Market for Lemon - Decisions under risk and uncertainty
Traders are divided into 2 groups, sellers and buyers. Each seller sells one or no cars, and each buyer buys one or no cars. There are more buyers than sellers and the market is competitive. Cars can be "lemons" with quality q=1 or "peaches" with quality q=3. The proportion of lemons is ½. The von Neumann Morgenstern utility functions of the sellers and buyer are, respectively:
Us=x+q
Ub=x+1.2q
Where x is a numeraire good with price 1.
(a) Determine the equilibrium outcome, or outcomes, when both the seller and the buyer observe directly the quality of any car traded.
(b) Determine the equilibrium outcome, or outcomes, when neither the seller nor the buyer observes directly the quality of any car traded.
(c) Determine the equilibrium outcome, or outcomes, when only the seller observes directly the quality of any car traded.
(d) Determine the equilibrium outcome, or outcomes, when there are more sellers than buyers.
(e) What are the characteristics of the "market for lemons?