Question

Suppose that there are three classes of homes in a small college town, with different qualities. The information about these homes is summarized in the table below:

Class	Value to Seller	Value to Buyer	Share of all Homes
High Quality	$100,000	$120,000	20%
Medium Quality	$80,000	$89,625	60%
Low Quality	$60,000	$60,096	20%

a. Suppose the BUYER is risk neutral. What is the Expected Monetary Value of homes in this town to buyers? b. What would be the equilibrium price (or range of prices) of homes in this market? What types of homes would be sold?

Answer 1

a. The expected value will be p1V1+p2V2+p3V3, where p1, p2, and p3 are the probabilities of high, medium and low-quality homes and V1, V2, V3 being their respective valuations. So, the expected monetary value of homes to buyers is (.20)(120,000)+(.60)(89,625)+(.20)(60,096) which is $89,794.20

b. The equilibrium price range of homes in the market would be $60,000-$80,000. Since the value buyer places for the homes is less than $100,000 which the seller values for the high-quality homes. So in the market, only the medium and low-quality homes would be sold.