This paper is not to be removed from the Examination Halls

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1 ~~EC2066 ZA d0 This paper is not to be removed from the Examination Halls UNIVERSITY OF LONDON EC2066 ZB BSc degrees and Diplomas for Graduates in Economics, Management, Finance and the Social Sciences, the Diplomas in Economics and Social Sciences and Access Route Microeconomics Tuesday, 21 May 2013 : 10.00am to 1.00pm Candidates should answer ELEVEN of the following SIXTEEN questions: EIGHT from Section A (5 marks each) and THREE from Section B (20 marks each). Candidates are strongly advised to divide their time accordingly. A calculator may be used when answering questions on this paper and it must comply in all respects with the specification given with your Admission Notice. The make and type of machine must be clearly stated on the front cover of the answer book. If more questions are answered than requested, only the first answers attempted will be counted. PLEASE TURN OVER University of London 2013 UL13/0034 Page 1 of 7 D1

2 SECTION A Answer eight questionsfromthissection(5markseach). 1. Mary s demand curve for food is given by Q = 10 2P where Q is the quantity of food and P is the price of food. Calculate her price elasticity of demand for food at P = Andy purchases only two goods, apples (A) andoranges(r). The price of apples is 2 and the price of oranges is 4. Andy has an income of 40 and his utility function is U(A, R) =3A + 5R What bundle of apples and oranges should Andy purchase to maximize utility? 3. Underfirst-degree price discrimination, a monopolist s marginal revenue is equal to average revenue. Is this true or false? Explain your answer. 4. Consider the following game. For what values of x does each player have a dominant strategy? Explain your answer. Player 2 A 2 B 2 C 2 A 1 3,3 3,0 1,2 Player 1 B 1 2,3 1,2 0,1 C 1 0,1 2,0 x, x 5. If the long-run average cost is decreasing in output, the long-run marginal cost must be decreasing in output as well. Is this true or false? Explain your answer. 6. If leisure is a normal good, the demand for leisure rises as wage rises. Is this true or false? Explain your answer. Page 2 of 7 UL13/0034 Page 2 of 7 D1

3 7. In an Edgeworth Box, a reallocation of resources from the initial endowment to any point on the contract curve always constitutes a Pareto improvement. Is this true or false? Explain your answer. 8. If consumption at all dates is a normal good, savers necessarily save less if the rate of interest falls. Is this true or false? Explain your answer. 9. Private provision of goods that are non-excludable and non-rival leads to overprovision compared to the socially optimal level. Is this true or false? Explain your answer. 10. The LSE requires mobile phones to be switched off in the library. Assuming this is strictly enforced, does such a restriction enhance efficiency? Explain your answer. Page 3 of 7 PLEASE TURN OVER UL13/0034 Page 3 of 7 D1

4 SECTION B Answer three questions from this section (20 marks each). 11. Suppose there are two identical firms in an industry. The output of firm 1 is denoted by q 1 and that of firm 2 is denoted by q 2. The total cost of production for firm i, i {1, 2}, is C(q i )=4 q i Let Q denote total output, i.e. Q = q 1 + q 2. The inverse demand curve in the market is given by P = 10 Q (a) Find the Cournot-Nash equilibrium quantity produced by each firm and the market price. (b) Suppose the firms can collude, and maximize joint profit. Calculate the deadweight loss arising under this scenario. (c) What would be the quantities produced by each firm and market price under Stackelberg duopoly if firm 1 moves first? (d) Now suppose the production process in the industry pollutes the environment and generates a marginal social cost given by MC E = 2Q Calculate the deadweight loss arising from the Cournot-Nash equilibrium in this case. Page 4 of 7 UL13/0034 Page 4 of 7 D1

5 12. Consider a market for used cars. There are some low quality cars and some high quality cars. Potential sellers have a car each, and there are many more buyers than possible sellers in the market. A high quality car never breaks down. A low quality car provides a poorer ride quality over longer journeys and also breaks down with positive probability. A seller values a high quality car at 9000 and a low quality car at A buyer values a high quality car at 10,000 and a low quality car at All agents are risk-neutral. In answering the following questions, assume that the sellers get the entire surplus from trade. (a) Suppose quality is observable to sellers but not to buyers. Buyers only know that a fraction 3/5 of the cars in the market are high quality and the rest are low quality. Would cars of both low and high qualities be traded in equilibrium? Derive the equilibrium price(s) at which such trade takes place. (b) Is the market outcome in part (a) efficient? Explain your answer. (c) Now suppose low quality cars break down with probability 0.7. Recall that high quality cars never break down. Suppose the sellers of high quality cars announce a guarantee that promises a full refund if the car breaks down. Show that with this guarantee, high quality cars sell for and low quality cars sell for (d) Suppose, as in part (c), that low quality cars break down with probability 0.7. Suppose the government decides to force each seller to offer a full refund if the car sold by the seller breaks down. How does this change the market outcome? Is the market outcome efficient? Explain your answer. Page 5 of 7 PLEASE TURN OVER UL13/0034 Page 5 of 7 D1

6 13. (a) Find the pure and mixed-strategy Nash equilibria of the following game. [8 marks] Player 2 A 2 B 2 Player 1 A 1 2,7 3,2 B 1 0,0 4,1 (b) Consider the following extensive-form game with two players. Player 2 moves after player 1. Each player can produce a high output or a low output. Player 1 s payoff is additionally influenced by an exogenous event which occurs with probability p [0, 1]. The payoffs are written as ((Payoff to 1), Payoff to 2). 1 L 1 H L 2 H 2 L 2 H 2 ((4 2p),1) ((3 2p),4) ((2 + p),2) ((1 + p),1) i. Suppose p > 1/3. Find the subgame perfect Nash equilibrium of the game above. [6 marks] ii. Suppose, before the start of the game, player 2 has the option of committing to produce a high output (H 2 ). Making such a commitment requires player 2 to incur a cost of 1. Find the range of values of p for which it is optimal to make such a costly commitment. [6 marks] Page 6 of 7 UL13/0034 Page 6 of 7 D1

7 14. Consider a competitive industry with several identical firms. You are given the following information about this industry Q D = 320 2P (Market demand) C(q) = q + 50q 2 (Total cost function of a firm) Here P is the market price and q denotes the output of the representative firm. (a) Derive the supply function of the representative firm, paying proper attention to the shut-down point. (b) Suppose there are 100 firms in the industry. Derive the market supply function and equilibrium market price and quantity. (c) Suppose a tax of 30 per unit of output is imposed on sellers. Calculate the deadweight loss from the tax. (d) For the per-unit tax in part (c), calculate the burden of the tax on consumers, and the burden of the tax on sellers. 15. (a) Explain the social cost arising from monopoly using a diagram. Suppose a lump-sum tax is imposed on a monopolist and the revenue is redistributed among consumers. Would such a measure reduce the social cost of monopoly? Explain your answer. (b) Write the monopolist s profit maximization condition in terms of the priceelasticity of demand. (c) Assuming marginal cost is positive, show that demand must be elastic (i.e. the absolute value of elasticity must be greater than 1) at the equilibrium output level under monopoly. (d) Explain, using a diagram, why attaining the socially optimal level of output under a natural monopoly requires a government subsidy. 16. (a) Explain how private individuals can avoid inefficiencies arising from the presence of externalities through (i) mergers and (ii) bargaining. [7 marks] (b) Identify examples in which the problem of externalities cannot be solved well by the methods discussed in part (a). [6 marks] (c) Briefly discuss how the government can address some types of externalities by creating a market for trading of permits in the externality-generating activity. [7 marks] Page 7 of 7 END OF PAPER END OF PAPER UL13/0034 Page 7 of 7 D1