Microeconomics 4: Information Economics Homework (due April 29 at the beginning of the lecture) CÊdric Argenton April 10, 2013 Students are allowed and encouraged to work in groups. Up to four students can join forces and submit a common answer sheet. Dividing up work between group members is the wrong way to go! If all group members work on all questions and then discuss their answers, then their chances of learning are much increased. Please answer all questions. If a question is unclear, ambiguous, or necessi- tates additional assumptions, please state how you understand it, and solve it! An explanation of any of your answer is asked for: no explanation, no points! 1 Market for lemons Consider the Dutch market for second-hand bikes. On this market, many buy- ers and many sellers are active. Assume that there are many more sellers than buyers. Bikes can be of di¤erent types: denote by q the quality of a bike. This number is known by the current owner but is not observable to prospective buyers. Buyers only know that in the population of all available bikes, q is dis- tributed between 0 and 1 according to the following probability density function: f(q) = 2 ?? 2q. Assume that the reservation value of sellers for a bike of quality q is given by VS = q, while the reservation value of potential buyers is given by VB = 1:5q. All agents have a utility function that is linear in money, and try to maximize expected utility. (a) Suppose counterfactually that q were observable by potential buyers and the market for second-hand bikes were perfectly competitive. What would the competitive equilibrium outcome? (b) Suppose counterfactually that q were observable neither by the sellers nor by the buyers. What would the the competitive equilibrium outcome? 1
(c) Reverting to the assumption that q is private information to the current owner, determine whether the Dutch market for second-hand bikes will unravel. 2 Screening P is an employer who is not able directly to observe the…