Market for Lemon - Decisions under risk and uncertainty

Solution Preview

See the attached file for complete solution. The text here may not be copied exactly as some of the symbols / tables may not print. Thanks

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.

Since both buyers and sellers can observe directly the quality of any car traded, they would not be willing to pay or receive an amount which is higher than the true utility of car. There will be two equilibriums in the market one for lemons and other for peaches. Since both can observe the quality there is no asymmetry of information.

Equilibrium for Lemons market:
Utility of car to the buyer = x+1.2*1=x+1.2
Utility of car to seller = x+1*1=x+1
Since x=1,
We have
Utility of car to the buyer =2.2
Utility of car to seller =2
Deal can take place for a price between 2.0 to 2.2, however, since there are more number of buyers than sellers, the competition among the buyers will push the price up and equilibrium will be attained at 2.2. At this equilibrium all lemons will be cleared (sold) by the market.

Equilibrium for Peaches market:
Utility of car to the buyer = x+1.2*3=x+3.6
Utility of car to seller = x+1*3=x+3
Since x=1,
We have
Utility of car to the buyer =4.6
Utility of car to seller =4
Deal can take place for a price between 4.0 to 4.6, however, since there are more number of buyers than sellers, the competition among the buyers will push the price up and equilibrium will be attained at 4.6. At this price all peaches will be cleared in the market (sold)

(b) Determine the equilibrium outcome, or outcomes, ...