ps3_ans - Department of Economics University of California...

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Economics 121 Page 1 Problem Set 3 Answers Department of Economics Fall 2004 University of California Woroch/Lopez/Sydnor Economics 121 PROBLEM SET 3 ANSWER SHEET TRUE/FALSE/UNCERTAIN AND EXPLAIN: 1. According to the Stackelberg model, the dominant firm allows the follower to produce a positive amount because it is not possible to completely exclude him from the market. False/Uncertain: According to the Stackelberg model as presented in class, the follower is already in the market (not an entrant) possibly with sunk fixed costs, so that it may be difficult for the market leader to produce a quantity high enough to cause the follower not to produce. Even in the case where the follower is an entrant not yet in the market, the leader may find it more profitable to accommodate than to exclude (even though exclusion is possible). 2. In a market where firms interact in a repeated context, a monopoly outcome can be sustained as a Nash equilibrium even though many firms operate in the market. True: See, for example, a cartel. The threat of punishment in the future can deter cheating and keep firms producing their share of the monopoly level. 3. The higher the interest rate, the easier it is for firms in the same industry to sustain a collusive outcome. False: The higher the interest rate, the harder it is to sustain a collusive outcome. This is because the higher the interest rate is, the more money today is worth compared to future profits. Thus, firms have more of an incentive to cheat today (and make higher profits now even though they will make less profits in the future). MULTIPART QUESTIONS 1. In the mainframe computer industry of the 1970s, IBM was the dominant supplier but it did face entry threats. To examine its behavior toward competitors, suppose that IBM produces q 1 and it incurs a cost of c 1 (q 1 ) = 6 q 1 measured in hundreds of thousands of dollars. IBM faces potential entry by Fujitsu, the Japanese mainframe maker. Fujitsu produces a computer that is a perfect substitute for the IBM machine but its production costs are: c 2 (q 2 ) = 100 + 12 q 2 where q 2 is Fujitsu’s production level and costs are measured in hundreds of thousands of dollars. Inverse demand for mainframes is given by p(Q) = 120 - Q, where Q = q 1 + q 2 is the total production by IBM and Fujitsu, and again price is measured in hundreds of thousands of dollars. Initially suppose that the incumbent, IBM can credibly commit to a quantity to produce, after which Fujitsu will choose its own quantity. a. Find Fujitsu’s reaction function. Fujistsu’s profit function is: p 2 = Pq 2 – C(q 2 ) = (P(q 1 ,q 2 ) – mc 2 )q 2 – F = (120 – q 1 – q 2 – 12)q 2 – 100 Maximizing with respect to q 2 (note that the fix cost drop out) gives r 2 (q 1 ) = ½(108 – q 1 ) = 54 – ½q 1 b. If IBM accommodates entry, find IBM’s profit-maximizing quantity and its resulting profits. If IBM accommodates entry, it will then act as a Stackelberg leader.
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This note was uploaded on 05/05/2008 for the course ECON 121 taught by Professor Woroch during the Fall '07 term at University of California, Berkeley.

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ps3_ans - Department of Economics University of California...

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