January Examination Period 2021 ECN361 Advanced Microeconomics Duration: 3 hours The paper has FIVE questions. Answer ALL questions. This examination paper MUST NOT be shared with anyone else. Doing so will be considered a very serious assessment offence under the Queen Mary Academic Misconduct Policy. This examination is an individual assessment and must be entirely your own work. All work will be run through the plagiarism software, Turnitin. The software will also compare your script against all other student submissions. Any evidence of plagiarism or collusion will be taken forward as academic misconduct. Calculators are permitted in this examination. Please ensure that your working is clearly shown with all steps of your calculation included in your answer document, including any formula used. When writing formulas, please note the following: • It is acceptable to use the standard alphabet rather than Greek letters. The following are recommended: a for α, b for β, h for θ, m for µ, s for σ, r for ρ, d for δ. • For mathematical operators: add +, subtract -, multiply *, and divide /. • Where appropriate, use an underscore to indicate a subscript, e.g. x a for x a . • Use the ˆ character for power, e.g. xˆ2 for x2, xˆ0.5 for √ x. • As an alternative to xˆ0.5 you may type sqrt(x). • Use brackets as necessary. To make your answer clearer use different brackets where appropriate, eg [ ] {} (). Examiner: A. Daripa © Queen Mary University of London, 2021 Page 2 ECN361 (2021) Question 1 Consider the strategic-form game below with two players, 1 and 2. Player 2 A2 B2 C2 A1 2,2 4,2 0,4 Player 1 B1 4,0 6,8 2,2 C1 6,4 4,0 X ,6 (a) Set X = 0. Solve the game by iteratively eliminating strictly dominated strategies. [5 marks] (b) Set X = 8. Eliminate any strictly dominated strategies and then find the pure strategy and mixed strategy Nash equilibria of the game. [10 marks] Continues on next page ECN361 (2021) Page 3 Question 2 Consider the following extensive-form game with two players, 1 and 2. a3 1 a2a1 b2 (1,2) b1 (0,1) b2 (0,3) b1 (2,2) 2 c2 (2,0) c1 (-1,-1) 2 (a) Find the pure-strategy Nash equilibria of the game. [5 marks] (b) Find the pure-strategy subgame-perfect equilibria of the game. [5 marks] (c) Find the pure-strategy perfect Bayesian equilibria of the game. [10 marks] Continues on next page Page 4 ECN361 (2021) Question 3 Suppose the following game is repeated infinitely. The players have a common discount factor δ ∈ (0, 1). 2 C D 1 C 2,1 -1,0 D 6,-1 1,0 (a) Show that for high enough values of δ, there is an equilibrium of the infinitely repeated game in which (C,C) is played in every period. Your answer must state the strategies of the players clearly. [5 marks] (b) Show that for high enough values of δ, there is an equilibrium of the infinitely repeated game in which players alternate between (C,C) and (D,D), starting with (C,C) in the first period. Your answer must state the strategies of the players clearly. [10 marks] Continues on next page ECN361 (2021) Page 5 Question 4 Consider a second-hand car market with two kinds of cars: • Type A cars are perfectly fine with probability 9/10 and turn out to be defective with probability 1/10 • Type B cars are perfectly fine with probability 1/2 and turn out to be defective with probability 1/2. Other than the difference in the probability of being defective, type A and type B cars are identical. Each seller knows the type of own car, but this information is not available to the buyers. The buyers only know that 1/2 the cars are type A and 1/2 are type B. Sellers value a car that is perfectly fine at 800, while buyers value a car that is perfectly fine at 1000. Both sellers and buyers have a zero value for a defective car. Both sellers and buyers are risk-neutral. There are many sellers and even more buyers, and you can assume that in any transaction the seller gets all the surplus. (a) Given that quality is observable to sellers but not to buyers, which type(s) of car(s) would be traded and at what price(s)? Is the market outcome efficient? [10 marks] [Hint: Note that the value of a type A car to a buyer is (9/10)1000 = 900, and the value of a type A car to a seller is (9/10)800 = 720. Similarly derive other values.] (b) Suppose any seller can offer a guarantee, which is a contract that promises to pay the buyer R if the car breaks down (no payment is made if the car does not break down). Find the range of values of R for which there is an equilibrium in which type A cars sell at 900 with a guarantee and type B cars sell at 500 without a guarantee. [10 marks] (c) Suppose the government forces all sellers to offer a guarantee that promises a refund of 1100 if the car breaks down. Would such a policy promote efficiency? Explain your answer. [10 marks] Continues on next page Page 6 ECN361 (2021) Question 5 (a) Consider a Vickrey auction of a single object with 2 symmetric, risk- neutral bidders whose private valuations v1 and v2 are independent draws from a uniform distribution on [0, 1]. This auction has inefficient Nash equilibria (equilibria in which the win- ner of the auction is not the bidder with the highest private value). Explain carefully with a suitable example. [10 marks] (b) Several generators pollute the environment by emitting carbon dioxide. Generators have different costs of reducing carbon emissions. The gov- ernment wants to put a cap on the total emission. Putting a cap on each generator is more efficient compared to issuing tradeable emissions permits to each generator. Is this true or false? Explain your answer. [10 marks] End of Paper
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