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 Thursday, 15 May 2014 : 10:00 to 13:00 Candidates should answer ELEVEN of the following FOURTEEN questions: all 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 2014 Page 1 of 8 D1

2 SECTION A Answer all EIGHT questions from this section (5 marks each). 1. Consider the following simultaneous-move game with two players, 1 and 2. If 1 and/or 2 have any dominated strategies, eliminate them. Once you have done this, consider the remaining game. In this remaining game, eliminate any dominated strategies of 1 and/or 2, and so on. This method is called iterated elimination of dominated strategies. Find the equilibrium using this method. Your answer must show each round of elimination clearly. Player 2 A 2 B 2 C 2 A 1 2,2 4,2 0,4 Player 1 B 1 4,0 6,8 2,2 C 1 6,4 4,0 0,6 2. Consider an exchange economy with two goods (milk and honey) and two consumers (A and B). There are 10 units available of each of the two goods. Consumer A is endowed with 6 units of milk and 4 units of honey. Consumer B is endowed with 4 units of milk and 6 units of honey. Let M denote units of milk and H denote units of honey. Consumer A has the following utility function: U A (M, H) = min[m, H] Consumer B has the following utility function: U B (M, H) = M+ H Draw an Edgeworth box and show the area of mutually beneficial trades between the two consumers. 3. A monopolist has a well-defined supply function. Is this true or false? Explain your answer. 4. A bond pays a fixed sum of 100 per year for ever (i.e. the bond is a perpetuity). The annual interest rate is 5%. What is the maximum amount an agent should pay to buy this bond? 5. Growth in the economy leads to a rise in the demand for labour. It follows that the equilibrium quantity of labour (measured in the number of hours worked) must rise. Is this true or false? Explain your answer. Page 2 of 8 Page 2 of 8

3 6. Suppose the inverse demand curve is given by P = 10 Q. This is shown in the picture below. At the point A shown in the picture, is the demand elastic or inelastic (with respect to price change)? Explain your answer. 10 Price A 5 P = 10 - Q Quantity 7. The short run supply function of a competitive firm is given by { 0 if P < 10 Q = 3P 30 if P 10 where Q is the quantity supplied and P is the price of output. Derive the equation for the firm s marginal cost curve. 8. Too few people use public transport in London relative to the social optimum. Provide an economic argument in support of this statement. Page 3 of 8 Page 3 of 8 PLEASE TURN OVER

4 SECTION B Answer THREE questions from this section (20 marks each). 9. 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. Each firm can produce output at a constant marginal cost of 6. There are no fixed costs. Let Q denote total output, i.e. Q = q 1 + q 2. The inverse demand curve in the market is given by P = 30 2Q (a) Find the Cournot-Nash equilibrium quantity produced by each firm and the market price. (b) What would be the quantities produced by each firm and market price under Stackelberg duopoly if firm 1 moves first? (c) Calculate the deadweight loss arising from Cournot-Nash and Stackelberg duopoly. Which market structure is more efficient? (d) Suppose, as in part (b), firm 1 moves first and decides how much to produce. Firm 2 moves second and makes its production decision. There is then a third stage at which firm 1 can change its mind about how much to produce and makes a final decision. Find the equilibrium quantities produced by the two firms under this three-stage game. Page 4 of 8 Page 4 of 8

5 10. (a) Consider the following simultaneous-move game with two players, 1 and 2. Let p denote the probability with which player 1 plays A 1, where 0 p 1. B 1 is played with the residual probability. Next, let q denote the probability with which player 2 plays A 2, where 0 q 1. B 2 is played with the residual probability. Draw a picture with p along the horizontal axis and q along the vertical axis and draw the best response functions of players 1 and 2. Clearly label any equilibrium points in the picture. [6 marks] Player 2 A 2 B 2 Player 1 A 1 2,2 3,0 B 1 3,5 1,6 (b) Consider the following extensive-form game with two players. Player 1 can end the game by choosing Out. If player 1 chooses In, Player 2 then chooses between L and R. The payoffs are written as (Payoff to 1, Payoff to 2). Identify any subgame perfect Nash equilibrium. [6 marks] 1 In Out L 2 R 0,1 2,2-1,3 (c) Suppose the following game is repeated infinitely. Players discount the future, so that, for each player, a payoff of x received t periods from today is worth δ t x today, where 0 < δ < 1. Show that it is possible to sustain cooperation (which in this case involves each player playing C every period) in the infinitely repeated game for high enough values of δ. [8 marks] Player 2 C D Player 1 C 2,2 0,3 D 3,0 1,1 Page 5 of 8 Page 5 of 8 PLEASE TURN OVER

6 11. A monopolist can vary the quality of a good he produces. The cost of producing quality q is C(q) = q2 2 There are two types of consumers. From consuming a good of quality q 1 at price p 1, type 1 consumers get a utility of u 1 (q 1, p 1 ) = q 1 p 1 Type 2 consumers get a higher marginal benefit from quality. From consuming a good of quality q 2 at price p 2, type 2 consumers get a utility of u 2 (q 2, p 2 ) = 2q 2 p 2 Consumers buy the good so long as they get at least 0 utility. The profit of the monopolist from a quality-price pair of(q i, p i ) where i {1, 2} is then given by π(q i, p i ) = p i q2 i 2 (a) Suppose the monopolist knows the type of any consumer. In this case the monopolist produces a quality q 1 for a type 1 consumer and charges a price p 1. Similarly, type 2 consumers are offered quality q 2 at price p 2. For any i {1, 2}, the optimal pair (qi, p i ) maximises π(q i, p i ) subject to u i (q i, p i ) = 0. Find the optimal quality-price pairs (q1, p 1 ) and (q 2, p 2 ). (b) Suppose a consumer s own type is known only to the consumer. The monopolist cannot identify the type of any consumer. In this case, suppose the monopolist still offers the quality-price pairs (q1, p 1 ) and (q 2, p 2 ) from part (a). Which quality-price pair would a type 1 consumer choose? Which pair would a type 2 consumer choose? (c) Suppose the monopolist sets q 1 = 1/2, p 1 = 1/2 and q 2 = 2. The monopolist wants to set p 2 such that type 2 consumers would have the incentive to choose (q 2, p 2 ) rather than (q 1, p 1 ). What is the highest value of p 2 that satisfies the monopolist s objective? (d) Given the values of q 1, q 2, p 1 and p 2 from part (c), would a type 1 consumer have the incentive to choose (q 1, p 1 ) rather than (q 2, p 2 )? Page 6 of 8 Page 6 of 8

7 12. Consider an economy with two goods, 1 and 2. There is a competitive market for the goods. There are a 100 identical firms in the competitive industry producing good 1, and the cost of the representative firm producing q 1 units of good 1 is given by C(q 1 ) = q 1 + q2 1 2 There are a 100 identical consumers. The representative agent consuming q 1 units of good 1 and q 2 units of good 2 obtains an utility u(q 1, q 2 ) = ln q 1 + ln q 2 The price of good 1 is denoted by P and the price of good 2 is 1. Each consumer has an income of 12. (a) Derive the market supply function for good 1. (b) Derive the market demand function for good 1. (c) Calculate the market equilibrium price and quantity of good 1. (d) Calculate the price elasticity of demand for good 1 at the market equilibrium. 13. Rai spends her income on fuel for heating her house (H) and a composite of all other goods (Y). Her preferences are represented by the utility function u(h, Y) = H α Y 1 α The price of the composite good is 1, and the price of heating fuel is p. Let M denote Rai s income. (a) Derive Rai s demand for H and Y. (b) Suppose M = 300 and α = 2/3. Also suppose currently the unit price of fuel is p = 20. The energy company offers Rai the option to switch to a different tariff. Under the new tariff, Rai must pay a fixed fee of 100 and then she can buy fuel at a unit price of 10. Would Rai switch to the new tariff? Explain. [8 marks] (c) The government decides to give Rai a heating fuel subsidy of s per unit. This results in an increase in utility from u 0 before the subsidy to u 1 after the subsidy. Could the government follow an alternative policy that would result in the same increase in utility for Rai, but cost the government less? Explain using a suitable diagram. [7 marks] Page 7 of 8 Page 7 of 8 PLEASE TURN OVER

8 14. A monopolist has two customers with the following demand functions: Q 1 = 70 P 1 (Demand of customer 1) Q 2 = 110 P 2 (Demand of customer 2) Here P i is the price charged to customer i, i {1, 2}. The monopolist has a constant marginal cost of 10, and no fixed costs. (a) Suppose the monopolist can differentiate between the customers, and the customers cannot trade between themselves, allowing the monopolist to engage in third-degree price discrimination. What is the price charged to each consumer? (b) Now suppose the monopolist cannot differentiate between the customers and must charge them the same price. Calculate the monopolist s optimal single price P as well as the quantity sold to each customer. (c) Is the total surplus (consumer surplus plus profit) higher under a single price or under price discrimination? Explain. (d) Suppose, as in part (b), the monopolist cannot differentiate between the customers. However, in addition to a per-unit price P, the monopolist can also charge a fixed fee F. A customer must pay this fee irrespective of the quantity purchased when a positive amount is purchased. Derive the monopolist s optimal price and fee. ENDOFPAPER Page 8 of 8 Page 8 of 8 END OF PAPER