[Adverse Selection] A buyer wants to purchase a house from a seller. Let v be the quality of this house. The quality v is known to the seller but unobservable to the buyer. The buyer thinks that the possible values of v are $10k,$100k,$150k,$200k and $300k with equal probability. The seller’s valuation of the house is v and the buyer’s valuation of the house is 1.5v.
a) Suppose both the buyer and seller see the value of v. Will trade occur? If yes then what are the possible transaction prices?
b) Suppose the buyer cannot see v and offers $150k to the seller. What is the probability that the seller accepts the offer? Calculated the buyer’s expected profit. Is it positive or negative?
c) Suppose the buyer is allowed to make any offer to the seller and the seller sells if the offered price is above v. What is the buyer’s profit maximizing offer? What is the buyer’s maximum profit? Will trade take place?
d) Explain why the $300k house will never be traded.