IO Field Examination Department of Economics, Michigan State University May 17, 2004

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1 IO Field Examination Department of Economics, Michigan State University May 17, 004 This examination is four hours long. The weight of each question in the overall grade is indicated. It is important to show how you arrive at your answers and offer whatever insights you may otherwise provide into the issue at hand, so that you can be given partial credit even if you are unable to derive analytic results. If you believe there is some ambiguity in the question (which I doubt), be sure to spell out exactly how you are interpreting the question. Good Luck! Choose SIX out of the following nine problems. 1. Consider an oligopolistic industry in which N firms compete on quantities. Suppose that (inverse) demand is given by P(Q). Let mc i be the marginal cost of firm i. a) Show that share weighted average firm markup in an industry, PCM Σ [(P-mc i )/P]s i =HHI/η, where HHI is the Herfindahl index (Σs i ) and η = -P dq/(q dp) is the industry elasticity of demand. b) Suppose that you wanted to examine the effect of concentration on profitability so that you estimated the following regression equation for many industries: ln(pcm)= α 0 + α 1 ln(hhi) + α ln(η) +ε. Show how you can derive this equation from (a). What (if any) are the restrictions on the parameters? c) Suppose that you estimated the equation using OLS. Briefly discuss any problems with such a regression. (Please limit your answer to ½ of a page.). Consider a mobile telephone industry with three firms. Suppose that you want to estimate demand and employ the following model: U ij = β 0 + β 1F j + β S j - β 3 p j +ξ j +ε ij, where: F j is a dummy variable that equals one for the first firm and zero otherwise, S j is a dummy variable that equals one for the second firm and zero otherwise, ξ j is the average value of the unobserved characteristic for product j. ε ij is iid with the Weibull (extreme value) distribution. Let δ j = β 0 + β 1F j + β S j - β 3 p j +ξ j be the mean utility of product j. 1

2 a) Write down the expression for the market share of firm j. b) Assuming that δ 0 = 0, that is, the mean utility of the outside good is zero, show that δ j = ln(s j /s 0 ) and write down the demand function that would be employed in order to estimate the unknown (β) parameters. c) Briefly discuss the strengths and weaknesses of this specification of demand. (Please limit your answer to ½ of a page.) 3. Technological progress (of a sort) has led to the WalkDVD. As the name suggests, this is a miniature DVD player. It is attached to a pair of headphones and special viewing glasses which, together, allow for highly realistic sound and image effects, as well as easy mobility. Three firms, Son, Tosh and Phil, are planning to launch their WalkDVD players. There are two possible formats to choose from, S and T, and the three competitors have not agreed on which standard to adopt. Son prefers standard S, whereas Tosh prefers standard T. Phil does not have any strong preference other than being compatible with the other firms. Specifically, the payoffs for each player as a function of the standard they adopt and the number of firms that adopt the same standard are as follows: Standard chosen by firm and number of firms choosing that standard Firm S1 S S3 T1 T T Son Tosh Phil (For example, the value 00 in the Son row and S column means that if Son chooses the S standard and one other firm chose the S standard, then Son's payoff is 00.) Suppose that all three firms simultaneously choose which standard to adopt. a) Show that all firms choosing S and all firms choosing T are both Nash equilibria of this game. b) Determine whether there are any other (pure-strategy) Nash equilibria in this simultaneous-move game. c) Son has just acquired a firm that manufactures DVDs for the S format. For all practical purposes, this implies that Son is committed to the S format. It is now up to Tosh and Phil to simultaneously decide which format to choose. Write down the x payoff matrix for the game now played by Tosh and Phil. Find the Nash equilibrium of this game. d) Do you think Son's move in part (c) was a good one? Explain.

3 4. Consider a Hotelling model of spatial competition. The market is served by firm 1 and firm. It is a differentiated market on the line interval [0, 1]. Transportation costs are linear (t per unit of distance). The density of consumers is uniform and equal to 1 along the segment of length 1. Firm 1 is located at the left extreme point, i.e., x = 0 and firm is located at the right extreme point of the city, i.e., x = 1. Their marginal cost is c. Consumers have unit demands in the market. One major departure from the standard Hotelling model is that we assume that consumers care about the number of other consumers who go to the same firm. More specifically, if firm i has n i consumers, the utility of a consumer located at point x going to firm 1 is given by v + β n 1 tx p 1, where p 1 is the price by firm 1 and the parameter β measures the network externality. If she goes to firm, her utility is given by v + β n t(1 x) p. We can interpret v as the stand-alone value of the product and β n i as the network benefits. Assume that v is sufficiently high and the market is covered (i.e., n 1 + n =1) and t > β > 0. What are the equilibrium prices and profits in this market? 5. Consider a two period model of durable-goods monopolists. The demand for the service flow of the good in each period is given by P = 1 Q. There is no production cost. The monopolist cannot rent the good. Assume no discounting. a) If the monopolist can commit to the future production plan, what is the optimal production plan in each period? b) If the monopolist cannot commit to the future production plan, show that the optimal production plan in (a) is not dynamically consistent. What is the reason for the dynamic inconsistency? c) What is the dynamically consistent production plan? Show that the profit is lower without commitment. d) Now suppose that the monopolist can rent the good. Show that the rental solution can replicate the commitment solution. Also provide an economic intuition for this result. e) Suppose that the monopolist faces a potential entrant (with production cost of zero) who can enter in the second period. Will the monopolist prefer renting to sales? 6. Consider the equilibrium foreclosure model by Ordover-Saloner-Salop (1990, AER). Two upstream firms, U1 and U, provide a homogeneous input to two downstream firms, D1 and D. Assume that the input is produced with zero cost. The downstream firms produce differentiated products and use prices as their strategic variables. The demand function for the product of downstream firm i is given by: Q i (p i, p j ) = 1 p i + p j, j i, i, j =1,. a) Consider the benchmark case where all firms are independently owned. What are the equilibrium prices for the upstream inputs and downstream products? What are the profits for each firm (U1, U, D1, and D)? 3

4 b) Now suppose that U1 and D1 are merged. As in Ordover-Saloner-Salop (1990), let us assume that the merged firm can commit to supply D at some price k. Given k, U s best response is to undercut it infinitesimally. Derive the range of k that will prevent a countermerger between U and D. c) What is the optimal k for the merged firm? Given the optimal k, what are the equilibrium profits for the merged firm and U and D? d) Now consider the bidding stage where D1 and D compete to acquire U1. What would be the equilibrium price to acquire U1 as a result of the bidding process? Does U1 has an incentive to hold-out (i.e., incentive not to be acquired and to remain as an independent firm)? 7. Suppose that there are two firms with constant average costs of AC = MC = c, supplying a market with inverse demand of P = a bq, where a > cand Q is the total market output of both firms. a) Calculate the (one period) Cournot equilibrium to this scenario. b) Define what is meant by drastic innovation. c) Suppose one firm and only one firm has the opportunity to engage in R&D in order to decrease its marginal cost to c< c. If this innovation is drastic, how much money would the firm at most be willing to spend, if it were to be granted a perpetual (infinitely lived) patent on the improved technology, while the rival firm remains with the old technology, and both firms discount rates are δ < 1? d) Now suppose instead, that someone outside of the industry has invented the technology described in part 1c and is willing to auction the associated perpetual patent to the highest bidder amongst the two firms in the industry (again, the firm that does not have the patent continues to use the old technology for ever after). How much will the patent be sold for? Explain. e) Repeat the above questions when firms engage in Bertrand competition, again assuming that the innovation is drastic. f) Briefly comment on your results, making sure to define and comment on the socalled efficiency effect and the replacement effect. A B 8. Two firms, A and B, compete in Cournot fashion in Market 1 by producing q1 and q 1. A In addition, Firm A also supplies q to a second market (Market ) as a monopolist. The firms total costs are given by, 4

5 A 1 ( A A = 1 + ) +, TC q q FC B 1 ( B TC = q1 ) + FC, where FC > 305 are fixed costs. Inverse market demand in the two markets are given by, A B P1 = 00 q1 q1, P = 50. a) Find the equilibrium and the associated profit for the firms. b) Suppose that demand in Market rises to P = 55 (for example the government gives a per-unit subsidy of 5). Find the new equilibrium outputs in each market, and the new profits for each firm. c) Carefully discuss and explain the result under part b in comparison to your answer in part a. 9. An employer (the principal) hires a worker (the agent) to employ effort, e, to a production process given by, q = eθ, whereθ is a productivity parameter taking on the value of either θ, or θ, with 0 < θ < θ. The agent knows the value of θ and has a reservation level of utility of 0. If the agent exerts effort e and receives a payment of r from the principle his utility is, u = r e. The principal does not know the true value of θ and has beliefs that θ = θ with probability ω and θ = θ with probability 1 ω. The principal s payoff is given by, v = q r. Both the principal and the agent observe output, q, but only the agent knows the effort, e, that is applied. Assuming that the principal makes take-it-or-leave-it offers, 5

6 a) Derive the first best contract for an agent whose type is known. b) Set up and discuss the problem the principal faces when the agent s type is not known. c) Solve the principal s problem when the type of the agent is not known. d) Carefully discuss the optimal contract when the agent s type is not known. e) What additional issues arise if the worker and employer have a multi-period relationship, but contracts can only be agreed to for one-period duration? 6