# HW4

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Managerial Economics Indian School of Business Term 1, 2019-20 HOMEWORK 4 Due: Thursday, May 27 at 8 am Instructions. Complete all problems. Turn in a single hard copy per study group, with name and PGID of all members on top, to the academic associate. Please note that code 2N-b is applicable for submission of all homework assignments. This means that you can discuss general concepts and ideas relevant to the assignment with others and refer to external material but not discuss specific issues associated with the assignment with others or refer to problem set solutions.  Problem 1 An old lady is looking for help crossing the street. 1  Only one person is needed to help her; more are okay but no better that one. Sunny and Simran are the two people in the vicinity who can help; each has to choose simultaneously whether to do so. Each of the two will get utility worth 3 from the old lady’s success (no matter who helps her). But each one who goes to help will bear a cost of 1, this being the utility value of the person’s time taken up in helping. Set this up as a game. Write the payoff table, and find all pure-strategy Nash equilibria. Problem 2 Having muscled out the other bhelpuri vendors on Chowpatty Beach in Bombay, the proprietors of Royal Bhelpuri and Modern Bhelpuri have to decide where to locate their stalls. Customers are situated uniformly along the beach, and will purchase from the vendor closest to them. a.   If the beach is 1 km long, what are the Nash equilibrium locations for Royal and Modern?  b.   If a new entrant, Tasty Bhelpuri, enters the market, what are the equilibrium locations? Problem 3 Find the Cournot-Nash Equilibrium in a game with two French fry manufacturers, Freddie’s Fries and Charlie’s Chips. There are five levels of production: produce 200, 300, 400, 500 or 600 thousands tons of output. The numbers in the table below represent as (FF,CC) the profits for Freddie’s Fries and Charlie’s Chips corresponding to the quantities they produce. 1  This problem is from Dixit and Skeath’s Games of Strategy .    200 300 400 500 600 200 63,-1 28,-1 -2,0 -2,45 -3,19 300 32,1 2,2 2,5 33,0 2,3 400 54,1 95,-1 0,2 4,-1 0,4 500 1,-33 -3,43 -1,39 1,-12 -1,17 600 -22,0 1,-13 -1,88 -2,-57 -3,72 a. What is the Nash Equilibrium output for this game assuming that the two firms choose their production quantities simultaneously?  b. What would be the equilibrium if Charlie’s Chips could choose its output first and Freddie’s Fries chose second, taking Charlie’s decision as given. Problem 4 Consider a Cournot duopoly in which the two firms have different marginal costs. The inverse demand in the market is P(Q) = 15 – Q. The costs of firm A and firm B are C A (q A ) = 6q A  and C B (q B ) = 3q B , respectively. a.   What is the best response (or reaction) function of firm A?  b.   What is the best response (or reaction) function of firm B? c.   What are the equilibrium quantities produced by each firm? d.   What is the market price? e.   What are the profits of each firm? Problem 5 a.   Firm A currently monopolizes its market and earns profits of \$10 million. 2  Firm B is a  potential entrant that is thinking about entering the market. If B does not enter the market, it earns profits of \$0, while A continues to earn profits of \$10 million. If B enters, then A must choose between accommodating entry, or fighting it. If A accommodates, then A earns \$5 million and B earns \$5 million. If A fights, then both firms lose \$5 million. Draw the game in extensive form and predict the outcome.  b.   Again, consider the above game. Now, suppose the decision of B to enter is reversible in the following way. After B enters the market, and A has decided to either fight or accommodate, B can choose to remain in the market or exit. All payoffs from the above game remain the same. However, if B decides to exit the market, then B suffers a loss of \$1 million, while A 2  This is Problem 6, Chapter 11 from Allen et al’s Managerial Economics.  regains its old profits of \$10 million. Draw the game in extensive form and predict the outcome. Problem 6 The accompanying article presents a decision facing Robert Gates, the US Secretary of Defense, who is trying to reduce costs for the US Air Force’s F-35 fighter program. The engines for the  plane are currently produced by Pratt and Whitney in Connecticut. Some lawmakers want to start a second production line for the engines in Ohio, run by GE and Rolls Royce. Mr. Gates argues that a single production line will save costs for the military, while Ohio lawmakers (who value the jobs the second line will create) say that competition will lower engine prices and increase the welfare accruing to the sole consumer – the US military. As a budget analyst at the Pentagon, you have been asked to analyze two possible scenarios and advise Secretary Gates on production strategy. You determine that the military’s demand curve for F-35 engines is given by P=1000-Q. The marginal cost of production (revealed in Congressional filings) is \$120 mm per plane for Pratt and Whitney (the srcinal incumbent) and \$160 mm per plane for GE-Rolls Royce (the potential entrant). a.   What is the quantity of engines produced if Pratt and Whitney is the monopolist supplier in the market? What is the price that the government has to pay for the engines? What is the consumer surplus for the military in this case?  b.    Now consider the duopoly case where Pratt and Whitney is the Stackelberg leader and GE-Rolls Royce is the Stackelberg follower. What is the price that the government has to  pay for the engines? How many engines are produced and what is the consumer surplus for the military in this case? c.   Should Secretary Gates agree to the second production line? Explain briefly.

Sep 22, 2019

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Sep 22, 2019
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