve months moving average forecast for sales of a product for March 2009 is the average of sales for the previous twelve month (March 2008 - Feb 2009)
Forecasting Techniques • Exponential Smoothing: allows for decreasing importance of information in the more distant past, through geometric progression Et+1 = w·Xt + (1-w) · Et
• w: weight assigned to an actual observation at period t
Forecasting Techniques • Econometric Models: causal or explanatory models of forecasting – Regression analysis – Multiple equation systems • Endogenous variables: comparable to dependent variables of single-equation model, but may influence other endogenous variables • Exogenous variables: from outside the system, truly independent variables
Forecasting techniques • Example: econometric model
– Suits (1958) forecast demand for new automobiles ∆R = a0 + a1 ∆Y + a2 ∆P/M + a3 ∆S + a4 ∆X
R = retail sales Y = real disposable income P = real retail price of cars M = average credit terms S = existing stock X= dummy variable
Global application • Example: forecasting exchange rates – The forward exchange rate is a predictor of a the spot exchange rate, if today’s spot rate is $1.998 for 1 British Pound and the 90-forward rate is $1.989, then what? – GDP – interest rates – inflation rates – balance of payments
Estimating Demand Outline •Where do demand functions come from? •Sources of information for demand estimation •Cross-sectional versus time series data •Estimating a demand specification using the ordinary least squares (OLS) method. •Goodness of fit statistics.
The goal of forecasting
To transform available data into equations that provide the best possible forecasts of economic variablesâ&#x20AC;&#x201D;e.g., sales revenues and costs of productionâ&#x20AC;&#x201D;that are crucial for management.
Demand for air travel Houston to Orlando
Recall that our demand function was estimated as follows: Now we will explain how we estimated this demand equation
Q = 25 + 3Y + PO â&#x20AC;&#x201C; 2P
[4.1]
Where Q is the number of seats sold; Y is a regional income index; P0 is the fare charged by a rival airline, and P is the airlineâ&#x20AC;&#x2122;s own fare.
Questions managers should ask about a forecasting equations
1.
What is the â&#x20AC;&#x153;bestâ&#x20AC;? equation that can be obtained (estimated) from the available data?
2.
What does the equation not explain?
3.
What can be said about the likelihood and magnitude of forecast errors?
4.
What are the profit consequences of forecast errors?
How do get the data to estimate demand forecasting equations?
â&#x20AC;˘Customer surveys and interviews. â&#x20AC;˘Controlled market studies. â&#x20AC;˘Uncontrolled market data.
Campbellâ&#x20AC;&#x2122;s soup estimates demand functions from data obtained from a survey of more than 100,000 consumers
Survey pitfalls • • • •
Sample bias Response bias Response accuracy Cost
Types of data Time -series data: historical data--i.e., the data sample consists of a series of daily, monthly, quarterly, or annual data for variables such as prices, income , employment , output , car sales, stock market indices, exchange rates, and so on. Cross-sectional data: All observations in the sample are taken from the same point in time and represent different individual entities (such as households, houses, etc.)
Time series data: Daily observations, Korean Won per dollar
Year Month Day Won per Dollar 1997 3 10 877 1997 3 11 880.5 1997 3 12 879.5 1997 3 13 880.5 1997 3 14 881.5 1997 3 17 882 1997 3 18 885 1997 3 19 887 1997 3 20 886.5 1997 3 21 887 1997 3 24 890 1997 3 25 891
Example of cross sectional data
Student ID
Sex
Age
Height
Weight
777672431
M
21
6’1”
178 lbs.
231098765
M
28
5’11”
205 lbs.
111000111
F
19
5’8”
121 lbs.
898069845
F
22
5’4”
98 lbs.
000341234
M
20
6’2”
183 lbs
Estimating demand equations using regression analysis
Regression analysis is a statistical technique that allows us to quantify the relationship between a dependent variable and one or more independent or â&#x20AC;&#x153;explanatoryâ&#x20AC;? variables.
Regression theory Y
X and Y are not perfectly correlated. However, there is on average a positive relationship between Y and X
0
X1
X2
X
We assume that expected conditional values of Y associated with alternative values of X fall on a line. Y
E(Y |Xi) = 0 + 1Xi
Y1 1
1 = Y1 - E(Y|X1)
E(Y|X1)
0
X1
X
Specifying a single variable model Our model is specified as follows: Q = f (P) where Q is ticket sales and P is the fare
Q is the dependent variable—that is, we think that variations in Q can be explained by variations in P, the “explanatory” variable.
Estimating the single variable model
Q i 0 1P i Q i 0 1P i i
[1]
Since the data points are unlikely to fall exactly on a line, (1) must be modified to include a disturbance term (εi)
[2]
0 and 1 are called parameters or population parameters. We estimate these parameters using the data we have available
Estimated Simple Linear Regression Equation
The estimated simple linear regression equation
yˆ b0 b1 x •
The graph is called the estimated regression line.
•
b0 is the y intercept of the line.
•
b1 is the slope of the line.
• yˆis the estimated value of y for a given x value.
Estimation Process Regression Model y = 0 + 1 x + Regression Equation E(y) = 0 + 1x Unknown Parameters 0, 1
b0 and b1 provide estimates of 0 and 1
Sample Data: x y x1 y1 . . . . xn yn
Estimated Regression Equation
yˆ b0 b1 x Sample Statistics b0, b1
Least Squares Method • Least Squares Criterion min (y i y i ) 2 where: yi = observed value of the dependent variable for the ith observation y^i = estimated value of the dependent variable for the ith observation
Least Squares Method • Slope for the Estimated Regression Equation
b1
( x x )( y y ) (x x ) i
i
2
i
Least Squares Method
y-Intercept for the Estimated Regression Equation
b0 y b1 x where: xi = value of independent variable for ith observation yi = value of dependent variable for ith observation _ x = mean value for independent variable _ y = mean value for dependent variable n = total number of observations
Line of best fit The line of best fit is the one that minimizes the squared sum of the vertical distances of the sample points from the line
The 4 steps of demand estimation using regression 1. Specification 2. Estimation 3. Evaluation 4. Forecasting
Year and Quarter 97-1 97-2 97-3 97-4 98-1 98-2 98-3 98-4 99-1 99-2 99-3 99-4 00-1 00-2 00-3 00-4 Mean Std. Dev.
Average Number Average Coach Seats Fare 64.8 250 33.6 265 37.8 265 83.3 240 111.7 230 137.5 225 109.6 225 96.8 220 59.5 230 83.2 235 90.5 245 105.5 240 75.7 250 91.6 240 112.7 240 102.2 235 87.3 239.7 27.9 13.1
Table 4-2 Ticket Prices and Ticket Sales along an Air Route
Simple linear regression begins by plotting Q-P values on a scatter diagram to determine if there exists an approximate linear relationship:
Scatter plot diagram 290 280 270
Fare
260 250 240 230 220 210 20
40
60
80
100
Passengers
120
140
160
Scatter plot diagram with possible line of best fit Average One-way Fare Demand curve: Q = 330-P $ 27 0 26 0 25 0 24 0 23 0 22 0 0
50
100 150 Number of Seats Sold per Flight
Note that we use X to denote the explanatory variable and Y is the dependent variable. So in our example Sales (Q) is the “Y” variable and Fares (P) is the “X” variable.
Q=Y P=X
Computing the OLS estimators
We estimated the equation using the statistical software package SPSS. It generated the following output:
Coefficientsa
Model 1
(Constant) FARE
Unstandardized Coefficients B Std. Error 478.690 88.036 -1.633 .367
a. Dependent Variable: PASS
Standardi zed Coefficien ts Beta -.766
t 5.437 -4.453
Sig. .000 .001
Reading the SPSS Output From this table we see that our estimate of 0 is 478.7 and our estimate of 1 is –1.63.
Thus our forecasting equation is given by:
Qˆ i 478.7 1.63Pi
Step 3: Evaluation Now we will evaluate the forecasting equation using standard goodness of fit statistics, including: 1.
The standard errors of the estimates.
2.
The t-statistics of the estimates of the coefficients.
3.
The standard error of the regression (s)
4.
The coefficient of determination (R2)
Standard errors of the estimates â&#x20AC;˘We assume that the regression coefficients are normally distributed variables. â&#x20AC;˘The standard error (or standard deviation) of the estimates is a measure of the dispersion of the estimates around their mean value. â&#x20AC;˘As a general principle, the smaller the standard error, the better the estimates (in terms of yielding accurate forecasts of the dependent variable).
The following rule-of-thumb is useful: The standard error of the regression coefficient should be less than half of the size of the corresponding regression coefficient.
Computing the standard error of 1 Let
s ˆ 1
denote the standard error of our estimate of 1 Note that:
Thus we have:
xi Xi X
s
ˆ
1
s
ˆ
2
and
1
e i Q i Qˆ i
Where:
s ˆ 1 2
n
e
k
i
and
2
x
i
2
k is the number of estimated coefficients
Coefficientsa
Model 1
(Constant) FARE
Unstandardized Coefficients B Std. Error 478.690 88.036 -1.633 .367
Standardi zed Coefficien ts Beta -.766
t 5.437 -4.453
Sig. .000 .001
a. Dependent Variable: PASS
By reference to the SPSS output, we see that the standard error of our estimate of 1 is 0.367, whereas the (absolute value)our estimate of 1 is 1.63 Hence our estimate is about 4 ½ times the size of its standard error.
The SPSS output tells us that the t statistic for the the fare coefficient (P) is â&#x20AC;&#x201C;4.453 The t test is a way of comparing the error suggested by the null hypothesis to the standard error of the estimate.
The t test To test for the significance of our estimate of 1, we set the following null hypothesis, H0, and the alternative hypothesis, H1 H0: 1 0 H1: 1 < 0 The t distribution is used to test for statistical significance of the estimate:
ˆ 1 1 1.63 0 t 4.45 sˆ 1 0.049
Coefficient of determination (R2) The coefficient of determination, R2, is defined as the proportion of the total variation in the dependent variable (Y) "explained" by the regression of Y on the independent variable (X). The total variation in Y or the total sum of squares (TSS) is defined as: 2
n
TSS
Y
i
Y
n
i 1
yi2
Note:
yi Yi Y
i 1
The explained variation in the dependent variable(Y) is called
the regression sum of squares (RSS) and is given by: 2
n
RSS
Yˆ i 1
i
Y
n
i 1
yˆ i 2
What remains is the unexplained variation in the dependent variable or the error sum of squares (ESS) n
2
n
ESS Yi Yˆ ei 2 i 1
i 1
We can say the following: •TSS = RSS + ESS, or •Total variation = Explained variation + Unexplained variation R2 is defined as: n
R
2
RSS TSS
ESS 1 RSS
n
yˆ i
2
i 1 n
i 1
1
yi2
ei2
i1 n
i 1
yi2
ANOVAb
Model 1
Regression Residual Total
Sum of Squares 6863.624 4846.816 11710.440
df 1 14 15
Mean Square 6863.624 346.201
F 19.826
a. Predictors: (Constant), FARE b. Dependent Variable: PASS
Model Summary
Model 1
R R Square .766a .586
Adjusted R Square .557
Std. Error of the Estimate 18.6065
a. Predictors: (Constant), FARE
We see from the SPSS model summary table that R2 for this model is .586
Sig. .001a
Notes on R2 Note that: 0 R2 1 If R2 = 0, all the sample points lie on a horizontal line or in a circle If R2 = 1, the sample points all lie on the regression line In our case, R2 0.586, meaning that 58.6 percent of the variation in the dependent variable (consumption) is explained by the regression.
This is not a particularly good fit based on R2 since 41.4 percent of the variation in the dependent variable is unexplained.
Standard error of the regression
The standard error of the regression (s) is given by:
n
s
ei
i 1
n k
2
Model Summary
Model 1
R R Square .766a .586
Adjusted R Square .557
Std. Error of the Estimate 18.6065
a. Predictors: (Constant), FARE
The model summary tells us that s = 18.6 Regression is based on the assumption that the error term is normally distributed, so that 68.7% of the actual values of the dependent variable (seats sold) should be within one standard error ($18.6 in our example) of their fitted value. Also, 95.45% of the observed values of seats sold should be within 2 standard errors of their fitted values (37.2).
Step 4: Forecasting Recall the equation obtained from the regression results is :
Qˆ i 478.7 1.63Pi Our first step is to perform an “in-sample” forecast.
At the most basic level, forecasting consists of inserting forecasted values of the explanatory variable P (fare) into the forecasting equation to obtain forecasted values of the dependent variable Q (passenger seats sold).
In-Sample Forecast of Airline Sales Year and Quarter 97-1 97-2 97-3 97-4 98-1 98-2 98-3 98-4 99-1 99-2 99-3 99-4 00-1 00-2 00-3 00-4
Predicted Sales (Q*) 64.8 33.6 37.8 83.3 111.7 137.5 109.6 96.8 59.5 83.2 90.5 105.5 75.7 91.6 112.7 102.2
Actual Sales (Q) 70.44 45.94 45.94 86.77 103.1 111.26 111.26 119.43 103.1 94.94 78.61 86.77 70.44 86.77 86.77 94.94
Q* - Q (Q* - Q)sq 5.64 31.81 12.34 152.28 8.14 66.26 3.47 12.04 -8.6 73.96 -26.24 688.54 1.66 2.76 22.63 512.12 43.6 1900.96 11.74 137.83 -11.89 141.37 -18.73 350.81 -5.26 27.67 -4.83 23.33 -25.93 672.36 -7.26 52.71
Sum of Squared Errors
4846.80
In-Sample Forecast of Airline Sales 160
140
Passengers
120
100
80
60
40
Actual
20 97.1
Fitted 97.3
98.1
98.3
99.1
Year/Quarter
99.3
00.1
00.3
Can we make a good forecast? Our ability to generate accurate forecasts of the dependent variable depends on two factors: â&#x20AC;˘Do we have good forecasts of the explanatory variable? â&#x20AC;˘Does our model exhibit structural stability, i.e., will the causal relationship between Q and P expressed in our forecasting equation hold up over time? After all, the estimated coefficients are average values for a specific time interval (1987-2001). While the past may be a serviceable guide to the future in the case of purely physical phenomena, the same principle does not necessarily hold in the realm of social phenomena (to which economy belongs).
Single Variable Regression Using Excel
We will estimate an equation and use it to predict home prices in two cities. Our data set is on the next slide
City
Income
Home Price
Akron, OH
74.1
114.9
â&#x20AC;˘Income (Y) is average family income in 2003
Atlanta, GA
82.4
126.9
Birmingham, AL
71.2
130.9
Bismark, ND
62.8
92.8
Cleveland, OH
79.2
135.8
â&#x20AC;˘Home Price (HP) is the average price of a new or existing home in 2003.
Columbia, SC
66.8
116.7
Denver, CO
82.6
161.9
Detroit, MI
85.3
145
Fort Lauderdale, FL
75.8
145.3
Hartford, CT
89.1
162.1
Lancaster, PA
75.2
125.9
Madison, WI
78.8
145.2
Naples, FL
100
173.6
Nashville, TN
77.3
125.9
87
151.5
Savannah, GA
67.8
108.1
Toledo, OH
71.2
101.1
Washington, DC
97.4
191.9
Philadelphia, PA
Model Specification
HP b0 b1Y
Scatter Diagram: Income and Home Prices 200 Home Prices
180 160 140 120 100 80 50
60
70
80 Income
90
100
110
Excel Output ANOVA df
SS 1
9355.71550 2
Residual
16
2017.36949 8
Total
17
11373.085
Regression
Coefficients
Regression Statistics Multiple R
0.906983447
R Square
0.822618973
Adjusted R Square
0.811532659
Standard Error
11.22878416
Observations
18
Standard Error
t Stat
Intercept
-48.11037724
21.58459326
-2.228922114
Income
2.332504769
0.270780116
8.614017895
Equation and prediction
HP 48.11 2.33Y City
Income
Predicted HP
Meridian, MS
59,600
$ 138,819.89
Palo Alto, CA
121,000
$ 281,881.89
Chapter 6 The Theory and Estimation of Production
The Theory and Estimation of Production The Production Function Short-Run Analysis of Total, Average, and Marginal Product Long-Run Production Function Estimation of Production Functions Importance of Production Functions in Managerial Decision Making
Learning Objectives Define production function and explain difference between short-run and long-run production function Explain “law of diminishing returns” and how it relates to the Three Stages of Production Define the Three Stages of Production and explain why a rational firm always tries to operate in Stage II
Learning Objectives Provide examples of types of inputs that might go into a production function for a manufacturing or service company Describe various forms of a production function that are used in statistical estimation of these functions Briefly describe the Cobb-Douglas function and cite a few statistical studies that used this particular functional form in their analysis
The Production Function Production function: defines the relationship between inputs and the maximum amount that can be produced within a given period of time with a given level of technology. Mathematically, the production function can be expressed as Q=f(X1, X2, ..., Xk) Q: level of output X1, X2, ..., Xk: inputs used in the production process
The Production Function Key assumptions Some given “state of the art” in the production technology. Whatever input or input combinations are included in a particular function, the output resulting from their utilization is at the maximum level.
The Production Function For simplicity we will often consider a production function of two inputs: Q=f(X, Y) Q: output X: Labor Y: Capital
The Production Function ď Ż The short-run production function shows the maximum quantity of good or service that can be produced by a set of inputs, assuming the amount of at least one of the inputs used remains unchanged. ď Ż The long-run production function shows the maximum quantity of good or service that can be produced by a set of inputs, assuming the firm is free to vary the amount of all the inputs being used.
Short-Run and Long-Run Production In the short run some inputs are fixed and some variable e.g. the firm may be able to vary the amount of labor, but cannot change the amount of capital in the short run we can talk about factor productivity
Short-Run and Long-Run Production In the long run all inputs become variable e.g. the long run is the period in which a firm can adjust all inputs to changed conditions in the long run we can talk about returns to scale (compare latter with economies of scale, which is a cost related concept)
Short-Run Changes in Production (Factor Productivity) Units of K Employed 8 7 6 5 4 3 2 1
37 42 37 31 24 17 8 4 1
60 64 52 47 39 29 18 8 2
83 78 64 58 52 41 29 14 3
Output Quantity (Q) 96 107 117 127 90 101 110 119 73 82 90 97 67 75 82 89 60 67 73 79 52 58 64 69 39 47 52 56 20 27 24 21 4 5 6 7 Units of L Employed
How much does the quantity of Q change, when the quantity of L is increased?
128 120 104 95 85 73 52 17 8
Short-Run Analysis of Total, Average, and Marginal Product Alternative terms in reference to inputs Inputs Factors Factors of production Resources
Alternative terms in reference to outputs Output Quantity (Q) Total product (TP) Product
Short-Run Analysis of Total, Average, and Marginal Product Marginal product (MP): change in output (or Total Product) resulting from a unit change in a variable input. Q MPX X
Average Product (AP): Total Product per unit of input used. AP X
Q X
Short-Run Analysis of Total, Average, and Marginal Product If MP > AP then AP is rising. If MP < AP then AP is falling. MP=AP when AP is maximized.
Short-Run Analysis of Total, Average, and Marginal Product Units of Output Total Product
196 184 161
Q from hiring fourth worker
130
Q from hiring third worker 90 Q from hiring second worker 30 Q from hiring first worker 1 increasing marginal returns
2
3
4
5
diminishing marginal returns
6
Number of Workers
Short-Run Analysis of Total, Average, and Marginal Product Law of Diminishing Returns: As additional units of a variable input are combined with a fixed input, at some point the additional output (i.e., marginal product) starts to diminish. Nothing says when diminishing returns will start to take effect, only that it will happen at some point. All inputs added to the production process are exactly the same in individual productivity
Short-Run Analysis of Total, Average, and Marginal Product The Three Stages of Production in the Short Run Stage I: From zero units of the variable input to where AP is maximized (where MP=AP) Stage II: From the maximum AP to where MP=0 Stage III: From where MP=0 on
Short-Run Analysis of Total, Average, and Marginal Product AP,MP
Stage I
Stage II
Stage III
APX Fixed input grossly underutilized; specialization and teamwork cause AP to increase when additional X is used
Specialization and teamwork continue to result in greater output when additional X is used; fixed input being properly utilized
MPX Fixed input capacity is reached; additional X causes output to fall
X
Short-Run Analysis of Total, Average, and Marginal Product In the short run, rational firms should only be operating in Stage II. Why not Stage III? Firm uses more variable inputs to produce less output
Why not Stage I? Underutilizing fixed capacity Can increase output per unit by increasing the amount of the variable input
Short-Run Analysis of Total, Average, and Marginal Product ď ŻWhat level of input usage within Stage II is best for the firm? ď ŻThe answer depends upon how many units of output the firm can sell, the price of the product, and the monetary costs of employing the variable input.
Short-Run Analysis of Total, Average, and Marginal Product Total Revenue Product (TRP): market value of the firm’s output, computed by multiplying the total product by the market price. TRP = Q · P
Marginal Revenue Product (MRP): change in the firm’s TRP resulting from a unit change in the number of inputs used. MRP =
TRP =MP ·P X
Short-Run Analysis of Total, Average, and Marginal Product Total Labor Cost (TLC): total cost of using the variable input, labor, computed by multiplying the wage rate by the number of variable inputs employed. TLC = w · X
Marginal Labor Cost (MLC): change in total labor cost resulting from a unit change in the number of variable inputs used. Because the wage rate is assumed to be constant regardless of the number of inputs used, MLC is the same as the wage rate (w).
Short-Run Analysis of Total, Average, and Marginal Product Summary of relationship between demand for output and demand for input A profit-maximizing firm operating in perfectly competitive output and input markets will be using the optimal amount of an input at the point at which the monetary value of the input’s marginal product is equal to the additional cost of using that input. MRP = MLC
Example 1
Note: P = Product Price = $2 W = Cost per unit of labor = $10000 TRP = TP x P, MRP = MP x P TLC = X x W MLC = TLC / X
Table 7.6 Combining Marginal Revenue Product (MRP) with Marginal Labor Cost (MLC) Total Marginal Total Marginal Labor Total Average Marginal Revenue Revenue Labor Labor Unit Product Product Product Product Product Cost Cost (X) (Q or TP) (AP) (MP) (TRP) (MRP) (TLC) (MLC) TRP-TLC MRP-MLC 0 0 0 0 0 0 0 1 10000 10000 10000 20000 20000 10000 10000 10000 10000 2 25000 12500 15000 50000 30000 20000 10000 30000 20000 3 45000 15000 20000 90000 40000 30000 10000 60000 30000 4 60000 15000 15000 120000 30000 40000 10000 80000 20000 5 70000 14000 10000 140000 20000 50000 10000 90000 10000 6 75000 12500 5000 150000 10000 60000 10000 90000 0 7 78000 11143 3000 156000 6000 70000 10000 86000 -4000 8 80000 10000 2000 160000 4000 80000 10000 80000 -6000
Short-Run Analysis of Total, Average, and Marginal Product Multiple variable inputs Consider the relationship between the ratio of the marginal product of one input and its cost to the ratio of the marginal product of the other input(s) and their cost.
MP1 MP2 MP k w1 w2 wk e.g., country 1 w=$2 MP(L)=2 country 2 w=$4 MP(L)=6 Then, where to produce a product? Other factors may outweigh this relationship Political/Economic risk factors`
The Long-Run Production Function In the long run, a firm has enough time to change the amount of all its inputs. Effectively, all inputs are variable.
The long run production process is described by the concept of returns to scale.
The Long-Run Production Function If all inputs into the production process are doubled, three things can happen: output can more than double increasing returns to scale (IRTS)
output can exactly double constant returns to scale (CRTS)
output can less than double decreasing returns to scale (DRTS)
The Long-Run Production Function One way to measure returns to scale is to use a coefficient of output elasticity:
Percentage change in Q EQ Percentage change in all inputs If EQ > 1 then IRTS If EQ = 1 then CRTS If EQ < 1 then DRTS
The Long-Run Production Function Returns to scale can also be described using the following equation hQ = f(kX, kY) If h > k then IRTS If h = k then CRTS If h < k then DRTS
Long-Run Changes in Production (Returns to Scale) Units of K Employed 8 7 6 5 4 3 2 1
37 42 37 31 24 17 8 4 1
60 64 52 47 39 29 18 8 2
83 78 64 58 52 41 29 14 3
Output Quantity (Q) 96 107 117 127 90 101 110 119 73 82 90 97 67 75 82 89 60 67 73 79 52 58 64 69 39 47 52 56 20 27 24 21 4 5 6 7 Units of L Employed
128 120 104 95 85 73 52 17 8
How much does the quantity of Q change, when the quantity of both L and K is increased?
The Long-Run Production Function ď ŻGraphically, the returns to scale concept can be illustrated using the following graphs.
Q
IRTS
Q
X,Y
DRTS
CRTS Q
X,Y
X,Y
Estimation of Production Functions Forms of Production Functions Short run: existence of a fixed factor to which is added a variable factor One variable, one fixed factor Q = f(L)K Increasing marginal returns followed by decreasing marginal returns Cubic function Q = a + bL + cL2 – dL3 Diminishing marginal returns, but no Stage I Quadratic function Q = a + bL - cL2
Estimation of Production Functions Forms of Production Functions Power function Q = aLb If b > 1, MP increasing If b = 1, MP constant If b < 1, MP decreasing Can be transformed into a linear equation when expressed in logarithmic terms logQ = loga + bLogL
Estimation of Production Functions Forms of Production Functions Cobb-Douglas Production Function: Q = aLbKc Both capital and labor inputs must exist for Q to be a positive number Can be increasing, decreasing, or constant returns to scale b + c > 1, IRTS b + c = 1, CRTS b + c < 1, DRTS
Permits us to investigate MP for any factor while holding all others constant Elasticities of factors are equal to their exponents
Estimation of Production Functions Forms of Production Functions Cobb-Douglas Production Function Can be estimated by linear regression analysis Can accommodate any number of independent variables Does not require that technology be held constant Shortcomings: Cannot show MP going through all three stages in one specification Cannot show a firm or industry passing through increasing, constant, and decreasing returns to scale Specification of data to be used in empirical estimates`
Estimation of Production Functions Statistical Estimation of Production Functions Inputs should be measured as “flow” rather than “stock” variables, which is not always possible. Usually, the most important input is labor. Most difficult input variable is capital. Must choose between time series and cross-sectional analysis.
Estimation of Production Functions Aggregate Production Functions Many studies using Cobb-Douglas did not deal with individual firms, rather with aggregations of industries or an economy. Gathering data for aggregate functions can be difficult. For an economy: GDP could be used For an industry: data from Census of Manufactures or production index from Federal Reserve Board For labor: data from Bureau of Labor Statistics
Importance of Production Functions in Managerial Decision Making Production levels do not depend on how much a company wants to produce, but on how much its customers want to buy. Capacity Planning: planning the amount of fixed inputs that will be used along with the variable inputs. Good capacity planning requires: Accurate forecasts of demand Effective communication between the production and marketing functions
How to determine optimal combination of inputs in the long-run • To illustrate this case, use “production isoquants” An isoquant is a curve showing all possible combinations of inputs physically capable of producing a given fixed level of output
Example 2 Production Table Units of KK Units of Employed Employed 8 7 6 5 4 3 2 1
37 42 37 31 24 17 8 4 1
60 64 52 47 39 29 18 8 2
83 78 64 58 52 41 29 14 3
Output Quantity (Q) Isoquant 96 107 117 127 128 90 101 110 119 120 73 82 90 97 104 67 75 82 89 95 60 67 73 79 85 52 58 64 69 73 39 47 52 56 52 20 27 24 21 17 4 5 6 7 8 Units of of KL Employed
An Isoquant Curve Graph of Isoquant Y
7 6
Q=52
5 4 3 2 1 0 1
2
3
4
6
X
Substituting Inputs There exists some degree of substitutability between inputs. Different degrees of substitution: Natural flavoring
Capital
Q
Sugar a) Perfect substitution
All other ingredients b) Perfect complementarity
K1 K2 K3
K4
Corn syrup
Q
L1 L2
L3
L4
Labor
c) Imperfect substitution
Substituting Inputs (continued) ď ŻIn case the two inputs are imperfectly substitutable, the optimal combination of inputs depends on the degree of substitutability and on the relative prices of the inputs
Substituting Inputs (continued) • The degree of imperfection in substitutability is measured with marginal rate of technical substitution (MRTS): MRTS = Y/X (in this MRTS some of L is removed from the production and substituted by K to maintain the same level of output)
Law of Diminishing Marginal Rate of Technical Substitution: Table Input Combinations for Isoquant Q = 52 Combination Y X A 6 2 B 4 3 C 3 4 D 2 6 E 2 8
Y -2 -1 -1 0
X 1 1 2 2
MRTS 2 1 1/2
Law of Diminishing Marginal Rate of Technical Substitution (continued) Y 7
A
6 5
B
Y =- 2
4
C
X = 1 Y = -1
3
D
X = 1
2
E
Y = -1 X = 2
1 0 2
3
4
6
8
X
MRTS = Y/X = MPX /MPY Units of Y Employed 8 7 6 5 4 3 2 1
37 42 37 31 24 17 8 4 1
60 64 52 47 39 29 18 8 2
83 78 64 58 52 41 29 14 3
Output Quantity (Q) 96 107 117 127 90 101 110 119 73 82 90 97 67 75 82 89 60 67 73 79 52 58 64 69 39 47 52 56 20 27 24 21 4 5 6 7 Units of of K X Employed
128 120 104 95 85 73 52 17 8
MRTS = Y/X = MPX /MPY MPX / MPY in Relation to MRTS (X for Y) Combination A B C D
Q 52 52 52 52
Y MPx X Mpy MRTS (L for K) MPL / MPK 6 2 4 13 3 6.5 2 2 3 11 4 11 1 1 2 6.5 6 13 1/2 1/2
Importance of production functions in managerial decision making • Example: cell phones • Asian consumers want new phone every 6 months • demand for 3G products • Nokia, Samsung, SonyEricsson must be speedy and flexible (lean manufacturing)
Importance of production functions in managerial decision making • Example: Zara • Spanish fashion retailer • factories located close to stores • quick response time to suggestion in 2-4 weeks (competitors’ responding time in 4 to 12 months)
Importance of production functions in managerial decision making • Application: call centers • service activity • production function is Q = f(X,Y) where Q = number of calls X = variable inputs Y = fixed input
Importance of production functions in managerial decision making • Application: China’s workers • is China running out of workers? • industrial boom • e.g., bicycle factory in Guangdong Province