Y5

Consider a market of used cars. The owners know the quality of their cars, denoted by 0. That is their private information, which cannot be observed by buyers. Assume that is distributed over [0, 1] according to the density function

f() = (1 ).

If a buyer gets a used car with quality of at price of p, his surplus is p. Each owner can show the record of his car to the potential buyers, which will completely reveal the quality of his car to the buyers. However, it hurts privacy to do so and thus incurs a psychological cost, denoted by c 0. We assume that c is uniformly distributed over [0, 1] and is independent of . So now sellers have two-dimensional types (, c), which can be represented by the unit square. (Use x axis to denote , and y axis to denote c.)

A seller with type of (, c) gets a utility of p c if he reveals the record and sells his car at price of p; gets utility of p, if he sells his car at price of p without revealing the record, and gets utility of

58 , if he keeps his car and leaves the market.

(a) (7 points) (Policy 1: Revealing is forbidden). What is the stable equilibrium if revealing record is forbidden? Depict sellers' choice in equilibrium in the unit square.

(b) (5 points) (Policy 2: Mandatory revealing). What is the equilibrium if the seller MUST show their record to the buyers before any deal in the market? (They do not need to show the record if they quit the market.) Depict sellers' choice in equilibrium in the unit square.

(c) (13 points) (Policy 3: Voluntary revealing). Now suppose that sellers can freely choose whether to reveal their record or not. Compared with the stable equilib- rium under Policy 1, how will sellers' behavior change in equilibrium? Depict the change in the unit square.