Homework 3 Managerial Economics Due: May 6

Transcription

1 Homework 3 Managerial Economics Due: May 6 1.In 2004, U.S. consumer products manufacturers distributed billion coupons, with a face value of over $280 billion, of which a mere 1.2% were redeemed by consumers. Why do manufacturers spend millions of dollars to distribute coupons when the redemption rate is so low? Why don t they manufacturers directly cut the wholesale prices of the products, which would be much cheaper to administer? (A)Some say that retailers would absorb a direct wholesale price cut instead of passing it on to consumers. They argue that, by contrast, retailers cannot absorb the value of coupons. Suppose that the retail sector is perfectly competitive. Compare the demand-supply equilibrium in the retail market with (i) a wholesale price cut of 50 cents and (ii) widespread distribution of 50-cent coupons. For this part, you may assume that all consumers use coupons. (B) Would there be any difference between the wholesale price cut and using coupons if the retailer were a monopoly? 1

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3 2.For many years, the NBA had a monopoly over basketball and, consequently, monopsonized the market for players. This monopsony over players began to erode in 1967 with the formation of the ABA. Finally, in 1983, basketball team owners agreed to allow free agency, which removed the restrictions against players moving between teams. An analysis of earnings showed that a player who scored 10% more points would have earned 2.05% more salary between 1968 and 1975, but 3.21% more salary between 1984 and (A)Explain the connection between having a monopoly over basketball and a monopsony over basketball players. (B)Compare the wage rate when the demand side of the market is a monopsony with the perfectly competitive wage. (C)Explain the differences in player earnings between as compared with (D)When the ABA and NBA proposed to merge, the basketball players opposed the proposal. Explain why. (A) The only seller of basketball games is the only buyer for basketball players. (B) 3

4 wage ME S W C comparative W m monopsony Q m Q C MB players (C) : Monoposony; : More competitive. Therefore, the player earnings were higher between (D) When both merge, the basketball player's earnings may decrease. 3.Hong Kong Director-General of Telecommunications Anthony Wong expressed concern about the effect of license auctions on the price of telecommunications: There s good and bad in auctioning off spectrum it may raise costs for telecoms providers ( Telecoms chief sees further fall in long-distance tariffs, South China Morning Post, December 31, 1999, Business 1.) (A)Typically, licenses are transferable, but the one-time license fee, once paid, is not refundable. From an operational standpoint, how does the cost of a license depend on the price, if any, that the owner paid for it? (B)How does the one-time license fee affect the marginal cost of providing telecommunications service? How does it affect the profit-maximizing scale of operations? (C)Suppose that the one-time license fee is changed to an annual charge based on the telecommunications provider s revenue. How would the new policy affect the service provider s profit-maximizing scale of operations? Answer (A) The cost of a license depends on the prevailing market price of licenses, 4

5 which may have little or no relation to the price that the owner paid for it at an earlier time. (B) The one-time license fee is a fixed cost with respect to the scale of operations and does not affect the marginal cost. Hence it does not affect the profit-maximizing scale of operations. (C)The annual charge based on the telecommunications provider s revenue would raise the provider s marginal cost, and hence reduce the profit-maximizing scale. 4.Suppose that Iron Music has the copyright to the latest CD of the heavy Iron band. The market demand curve for the CD is Q= P, where Q represents quantity demanded in thousands and P represents the price in dollars. Production requires a fixed cost of $100,000 and a constant marginal cost of $2 per unit. (A)What price will maximize profits? (B)At that price, how will be the sales? (C)What is the maximum profit? (D)Calculate the Lerner Index at the profit-maximizing scale of production. (E)Suppose that the fixed cost rises to $200,000. How would this affect the profit-maximizing price? Answer (a) Since demand, Q = p, the price is p = 8 - Q/100. Hence, total revenue, R(Q) = pq = (8 - Q/100) Q = 8Q - Q2/100. Differentiating, the marginal revenue is 8 - Q/50. Since the marginal cost is $2, by equating marginal revenue with marginal cost, we have 8 - Q/50 = 2, which implies that, at the profit maximum, Q = 6 x 50 = 300. By the demand equation, the profit-maximizing price is 8-300/100 = $5 per unit. (b) At the profit-maximizing price of $5 per unit, Q = 300. The question states that Q represents the quantity demanded in thousands, hence the profit-maximizing sales is 300,000 units. (c) The maximum profit is R(Q) - 100,000 - (Q x 2) = (5 x 300,000) - 100,000 - (2 x 300,000) = $800,000. (d) At the profit-maximizing scale, the Lerner Index is (p - 2)/p = 3/5 = 5

6 0.6. (e) The increase in fixed cost would not affect the profit-maximizing price. 5.Referring to the following figure, suppose that Mercury Airlines marginal revenue and demand curves cross the marginal cost curve at quantities of 3,000 and 6,000 seats a week, respectively. All other data remain the same. (A)Calculate the profit under policies of (i) uniform pricing, and (ii) complete price discrimination. (B)Suppose that Mercury implements complete price discrimination. Explain why it should sell up to the quantity where the buyer s marginal benefit equals Mercury s marginal cost. (C)Explain why Mercury s profit is higher with complete price discrimination than with uniform pricing p quantity (seats per week) 6

7 Answer: (i) Under uniform pricing, the profit-maximizing quantity is where MR=MC or Q=3000. Referring to the figure, at that Q, the price p on the demand curve must be halfway between 800 and Hence, p = 2400, and profit = ( ) x 3000 = 4.8 million dirhams a week. (ii) Under complete price discrimination, the seller should sell the quantity where MB = MC. Referring to the Figure, that quantity is Q = Then, total revenue is the area under the demand curve up to Q = 6000, hence TR = [( )/2] x 6000 = 14.4 million dirhams a week. Now total cost, TC = 800 x 6000 = 4.8 million dirhams, hence the profit = = 9.6 million dirhams a week. (b) Mercury maximizes its profit by producing the quantity where the buyer s marginal benefit equals Mercury s marginal cost. If it sold a larger quantity, so that the marginal benefit is less than the marginal cost, then its profit would be lower. By contrast, if it sold a smaller quantity, it could increase profit by selling more. (c) Complete price discrimination yields more profit than uniform pricing because it extracts a higher price from existing buyers and extends sales to new buyers who would not be served under uniform pricing. 6.The National Collegiate Athletic Association(NCAA) restricts the amount that colleges and universities may pay their student athletes. Suppose that there are just two colleges in the NCAA: Ivy and State. Each must choose between paying athletes according to NCAA rules and paying more. If both Ivy and State follow the NCAA salaries, then each would earn $3 million. If one follows the NCAA salaries and the other pays more than NCAA salaries, then the college paying more can attract better players and would earn $5 million, while the college following NCAA would earn just $1 million. If both colleges pay more than NCAA salaries, they would increase their costs but not get better players, so both would earn 2 million. (A) Construct a game in strategic form to analyze the choices of Ivy and State, and identify the equilibrium/equilibria? (B)With government backing, the NCAA can punish colleges that pay more than the NCAA permitted salaries. How would this affect the equilibrium/equilibria? (C)Which of the following concepts best describes the NCAA rules on player salaries:(i) monopoly;(ii) monopsony;(iii) economies of scale;(iv) economies of scope. Explain your answer. 7

8 Answer: (a) The key to this question is constructing the game in strategic form. The NCAA functions as a buyer cartel in the market for college athletes. If both Ivy and State pay according to NCAA rules, then they succeed as a cartel they receive 3 each. If Ivy breaks the cartel and pays more, while State keeps to the cartel, then Ivy will benefit and State will lose Ivy gets 4, and State gets 1. Similarly, if Ivy keeps to the cartel and State breaks it, Ivy gets 1 and State gets 4. Finally, if they both pay more, then both will be worse off each receives 2. State College Pay by NCAA rule Ivy College Pay by NCAA I: 3, Pay more I: 1, S: 3 S: 4 Pay more I: 4, I: 2, S: 1 S: 2 (b) The Nash equilibrium is both colleges will pay more than the NCAA allows. (c) If the NCAA has government backing, then both colleges will follow the NCAA recruiting rules, and achieve the highest combined profit. 7.Dial-up Internet users need modems to convert digital data into analog signals and Internet access providers (IAPs) need matching modems to convert the analog signals back to digital data. In the mid-1990s, the dominant standard for modems was the V.34, providing a speed of 28.8 or 36.6 kilobits per second (kbps). In Autumn 1996, two incompatible technologies for 56 kbps modems Rockwell s K56Flex and U.S. Robotics s X2 -- were launched. (A)Construct the following game in strategic form. End-users choose among the three alternatives of buying K56Flex, buying X2, or remaining with the old 8

9 technology, while IAPs have the same choice. If both end-users and IAPs choose K56Flex, each group receives a net benefit of 100, and similarly, if both groups choose X2. If end-users or IAPs buy K56Flex or X2, while the other does not buy the matching technology, the buyer receives a net benefit of 50. Anyone that remains with the old technology receives 0. Identify the equilibrium/equilibria in pure strategies. (B)In February 1998, Rockwell and U.S. Robotics agreed on a common V.90 standard. How did this affect the game and its equilibrium/equilibria? 9