Consider the lemons model with variable quality discussed in class. The quality of sellers is denoted by v; also, the buyer is willing to pay a price equal to the average quality of a car on the market. The buyer does not know the quality of the car he buys: he only knows that the quality is uniformly distributed in [0,1] (each v between 0 and 1 is equally likely).
a. Find the market price if the cost of quality v to a seller is c(v) = v/4
b. Find the market price if the cost of quality v to a seller is c(v) = 2v^3 Consider case b. and suppose the utility the buyer receives from a car of quality v is U(v).
c. If the buyer is risk averse, does the price go up or down compared to b.? How about the highest quality available in the market? Explain your answer carefully (No math is necessary).