18.8

a. Compute a buyer's maximum willingness to pay for a car if he or she cannot observe the car's quality.

b. Suppose that there are enough buyers relative to sellers that competition among them leads cars to be sold at their maximum willingness to pay. What would the market equilibrium be if sellers value good cars at $8,000? At $6,000? Consider the following simple model of a common values auction. Two buyers each obtain a private signal about the value of an object. The signal can be either high (H) or low (L) with equal probability. If both obtain signal H, the object is worth 1; otherwise, it is worth 0.

a. What is the expected value of the object to a buyer who sees signal L? To a buyer who sees signal H?

b. Suppose buyers bid their expected value computed in part (a). Show that they earn negative profit conditional on observing signal H-an example of the winner's curse.