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 ZA 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 UL13/0033 Page 1 of 8 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. As the rate of interest falls, a saver might save less but never becomes a borrower. Is this true or false? Explain your answer. Page 2 of 8 UL13/0033 Page 2 of 8 D1

3 7. Consider a competitive industry with several identical firms. The total cost function of the representative firm is given by C(q) =q q 2 + q3 2 where q denotes the output of the representative firm. Derive the supply function of the representative firm, paying proper attention to the shut-down point. 8. If lenders cannot observe the quality of projectsofborrowers,theusualcompetitive market supply logic of lending more at higher interest rates does not always hold. Is this true or false? Explain your answer. 9. If market demand is infinitely elastic and market supply elasticity is finite, a per unit tax on suppliers creates no deadweight loss. Is this true or false? Explain your answer. 10. Suppose an agent borrows funds and invests in a project. His effort must be monitored by lenders to ensure that the investment is successful, and monitoring is costly. If the agent borrows from several lenders, he is likely to be monitored at an inefficient level. Is this true or false? Explain your answer. Page 3 of 8 PLEASE TURN OVER UL13/0033 Page 3 of 8 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 8 UL13/0033 Page 4 of 8 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 8 PLEASE TURN OVER UL13/0033 Page 5 of 8 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 8 UL13/0033 Page 6 of 8 D1

7 14. (a) Jean spends her income on fuel for heating her house and other goods ( other goods represents a composite of all other goods). The price of the composite of other goods is 1, and the price of heating fuel is p. The government decides to put a tax of t per unit on heating fuel. i. Suppose the government asked for a lump-sum tax that would leave Jean with the same level of utility as after the per-unit tax. Would Jean pay more or less tax under the lump-sum tax scheme compared to the per-unit tax scheme? Explain using a diagram. ii. Suppose the per-unit tax has been imposed. The local council starts a scheme to help certain residents with their fuel tax bill. Jean qualifies for the scheme, and she receives extra income equal to the amount of tax she pays. Would this make Jean s utility as high as her pre-tax level of utility? Explain using a diagram. (b) Jo has a wealth of 10,000, but faces the risk of losing 3600 with probability 0.2. An insurance company offers Jo the following scheme: in exchange for apremiumofx, the insurance company would pay out 5X in the event of a loss. i. Suppose Jo s utility function is given by u(w) =ln w where w denotes wealth. What is the optimal choice of X for Jo? ii. Now suppose Jo s utility function is given by u(w) =1 1 w where w denotes wealth. What is the optimal choice of X for Jo in this case? Page 7 of 8 PLEASE TURN OVER UL13/0033 Page 7 of 8 D1

8 15. A society consists of 2 identical individuals who derive utility from a public good. The public good can be provided at a constant marginal cost of 6. Let x i denote the level of public good provision by i and let X denote the total provision of the public good. The net benefit enjoyed by individual i from providing x i units of the public good is given by where i {1, 2}. U i (x i, X) = 1 2 (10 X)2 6x i (a) Derive the socially optimal level of provision of the public good.[6 marks] (b) If every individual optimally chooses how much public good to provide, derive the total level of provision of the public good. [7 marks] (c) Suppose n > 1 new individuals arrive in the society. The net benefit enjoyed by new individual j from providing x j units of the public good is given by V j (x j, X) = 1 3 (9 X)2 6x j Suppose every individual optimally chooses how much public good to provide. Does the total level of public good provision change compared to part (b) as a result of the new arrivals? Explain your answer. [7 marks] 16. (a) Explain the incentive properties of residual claimant contracts relative to flat salaries in terms of reducing unobservable shirking by an employee. [10 marks] (b) Carefully explainwhy flatsalariesare often observed, and residual claimant contracts are rarely observed. [10 marks] END OF PAPER Page 8 of 8 END OF PAPER UL13/0033 Page 8 of 8 D1