(Solution Manual) Managerial Economics Theory, Applications, and Cases

Allen, Doherty, Mansfield, 8

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Author(s): Allen, Doherty, Mansfield

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1Lecture Notes 1. Introduction • Objectives ÿ To provide a guide to making good managerial decisions ÿ To use formal models to analyze the effects of managerial decisions on mea sures of a fi rm’s success • Managerial Economics versus Microeconomics ÿ Managerial economics differs from microeconomics in that microeco- nomics focuses on description and prediction while managerial eco-nomics is prescriptive. ÿ Managerial economics prescribes behavior, whereas microeconomics describes the environment. ÿ Managerial economics is an integrative course that brings the various functi onal areas o f bus iness to g ether in a s in gl e anal yti cal frame-work. ÿ Managerial economics exhibits economies of scope by integrating material from other disciplines and thereby reinforcing and enhancing understanding of those subjects. 2. The Theory of the Firm • Managerial Objective ÿ To make choices that will increase the value of the fi rm ÿ Managers in profi t- oriented or ga ni za tions try to increase the net pres- ent value of expected future cash fl ows. ÿ The value of the fi rm is defi ned as the present value of future profi ts:Introduction CHAPTER 12 | Chapter 1 ÿ Present value of expected future profi ts ++ +++ +$ = 1( 1 ) ( 1 )12 2ii in n/H9266/H9266 /H9266 ÿ More compactly, we write: ÿ Present value of expected future profi ts ∑=+=(1 )1it t tn/H9266 ÿ Given that profi t /H11005 total revenue /H11002 total cost, then we write: ÿ Present value of expected future profi ts (1 )1TR TC itt t tn ∑=− += ÿ Notation * pt Profi t in time t /H11005 Total Revenue in time t /H11002 Total Cost in time t * i Interest rate * n Number of time periods * TRt Total Revenue in time t * TCt Total Cost in time t • Managerial Choices ÿ Infl uence total revenue by managing demand ÿ Infl uence total cost by managing production ÿ Infl uence the relevant interest rate by managing fi nances and risk • Managerial Constraints ÿ Environmental and antitrust laws ÿ Resource scarcity ÿ Legal or contractual limitations STRATEGY SESSION: Bono Sees Red, and Corporate Profi ts See Black Discussion Questions 1. How can a fi rm assess the benefi ts and costs of cause marketing? 2. What other examples of cause marketing can you identify? 3. What Is Profi t? • Two Mea sures of Profi t ÿ Accounting profi t * Historical costs, legal compliance, reporting requirements * The accountant is concerned with controlling the fi rm’s day- to- day operations, detecting fraud and embezzlement, satisfying tax and other laws, and producing rec ords for various interested groups ÿ Economic profi t * Market value; opportunity, or implicit costIntroduction | 3 * The economist is concerned with decision making, rational choice among strategies * A more useful mea sure for managerial decision making 4. Reasons for the Existence of Profi t • Profi t ÿ Mea sures the quality of managers’ decision- making skills ÿ Encourages good management decisions by linkage with incentives • Sources of Profi t: Three profi t- generating areas ÿ Innovation: Producing products that are better than existing products in terms of functionality, technology, and style ÿ Risk taking: Future outcomes and their likelihoods are unknown, as are the reactions of rivals. ÿ Market power: Managers also earn profi t by exploiting market ineffi - ciencies. Common tactics include * building barriers to entry * employing sophisticated pricing strategies * diversifi cation efforts * making good strategic production decisions 5. Managerial Interests and the Principal– Agent Problem • Principal–Agent Problem ÿ The interests of a fi rm’s own ers and those of its managers may differ, unless the manager is the own er. ÿ Separation of own ership and control * The principals are the own ers. They want managers to maximize the value of the fi rm. * The agents are the managers. They want more compensation and less accountability. Because the fi rm’s own ers fi nd it diffi cult to adequately distinguish between actions that maximize profi ts a n d t h o s e t h a t d o n o t , m a n a g e r s h a v e i n c e n t i v e s t o e n r i c h them selves. * The divergence in goals is the principal– agent problem. * T o d e a l w i t h t h i s p r o b l e m , o w n e r s ( t h e p r i n c i p a l s ) o f t e n use  contracts to converge their preferences and those of their agents. * Moral hazard exists when a person behaves differently when he or she is not subject to the risks associated with his or her behavior. * Managers who do not maximize the value of the fi rm may do so because they do not suffer as a result of their behavior.4 | Chapter 1 ÿ Solutions * Devise methods that lead to convergence of the interests of the fi rm’s own ers and its managers. * Examples: Stock option plans or bonuses linked to profi ts 6. Demand and Supply: A First Look • Market ÿ A group of fi rms and individuals that interact with each other to buy or sell a product ÿ Part of an economy’s infrastructure ÿ A social institution that exists to facilitate economic exchange ÿ Relies on binding, enforceable contracts STRATEGY SESSION: Baseball Discovers the Law of Supply and Demand Discussion Questions 1. Do you see a relationship between variable pricing of baseball game tick- ets and odds- making on horse races? 2. How do you think real- time variable pricing would infl uence the practice of ticket scalping? 7 . The Demand Side of a Market • Demand Curve ÿ It shows managers how many units they sell at a given price, holding other possible infl uences constant. ÿ It is negatively sloped. ÿ It pertains to a par tic u lar period of time. Other infl uences on demand decisions include * consumer income * prices of substitutes and complements * advertising expenditures * product quality * government fi at • Total Revenue Function ÿ A fi rm’s total revenue ( TR) for a given time period is equal to the price charged ( P) times the quantity sold ( Q) during that time period. ÿ TR /H11005 P /H11003 Q ÿ The demand function refl ects the effect of changes in P on quantity demanded ( Q) per time period and, hence, the effect of changes in P on TR.Introduction | 5 8. The Supply Side of a Market • Supply side is represented by a market supply curve. ÿ The market supply curve shows how many units of a commodity sell- ers will offer at any price. ÿ It is positively sloped. ÿ It pertains to a par tic u lar period of time. ÿ Decreases in the cost of inputs (labor, capital, land) or technological progress cause supply curves to shift to the right. 9. Equilibrium Price • Disequilibrium ÿ Price is too high. * Excess supply or surplus * Causes price to fall ÿ Price is too low. * Excess demand or shortage * Causes price to rise • Equilibrium Price ÿ A situation in which quantity demanded is equal to quantity supplied ÿ Price is sustainable. ÿ The market is in balance because everyone who wants to purchase the good can, and every seller who wants to sell the good can. 10. Actual Price • The price that is of interest to the manager • Invisible hand: When no governmental agency is needed to induce pro- ducers to drop or increase their prices • If the actual price is above the equilibrium price, there will be a surplus that will put downward pressure on the actual price. • If the actual price is below the equilibrium price, there will be a shortage that will put upward pressure on the actual price. • If the actual price is equal to the equilibrium price, then there will be nei- ther a shortage nor a surplus and the market is said to be in equilibrium. 11. What If the Demand Curve Shifts? • Demand and supply curves are not static. They shift in reaction to changes in the environment. • Increase in Demand ÿ Represented by a rightward or upward shift in the demand curve6 | Chapter 1 ÿ Result of a change that makes buyers willing to purchase a larger quantity of a good at the current price and/or to pay a higher price for the current quantity ÿ Will create a shortage and cause the equilibrium price to increase • Decrease in Demand ÿ Represented by a leftward or downward shift in the demand curve ÿ Result of a change that makes buyers purchase a smaller quantity of a good at the current price and/or continue to buy the current quantity only if the price is reduced ÿ Will create a surplus and cause the equilibrium price to decrease 12. What If the Supply Curve Shifts? • Increase in Supply ÿ May be caused by technological advances ÿ Represented by a rightward or downward shift in the supply curve ÿ Result of a change that makes sellers willing to offer a larger quantity of a good at the current price and/or to offer the current quantity at a lower price ÿ Will create a surplus and cause the equilibrium price to decrease • Decrease in Supply ÿ Represented by a leftward or upward shift in the supply curve ÿ Result of a change that makes sellers willing to offer a smaller quan- tity of a good at the current price and/or to offer the current quantity at a higher price ÿ Will create a shortage and cause the equilibrium price to increase STRATEGY SESSION: Life During a Market Movement Discussion Questions 1. Several factors are mentioned as contributing to disequilibrium in global f o o d m a r k e t s . A m o n g t h e m a r e e m o t i o n s ( p a n i c ) , g o v e r n m e n t r e s t r i c -tions on trade, the Malthusian specter of population growth outpacing food production, slowing productivity growth in the agricultural sector, rising incomes, and the production of ethanol. Which of these are supply factors and which are demand factors? How does each infl uence market price? 2. The market price for crude oil fl uctuated widely during 2008. What sup- ply and demand factors contributed to these fl uctuations? Is the petroleum market subject to any of the same factors cited as infl uencing agricultural markets?Introduction | 7 Chapter 1: Problem Solutions 1. A book is to be written by Britney Spears. Batman Books agrees to pay Britney $6 million for the rights to this not- yet- written memoir. According to one leading publisher, Batman Books could earn a profi t of roughly $1.2 million if it sold 625,000 copies in hardcover. On the other hand, if it sold 375,000 copies, managers would lose about $1.3 million. Publishing execu-tives stated that it was hard to sell more than 500,000 copies of a nonfi ction hardcover book, and very exceptional to sell 1 million copies. Were Batman managers taking a substantial risk in publishing this book? Solution: There was a substantial risk of loss. On the other hand, there was substantial opportunity for gain. Risk is often unavoidable. The appropriate balance between risk and return is what should determine managers’ decisions. Suc-cessful decisions in circumstances of risk are a source of profi t. 2. Some say that any self- respecting top manager joining a company does so with a front- end signing bonus. In many cases this bonus is in the seven fi g- ures. At the same time the entering manager may be given a bonus guaran-tee. No matter what happens to fi rm profi t, he or she gets at least a percentage of that bonus. Do long- term bonus guarantees help to solve the principal– agent problem, or do they exacerbate it? Why? Solution: An executive who spends a lifetime working for a single company or in a single industry has a poorly diversifi ed human capital portfolio. Such an executive also often has a signifi cant, undiversifi ed fi nancial investment in the form of stock options and pension plans that are used in partial substi-tution for current salary to align the long- term wealth of the executive with that of the shareholders. As an executive climbs the corporate ladder, the value of his or her human capital becomes more closely tied to the fortunes of the fi rm and industry. This lack of diversifi cation requires a compensating risk premium. A large signing bonus may allow a risk- averse executive to make an investment, which increases the value of the fi rm but which the executive would otherwise avoid because of concern for his or her own personal wealth; thus the bonus may reduce the principal– agent confl ict. Of course the bene- fi ts of reduced risk to the executive come at the potential cost of indifference to the wealth of the shareholders. Although a large signing bonus may help solve the incentive alignment problem, compensation that is too great and too insensitive to the fortunes of the shareholders makes the principal– agent problem worse.8 | Chapter 1 3. If the interest rate is 10%, what is the present value of the Monroe Corpora- tion’s profi t in the next 10 years? Number of Years in the FutureProfi t (millions of dollars) 1 8 21 0 31 2 41 4 51 5 61 6 71 7 81 5 91 310 10 Solution: Use formula (1.1) for t /H11005 1, 2, . . . , 10 to obtain the following table: Number of Years in the FutureProfi t (millions of dollars) (1 /H11001 i)/H11002tPresent Value (millions of dollars) 1 8 0.90909 7.27272 2 10 0.82645 8.264503 12 0.75131 9.015724 14 0.68301 9.562145 15 0.62092 9.313806 16 0.56447 9.031527 17 0.51316 8.723728 15 0.46651 6.997659 13 0.42410 5.51330 10 10 0.38554 3.85540 Total 77.55047 The answer is $77.55047 million. 4. Managers at Du Pont de Nemours and Company expect a profi t of $2.9 bil- lion in 2012. Does this mean that Du Pont’ s expected economic profi t will equal $2.9 billion? Why or why not? Solution: Economic profi ts differ from accounting profi ts because of differences in the way depreciation is mea sured, differences in the way revenues and costs are recognized in terms of timing, and the inclusion of the opportu-nity cost of owner- supplied inputs in the calculation of economic profi ts. Introduction | 9 Du Pont’s economic profi ts might well be negative if accounting profi ts do not exceed the risk- adjusted rate of return multiplied by the fi rm’s equity value. 5. William Howe must decide whether to start a business renting beach umbrel- las at an ocean resort during June, July, and August of next summer. He believes he can rent each umbrella to vacationers at $5 a day, and he intends to lease 50 umbrellas for the three- month period for $3,000. To operate this business, he does not have to hire anyone (but himself), and he has no expenses other than the leasing costs and a fee of $3,000 per month to rent the business location. Howe is a college student, and if he did not operate this business, he could earn $4,000 for the three- month period doing con-struction work.a. If there are 80 days during the summer when beach umbrellas are demanded and Howe rents all 50 of his umbrellas on each of these days, what will be his accounting profi t for the summer? b. What will be his economic profi t for the summer? Solution: a. TR /H11005 (80 days) /H11003 (50 umbrellas) /H11003 ($5 per day) /H11005 $20,000 TC /H11005 (3 months) /H11003 ($3,000 per month rent) /H11001 ($3,000 umbrella lease) /H11005 $12,000 Accounting Profi t /H11005 TR/H11002TC /H11005 $8,000 b. Economic Profi t /H11005 Accounting Profi t /H11002 Opportunity Cost Economic Profi t /H11005 $8,000 /H11002 $4,000 /H11005 $4,000 6. On March 3, 2008, a revival of Gypsy, the Stephen Sondheim musical, opened at the St. James Theater in New York. Ticket prices ranged from $117 to $42 per seat. The show’s weekly gross revenues, operating costs, and profi t were estimated as follows, depending on whether the average ticket price was $75 or $65: Average Price of $75Average Price of $65 Gross revenues $765,000 $680,000 Operating costs 600,000 600,000Profi t 165,000 80,000 a. With a cast of 71 people, a 30- piece orchestra, and more than 500 cos- tumes, Gypsy cost more than $10 million to stage. This investment was in addition to the operating costs (such as salaries and theater rent). How many weeks would it take before the investors got their money back, according to these estimates, if the average price was $65? If it was $75?10 | Chapter 1 b. George W achtel, director of research for the League of American The- aters and Producers, has said that about one in three shows opening on Broadway in recent years has at least broken even. Were the investors in Gypsy taking a substantial risk? c. According to one Broadway producer, “Broadway isn’t where you make the money any more. It’s where you establish the project so you can make the money. When you mount a show now, you really have to think about where it’s going to play later.” If so, should the profi t fi gures here be interpreted with caution? d. If the investors in this revival of Gypsy make a profi t, will this profi t be, at least in part, a reward for bearing risk? Solution: a. Given a price of $75, the weekly operating profi t of $165,000 would pay off the $10 million investment in 10,000/165 /H11005 60.6 or 61 weeks. If the price is $65, it would take 10,000/80 /H11005 125 weeks to pay off the investment. This does not provide for any return on investment, however. b. The investors in Gypsy were indeed taking a substantial risk. If only one in three shows breaks even, two out of three make losses. c. The profi t fi gures should be interpreted with caution because they do not take into account the likelihood of profi ts when, and if, the show goes on the road. d. Yes. 7. If the demand curve for wheat in the United States is P /H11005 12.4 /H11002 Q D where P is the farm price of wheat (in dollars per bushel) and QD is the quantity of wheat demanded (in billions of bushels), and the supply curve for wheat in the United States is P /H11005 /H110022.6 /H11001 2Q S where QS is the quantity of wheat supplied (in billions of bushels), what is  the equilibrium price of wheat? What is the equilibrium quantity of wheat sold? Must the actual price equal the equilibrium price? Why or why not? Solution: Setting demand equal to supply in equilibrium, that is, Q D /H11005 QS /H11005 QE, yields 12.4 /H11002 QD /H11005 /H110022.6 /H11001 2QS QE /H11005 15/3 /H11005 5 PE /H11005 12.4 /H11002 5 /H11005 /H110022.6 /H11001 (2)(5) /H11005 $7.40Introduction | 11 The actual price need not be equal to equilibrium price, although it will generally tend to move toward it because of the equilibrating effects of shortage and surplus. Factors that might prevent the actual price from equaling the equilibrium price include the cost and availability of infor-mation, transportation costs, and lack of opportunities for price- equalizing arbitrage. 8. The lumber industry was hit hard by the downturn in housing starts in 2010 and 2011. Prices plunged from $290 per thousand board feet to less than $200 per thousand board feet. Many observers believed this price decrease was caused by the slowing of new home construction because of the glut of unsold homes on the market. Was this price decrease caused by a shift in the supply or demand curve? Solution: Because the demand for lumber is derived in large part from the demand for new housing construction, a decline in construction would be likely to cause the demand for lumber to fall, leading to lower lumber prices since the demand curve shifts to the left. Supply would not be affected by changes in housing construction. 9. From November 2010 to March 2011 the price of gold increased from $1,200 per ounce to over $1,800 per ounce. Newspaper articles during this period said there was little increased demand from the jewelry industry but signifi - cantly more demand from investors who were purchasing gold because of the falling dollar.a. Was this price increase due to a shift in the demand curve for gold, a shift in the supply curve for gold, or both? b. Did this price increase affect the supply curve for gold jewelry? If so, how? Solution: a. A change in the value of the dollar causes the dollar price of globally traded commodities to change. If the value of the dollar falls, the dollar price of commodities will rise. In this case, a decline in the value of the dollar can be expected to cause the market for gold (with price mea sured in dollars) to experience an increase in demand and a decrease in supply and thus an increase in price. There may also have been an additional increase in demand due to expectations by investors that the dollar price of gold will continue to rise. Finally, there may have been a further supply decrease if producers, speculating that prices would rise further, withheld gold from the market.12 | Chapter 1 b. Gold is an input to the production of jewelry. An increase in the price of gold would therefore be expected to reduce the supply of jewelry, result-ing in higher jewelry prices.13Lecture Notes 1. Introduction • Objectives ÿ To explain the importance of market demand in managerial decision making ÿ To understand the many factors that infl uence the demand for a product ÿ To mea sure and analyze the sensitivity of demand to changes in fac- tors affecting demand. The tool used for this type of sensitivity analy-sis is demand elasticity . * Elasticity: Mea sures the percentage change in one factor given a small (marginal) percentage change in another factor * Elasticity: Mea sures the sensitivity of one factor to another * Demand elasticity: Mea sures the percentage change in quantity demanded of a product given a small (marginal) percentage change in another factor that affects the demand for the product ÿ Explain the role of managers in infl uencing and predicting market demand. * Managers can infl uence demand by controlling, among other things, advertising, product quality, and distribution strategies. * Managers cannot control, but need to understand, elements of the competitive environment that infl uence demand, including the availability of substitute or complement goods, their pricing, and the advertising strategies employed by their sellers. * Managers cannot control, but need to understand how, the macro- economic environment infl uences demand, including interest rates, taxes, and both local and global levels of economic activity such as the level of income in the economy.Demand Theory CHAPTER 214 | Chapter 2 2. The Market Demand Curve • Market Demand Schedule: A table showing the total quantity of the good purchased at each price during a given time period • Market Demand Curve: A plot of the market demand schedule on a graph • Example (Table 2.1): Demand schedule for tablets • It shows the total quantity of tablets demanded at each price, not the quan- tity demanded from a par tic u lar fi rm. ÿ Convention: Price is on the vertical axis and quantity is on the hori- zontal axis. ÿ Example (Figure 2.1): Demand curve for tablets • Characteristics of the Market Demand Curve ÿ Quantity demanded is for output of the entire market or the industry, not of a single fi rm. ÿ For most products and ser vices, the market demand curve slopes downward and to the right. ÿ Example: The quantity of tablets demanded increases as the price of tablets falls. ÿ Quantity demanded is defi ned with regard to a par tic u lar time period. • Determinants of the position and shape of the market demand curve— Some of the important factors includeÿ Consumer tastes or preferences * An increase in consumer tastes shifts the demand curve to the right. * A decrease in consumer tastes shifts the demand curve to the left. ÿ Consumer income (or more specifi cally per capita disposable income) * Normal and inferior goods * Example (Figure 2.3): Increase in income causes an increase in demand for tablets; that is, tablets are a normal good. ÿ Population size in the market STRATEGY SESSION: The Customer Is Always Right— Wrong! Discussion Questions 1. Like retail technology stores, clothing stores have their angels and dev ils. How do you think the dev ils prey on clothing stores, and how could their behavior be discouraged? How do you think angels could be encouraged to shop at a par tic u lar clothing store? Answer: Dev ils buy clothes, wear them, and then return them for a refund. Stores can refuse to provide refunds on returns and, instead, provide a credit for future purchases or only allow exchanges. Angels buy lots of clothes on impulse. Stores could offer quantity discounts or a “shoppers club” with special notifi cation of sales.Demand Theory | 15 2. Some electronics stores refuse to allow customers to return or exchange products, instead requiring them to deal directly with the manufacturer. What are the pros and cons of this approach with regard to the stores’ objective of encouraging angels and discouraging dev ils? 3. Industry and Firm Demand Functions • Market Demand Function: The relationship between the quantity demanded of a product and the various factors that infl uence this quantity ÿ Quantity demanded of good X: Q /H11005 f(factors) /H11005 f(P, P_r, I, T, N, A , …) ÿ Factors include * price of X: P * incomes of consumers: I * tastes of consumers: T * prices of related goods in consumption: P_r * population size: N * advertising expenditures: A * general demand function: Q /H11005 f(factors) /H11005 f(P, P_r,I,T,N,A, other factors) ÿ Example (equation 2.1): A linear demand function: Q /H11005 b 1P /H11001 b2I /H11001 b3S /H11001 b4A * Assumes that population is constant * P /H11005 price of tablets * I /H11005 per capita disposable income * S /H11005 average price of software * A /H11005 amount spent on advertising * b1, b2, b3, and b4 are pa ram e ters that are estimated using statistical methods, namely, regression analysis . ÿ Pa ram e ters: Constant or variable terms used in the function that helps managers determine the specifi c form of the function but not its gen- eral nature * Example: Q /H11005 /H110022,000 P /H11001 70I /H11002 375S /H11001 0.0001 A ÿ Relationship between the market demand function and the market demand curve * The market demand curve shows the relationship between Q and P when all other variables are held constant at specifi c values. * The market demand function does not explicitly hold any values constant. ÿ Example (equation 2.3): Suppose I /H11005 13,000, S /H11005 400, and A /H11005 50 mil- lion. Then ÿ Q /H11005 /H11002700P /H11001 200(13,000) /H11002 500(400) /H11001 0.01(50,000,000) That is16 | Chapter 2 * Q /H11005 2,900,000 /H11002 700P (direct demand function) Solving for P in terms of Q gives the inverse demand function: P /H11005 4,143 /H11002 0.001429 Q (graphed in Figure 2.4) ÿ Example : Shifting the demand curve Suppose the price of software falls from $400 to $200. Then Q /H11005 /H11002700P /H11001 200(13,000) /H11002 500(200) /H11001 0.01(50,000,000) Q /H11005 3,000,000 /H11002 700P * Solving for P gives P /H11005 4,286 /H11002 0.001429 Q (graphed in Figure 2.4) Note: Same slope; only the vertical intercept changes. • The Firm’s Demand Curve ÿ Negative slope with regard to own price * Slope may not be the same as that of the market demand curve ÿ Represents a portion of market demand * Market share * Responds to same market and macroeconomic factors as the mar- ket demand curve 4. The Own- Price Elasticity of Demand • Own- Price Elasticity of Demand: More simply referred to as the price elas- ticity of demand, it is the concept that managers use to mea sure the per-cen tag e c han g e in q uan ti ty deman ded o f the ir fi rm’s products resulting from a 1% change in the products’ own prices.ÿ The elasticity of a function is the percentage change in the dependent (Y) variable in response to a 1% change in the in de pen dent ( X) variable. ÿ The price elasticity of a demand function is the percentage change in quantity demanded in response to a 1% change in price. ÿ Formula: P QQ P/H9257/H9004 /H9004=⎛ ⎝⎜⎞ ⎠⎟ ÿ Along a demand function, it is given by P QQ P/H9257=⎛ ⎝⎜⎞ ⎠⎟∂ ∂ ÿ Price elasticity of demand generally is different at different prices and on different markets.Demand Theory | 17 • Terminology ÿ Price elasticity of demand is symbolized by the Greek letter eta ( h) (not a general convention). ÿ Fact: 0 ≥ h ≥ /H11002∞. That is, price elasticity of demand is always non- positive. ÿ When | h| /H11022 1, demand is elastic. ÿ When | h| /H11021 1, demand is inelastic. ÿ When | h| /H11005 1 or h /H11005 /H110021, demand is unitary. Limiting cases: ÿ When h /H11005 0, demand is perfectly inelastic and the demand curve is vertical. * Quantity demanded is the same at all prices. ÿ When h /H11005 /H11002∞, demand is perfectly elastic and the demand curve is horizontal. * Price is the same for all quantities demanded. * If price rises, quantity demanded falls to zero. * If price falls, quantity demanded increases without limit. • Linear Demand Curves ÿ The slope of a linear demand curve is constant. ÿ If the demand curve is neither vertical nor horizontal, the price elas- ticity will vary depending on price level. * At the midpoint of a linear demand curve, h /H11005 /H110021, with h approach- ing zero as price approaches the vertical intercept. * At prices above the midpoint, demand is elastic, with h approaching negative infi nity as quantity approaches zero or as price approaches the vertical intercept. * At prices below the midpoint, demand is inelastic, with h approach- ing 0 as price approaching 0. ÿ Given a demand curve defi ned as P /H11005 a/H11002bQ, the price elasticity of demand is: 1/( )bab Q QPaP /H9257=−⎛ ⎝⎜⎞ ⎠⎟−=−− 5. Point and Arc Elasticities • The point price elasticity formula should be used when working with an estimated demand curve or when the change in price is very small. It is written as P QQ P/H9257=⎛ ⎝⎜⎞ ⎠⎟∂ ∂ ÿ Calculated value of price elasticity for small changes in prices will differ depending on whether P and Q are the starting values or the ending values after the price change. The change will be small if the change is small.18 | Chapter 2 * Example: P1 /H11005 99.95, P2 /H11005 100.00, Q1 /H11005 20,002, and Q2 /H11005 20,000 * h /H11005 [(20,002 /H11002 20,000)/(99.95 /H11002 100)][99.95/20,002] /H11005 /H110020.1999 * h /H11005 [(20,000 /H11002 20,002)/(100 /H11002 99.95][100/200,000] /H11005 /H110020.22 ÿ If the price change is large, then the direction of change will infl uence the calculated elasticity. * Example: P1 /H11005 5, P2 /H11005 4, Q1 /H11005 3, and Q2 /H11005 40 * h /H11005 [(40 /H11002 3)/(4 /H11002 5)][5/3] /H11005 /H11002 61.67 * h /H11005 [(3 /H11002 40)/(5 /H11002 4)][4/40] /H11005 /H11002 3.70 ÿ This problem is corrected by using the arc or midpoint formula. • Recommendation: The midpoint or arc elasticity formula should be used to estimate the price elasticity of demand from a demand schedule where price differences are not very small. It is given by =⎛ ⎝⎜⎞ ⎠⎟+ +⎛ ⎝⎜⎞ ⎠⎟12 12Q PPP QQ/H9257/H9004 /H9004 ÿ Example: P1 /H11005 5, P2 /H11005 4, Q1 /H11005 3, and Q2 /H11005 40 ÿ h /H11005 [(40 /H11002 3)/(4 /H11002 5)][(5 /H11001 4)/(3 /H11001 40)] /H11005 /H110027.74 6. Using the Demand Function to Calculate the Price Elasticity of Demand Whenever the demand function is specifi ed, one usually uses the point price elasticity of demand.• Example: Given ÿ Q /H11005 /H11002 700P /H11001 200I /H11002 500S /H11001 0.01A ÿ Q /H11005 Quantity demanded of tablet computers ÿ Price /H11005 P /H11005 3,000 ÿ Income /H11005 I /H11005 13,000 ÿ Software /H11005 S /H11005 400 ÿ Advertising /H11005 A /H11005 50,000,000 • Derive the demand curve ÿ Q /H11005 /H11002 700P /H11001 (200)(13,000) /H11002 (500)(400) /H11001 (0.01)(50,000,000) ÿ Q /H11005 2,900,000 /H11002 700P • Determine Q ÿ Q /H11005 2,900,000 /H11002 (700)(3,000) /H11005 800,000. We have 700Q P∂ ∂=− . Thus • h /H11005 (/H11002700)(3,000/800,000) /H11005 /H110022.62 • For P /H11005 2,000, Q /H11005 2,900,000 /H11002 (700)(2,000) /H11005 1,500,000, so h /H11005 (/H11002700)(2,000/1,500,000) /H11005 /H110020.93Demand Theory | 19 7 . The Effect of Price Elasticity on the Firm’s Revenue • Derivation of relationship between marginal revenue ( /H9004TR//H9004Q or dTR/ dQ) and the price elasticity of demand ÿ Total revenue: TR /H11005 PQ ÿ Consider quantity as a function of price: Q /H11005 f(P). Then, differentiat- ing TR with respect to P, using the product rule for derivative, gives dTR/dP /H11005 Q(dP/dP) /H11001 P(dQ/dP) Dividing by Q gives (1/Q)(dTR/dP) /H11005 (dP/dP) /H11001 (P/Q)(dQ/dP) /H11005 1 /H11001 h • 1/ Q is positive. • Implications: ÿ Case 1: If h /H11005 /H110021, that is, unitary elastic demand, then 1 /H11001 h /H11005 0, and dTR/dP /H11005 0, so total revenue is at a maximum and a change in P will have no effect on total revenue. ÿ Case 2: If h /H11022 /H110021 (inelastic demand ), then 1 /H11001 h /H11022 0 and dTR/dP /H11022 0, so an increase in P (and consequent decrease in Q) will increase total revenue. ÿ Case 3: If h /H11021 /H110021 (elastic demand ), then 1 /H11001 h /H11021 0, and dTR/dP /H11021 0, so an increase in P (and consequent decrease in Q) will reduce total revenue. ÿ To summarize: • If the price elasticity is unitary, any price change will cause an equal and opposite percentage change in quantity demanded. Total revenue will remain constant. • If the price elasticity is in the inelastic range, then a 1% change in P will cause less than a 1% change in quantity in the opposite direction. There-fore, total revenue will change in the same direction as price. • If the price elasticity is in the inelastic range, then a 1% change in P will cause more than a 1% change in quantity in the opposite direction. There-fore, total revenue will change in the opposite direction from price. PROBLEM SOLVED: Price Elasticity of Demand: Philip Morris Discussion Questions 1. The decline in total revenue from cigarette sales in 1993 is attributed to Philip Morris’s cut in the price of cigarettes. Are there other factors that might have contributed to this decline in revenue? Answer: The price elasticity of demand assumes that “all other things” are held constant. Changes in taxes, consumer income, or attitudes toward 20 | Chapter 2 tobacco during this period might have reduced demand, while the price cut increased quantity demanded. If this was the case, then the true price elasticity would likely be closer to /H110021. 8. Funding Public Transit • Given ÿ Price (fare) elasticity of demand for public transit in the United States is estimated to be about /H110020.3. Facts:ÿ All public transit systems in the United States lose money. ÿ Public transit systems are funded by federal, state, and local govern- ments, all of which have bud get issues. • Which transit systems have the most diffi cult time getting public funding? ÿ Revenue from sales will increase if fares are increased because demand is inelastic. ÿ Costs will likely decrease if fares are increased because quantity demanded (ridership) will fall. ÿ Implication: Managers of public transit will therefore increase fares if they do not receive enough public funds to balance their bud gets. 9. Determinants of the Own- Price Elasticity of Demand • Number and Similarity of Available Substitutes Fact: A product with many close substitutes generally has elastic demand. • Product’s Price Relative to a Consumer’s Total Bud get ÿ Facts: * Products for which the typical consumer spends only a very small fraction of her income are quite elastic. ° Examples: Thimbles, rubber bands, salt * Products that command a larger percentage of the consumer’s total bud get tend to be more price elastic. ° Examples: Kitchen appliances, automobiles • Time Period Available for Adjustment to a Price Change ÿ Fact: For nondurable goods, demand is likely to be more elastic over a long period relative to a short period. ÿ Rationale: The longer the time period, the easier it is for consumers to substitute one good for another. 10. The Strategic Use of the Price Elasticity of Demand • Managers can change the price elasticity of demand for their products. • A Useful Tool: Product differentiationDemand Theory | 21 • Differentiation strategies convince consumers the product is unique; hence it has fewer substitutes. • Caution: Differentiation is not effective if consumers do not perceive it. • Example: Strategic pricing of fi rst- class ( h /H11005 /H110020.45), regular economy (h /H11005 /H110021.30), and excursion ( h /H11005 /H110021.83) airline tickets between the United States and Eu ropeÿ First- class prices should be relatively high because demand is inelastic. ÿ Regular economy and excursion prices should be relatively low because demand is elastic. ÿ If consumers perceive that a product has fewer substitutes, then their price elasticity of demand for the product will decrease (become less elastic) in absolute value. ÿ Differentiation strategies do not require actual differences in prod- ucts, only a perceived difference. STRATEGY SESSION: Elasticity in Use Discussion Questions 1. Suppose that a manufacturer sells a product through an upscale boutique and, with a different brand name, through a discount retailer. The elasticity of demand at the boutique is /H110021.2, and at the discount retailer it is /H110022.6. If the optimal price at the boutique is $85, what price ( P D) should be charged at the discount retailer? Answer: 85(1 /H11002 1/1.2) /H11005 PD(1 /H11002 1/2.6) so PD /H11005 $23.02 2. A consulting fi rm charges $250 per hour to Fortune 500 companies. The estimated elasticity of demand for consulting ser vices is /H110023.1. The fi rm is planning to spin off a subsidiary fi rm that will work with smaller businesses. The estimated elasticity of demand for these fi rms is /H110027.3. What price per hour ( PS), to the nearest dollar, should be charged by the subsidiary? Answer: 250(1 /H11002 1/3.1) /H11005 PS(1 /H11002 1/7.3) so PS /H11005 $200 11. Total Revenue, Marginal Revenue, and Price Elasticity • A fi rm’s total revenue ( TR) is equal to the total amount of money consumers spend on the product in a given time period.ÿ Linear demand curve: P /H11005 a– bQ ÿ Corresponding total revenue curve: TR /H11005 PQ /H11005 aQ– bQ 2 • Marginal Revenue: The incremental revenue earned from selling an addi- tional unit of outputÿ MR /H11005 dTR/dQ /H11005 d( aQ– bQ 2)/dQ /H11005 a /H11002 2bQ * h /H11005 (/H110021/b)[(a–bQ )/Q] /H11005 /H11002a/(bQ) /H11001 122 | Chapter 2 * Case 1: If Q /H11005 a/2b, then h /H11005 /H110021, unitary elastic demand. * Case 2: If Q /H11022 a/2b, then h /H11022 /H110021, and demand is inelastic. * Case 3: If Q /H11021 a/2b, then h /H11021 /H110021, and demand is elastic. ÿ MR /H11005 dTR/dQ /H11005 d(PQ)/dQ /H11005 P(dQ/dQ) /H11001 Q(dP/dQ) /H11005 P[1 /H11001 (Q/P) (dP/dQ). Thus MR /H11005 P(1 /H11001 1/h) * Case 1: |h| /H110221 (elastic) implies MR /H11022 0. * Case 2: |h| /H110211 (inelastic) implies MR /H11021 0. * Case 3: |h| /H110051 (unitary elastic) implies MR /H11005 0. 12. The Income Elasticity of Demand • Income Elasticity of Demand (hI): Mea sures the percentage change in quan- tity demanded ( Q) resulting from a 1% change in consumer income ( I) ÿ Income can be defi ned as aggregate consumer income or as per capita disposable income, depending on circumstances. ÿ =⎛ ⎝⎜⎞ ⎠⎟⎛ ⎝⎜⎞ ⎠⎟Q II QI/H9257/H9004 /H9004 ÿ For a demand function, it is given by I QQ I/H9257=⎛ ⎝⎜⎞ ⎠⎟∂ ∂ ÿ hI /H11022 0 for normal goods because 0Q I∂ ∂> for normal goods. * For most products, hI /H11022 0; that is, most goods are normal, since increases in aggregate income are associated with increases in aggregate consumer spending. ÿ h I /H11021 0 for inferior goods because 0Q I∂ ∂< for inferior goods. * Examples: Hamburgers and public transportation * Fact: When the economy is expanding, products with high- income elasticities will enjoy a signifi cant increase in sales and managers must prepare for probable signifi cant increase in sales. • Strategic Management and the Income Elasticity of Demand ÿ The demand for a product that has an income elasticity of demand that i s l ar g e in a b s o l u te v al u e will v ary wi d e l y wi th c h an g e s in in c o m e caused by economic growth and recessions. ÿ Managers can lessen the impact of economic changes on such prod- ucts by limiting fi xed costs so that changes in production capacity can be made quickly. ÿ Managers can forecast demand for products using the income elastic- ity of demand combined with forecasts of aggregate income.Demand Theory | 23 PROBLEM SOLVED: Income Elasticity of Demand Discussion Questions 1. S u p p o s e t h a t a m a r k e t d e m a n d f u n c t io n i s d e fi ned as Q /H11005 20,000 /H11002 8P /H11001 0.1I and suppose that P /H11005 2,000 and I /H11005 20,000. What is the income elasticity of demand at this point? Answer: Here, we have ∂ ∂0.1Q I/H11005 (a normal good). Then we have Q /H11005 6,000, so that hI /H11005 0.1(20,000/6,000) /H11005 /H110021/3 2. If the income elasticity of demand for a product is unitary, then a 1% chan g e in income will chan g e demand in the same directi on b y 1 % . If price remains constant, then spending on the product will change by 1% and, consequently, spending on the product will be the same percentage of income after the income change as it was before. If the income elastic-ity of demand is greater than one, then spending will increase as a per-centage of income as income increases. If it is less than one, spending will decrease as a percentage of income as income increases. How do you think the percentage of income spent on jewelry, food, clothing, housing, and automobiles responds to a 1% increase in income? 13. Cross- Price Elasticities of Demand • Cross- Price Elasticity of Demand (h XY): The percentage change in quan- tity demanded of one good ( QX) resulting from a 1% change in the price of a related good ( PY) ÿ Income can be defi ned as aggregate consumer income or as per capita disposable income, depending on circumstances. ÿ =⎛ ⎝⎜⎞ ⎠⎟⎛ ⎝⎜⎞ ⎠⎟Q PP QXYX YY X/H9257/H9004 /H9004 ÿ hXY /H11022 0 if the two products are substitutes. * Example: Wheat and corn ÿ hXY /H11021 0 if the two products are complements. * Example : Computers and computer software ÿ hXY /H11005 0 if the two products are in de pen dent or unrelated. * Example : Butter and airline tickets ÿ Example : A linear demand function * Given: QX /H11005 1,000 /H11002 0.2PX /H11001 0.5PY /H11001 0.04 I, QX /H11005 2,000, and PY /H11005 500 * hXY /H11005 0.5(500/2,000) /H11005 0.125 so the two products are substitutes.24 | Chapter 2 • Strategic management and the cross- price elasticity of demand ÿ Managers can use information about the cross- price elasticity of demand to predict the effect of competitors’ pricing strategies on the demand for their product. ÿ Antitrust authorities use the cross- price elasticity of demand to deter- mine the likely effect of mergers on the degree of competition in an industry. * A high positive cross- price elasticity, indicating that the two goods are strong substitutes, suggests that a merger would signifi cantly reduce competition in the industry. * A high negative cross- price elasticity of demand, indicating that the two goods are strong complements, suggests that a merger might give the merged fi rm excessive control over the supply chain. The merged fi rm may refuse to sell the intermediate product to other producers. 14. The Advertising Elasticity of Demand • Advertising Elasticity of Demand (h A): The percentage change in quantity demanded ( Q) resulting from a 1% change in advertising expenditure ( A) ÿ =⎛ ⎝⎜⎞ ⎠⎟⎛ ⎝⎜⎞ ⎠⎟Q AA QA/H9257/H9004 /H9004 ÿ Example calculation: A linear demand function * Suppose: Q /H11005 500 /H11002 0.5P /H11001 0.01I /H11001 0.82 A and suppose, A/Q, the amount of advertising per unit of output, is $2. Then * hA /H11005 0.82(2) /H11005 1.64, indicating that a 1% increase in income results in a 1.64% increase in the quantity demanded. 15. The Constant- Elasticity and Unitary Demand Function • Constant- Elasticity Demand Function: Mathematical form of a demand function that always yields that same elasticity, regardless of the product’s price and consumers’ income and other factors that infl uence demand ÿ Example: A multiplicative demand function Q /H11005 200P /H110020.3I 2 ÿ Price elasticity of demand /H11005 /H11002 0.3 ÿ Income elasticity of demand /H11005 2.0 ÿ More generally, an example of a constant elasticity demand function is Q/H11005 aP /H11002 bIc where a, b, c are pa ram e ters to be estimated. ÿ Price elasticity of demand /H11005 –b ÿ Income elasticity of demand /H11005 cDemand Theory | 25 ÿ Fact: For a multiplicative demand function, the exponents represent elasticities. • Unitary elastic demand function and total revenue ( TR) ÿ TR /H11005 PQ so if TR is constant, Q /H11005 (TR)(P /H11002 1) ÿ Price elasticity of demand /H11005 /H11002 1 ÿ More generally, a unitary elastic demand curve is given by the demand function Q /H11005 mP /H11002 1 or Q /H11005 m/P ÿ Its graph: A rectangular hyperbola Chapter 2: Problem Solutions 1. The Dolan Corporation, a maker of small engines, determines that in 2012 the demand curve for its product is P /H11005 2,000 /H11002 50Q where P is the price (in dollars) of an engine and Q is the number of engines sold per month.a. To sell 20 engines per month, what price would Dolan have to charge?b. If managers set a price of $500, how many engines will Dolan sell per month? c. What is the price elasticity of demand if price equals $500?d. At what price, if any, will the demand for Dolan’s engines be of unitary elasticity? Solution: a. For Q /H11005 20, P /H11005 2,000 /H11002 50(20) /H11005 $1,000. b. For P /H11005 500, we have 500 /H11005 2,000 /H11002 50Q. Solving for Q gives 50 Q /H11005 1,500, that is, Q /H11005 30. c. h /H11005 (≠Q /≠P)(P/Q) /H11005 ( /H110021/50)(500/30) /H11005 /H110021/3. d. For P /H11005 $1,000, h /H11005 (≠Q/≠ P)(P/Q) /H11005 ( /H110021/50)(1,000/20) /H11005 /H110021. Alternatively, set ( /H110021/50)(2,000 /H11002 50Q)/Q /H11005 /H11002 1. Solve for Q and then P. 2. The Johnson Robot Company’s marketing managers estimate that the demand curve for the company’s robots in 2012 is P /H11005 3,000 /H11002 40Q where P is the price of a robot and Q is the number sold per month. a. Derive the marginal revenue curve for the fi rm. b. At what prices is the demand for the fi rm’s product price elastic? c. If the fi rm wants to maximize its dollar sales volume, what price should it charge?