Homework 4 Managerial Economics MBA, NCCU

Transcription

1 Homework 4 Managerial Economics MBA, NCCU 1.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) (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

2 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. 2.The Chinese Visa Application Center in London charges applicants for visas an application service fee and a visa fee. The application service fee is for processing within four working days and 47 for processing within three working days. The single-entry visa fee is 30, 65, and 20 for citizens of the United Kingdom, United States, and other countries respectively. The corresponding double-entry visa fees are 45, 65, and 30. (Source: Chinese Visa Application Center, London, January 5, 2010.) (A) Explain the Visa Center's pricing policies in terms of direct segment discrimination. Discuss whether issuance of visas meets the conditions for such discrimination. (B) Explain the Visa Center's pricing policies in terms of indirect segment discrimination between tourists and business travelers. Discuss whether issuance of visas meets the conditions for such discrimination. (C) Should the Chinese government set the same visa fees in all foreign countries? Answer (a) The issuance of visas meets the conditions for direct segment discrimination. The Visa Centre can implement direct segment discrimination accordingly to the applicant s nationality. It is relatively easy to check each applicant s nationality. Moreover, people will not change their nationality just to avoid higher visa fees. Finally, visas are issued to individual persons, so they cannot be re-sold. (b) Visa Centre practices indirect segment discrimination according to the applicant s purpose of visit. Business travellers are more time sensitive and

3 will apply for shorter visa processing time. Further, business travellers are more likely to travel into China more than once. By contrast, tourists will have more time to apply for their visa and are more likely to visit China just once. The Visa Centre can control the visa processing time, to which buyers in the different segments are differentially sensitive. Finally, visas are issued to individual persons, so they cannot be re-sold. (c) Assuming that the Chinese Government aims to maximize profits, it should set different prices according to the demand in each market. 3.Suppose that you are the manager of a cable company proving two channels. Your potential customers include two types of households. The following table summarizes the marginal benefit (value) of a particular type of household from watching a particular channel. Household/Channel News Channel Entertainment Channel Type One Type Two (A)Suppose that the marginal cost of the cable company providing a channel to the household is 0. Will you provide all channels to all types of household from the efficiency perspective? What is your profit-maximizing pricing strategy? (B)Suppose that the marginal cost of the cable company providing a channel to the household is 50. Will you provide all channels to all types of household from the efficiency perspective? What is your profit-maximizing pricing strategy? Answer: (A) Yes. A bundle of two channels: 220 (B) No. We should not provide entertainment channel to Type One. A bundle of two channels:220; a single channel: The National Collegiate Athletic Association(NCAA) restricts the amount that colleges and universities may pay their student athletes. Suppose that there are just

4 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. 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

5 (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. 5.The demand for most new films is highest in the first few days after opening, then tapers off. Two key factors affecting potential demand are the season (the Summer and Christmas vacation periods are the best times) and the timing of other releases. Suppose that both Studio Luna and Moonlight Movies are producing major action movies. (A)The two studios simultaneously must choose between release on December 11 or 18. If both films open on December 11, each will sell 200,000 tickets. If one opens on December 11 and the other on December 18, then the early release will sell 350,000 tickets, while the later release will sell 150,000. If both open on December 18, each will sell 100,000 tickets. Construct a game in strategic form to illustrate the situation and identify the equilibrium or equilibria. (B)Now suppose that the publicity surrounding one movie will increase the demand for the other film. Specifically, each studio will sell 70,000 more tickets if both open on the same day. Adjust the data in (A) according to this new information. How does this affect the equilibrium or equilibria? Answer: (a) There is one Nash equilibrium: both studios open on December 11. MOONLIGHT Open Dec 11 Open Dec 18 L: 200,000 L: 350,000 LUNA Open Dec 11 M: 200,000 L: 150,000 M: 150,000 L: 100,000 Open Dec ,000 M: 100,000 M:

6 6.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 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?

7 7.With the growth of international trade and travel, more people are learning English. Major European companies have adopted English as a common language. English is also the standard language for communications among aircraft pilots and air-traffic controllers. Linguists estimate that, of 7000 languages in use worldwide, nearly half will disappear within this century. (A) Compare the benefit of speaking a common language among: (i) truckers; (ii) pilots. (B)Does the growth of English generate a positive or negative externality for: (i) people who are already fluent in English; (ii) people who do not speak English? (C)Can the externalities in (B) be described as network externalities? Explain your answer. (D)How do critical mass and expectations apply to the survival of a language? Answer

8 (a) The benefit would be greater for pilots than truckers. over longer distances and more countries than truckers. Pilots range (b) The growth of English generates a positive externality for people who are already fluent in English and a negative externality for people who are not fluent in English. (c) Yes. The greater the number of English speaking people, the larger the benefit other English speaking people will derive as they will have more people to speak English with. (d) If the number of speakers of a language is too small, then people will prefer to learn and speak other more widely used languages. Further, people will expect others not to learn the language which reinforces the main effect. Eventually, people who speak the language will die and the language will disappear. 8.Let b represent marginal benefit and q the amount of Sogo s investment in the new ZhongXiao Fushing store. Suppose that the investment generates marginal benefis, b=10-q for Sogo, b=4-0.4q for the florist, and b=1-0.2q for the shoe store. Given the marginal cost of 1, calculate (A) the profit-maximizing quantity of Sogo s investment (B) the economically efficient quantity of Sogo s investment. (A) b=10-q, 10-q=1, q=9 (B) b=15-1.6q, 0<q<5; b=14-1.4q, q>5; q=1, q=9.28.