Question

In the country of Autolandia, used cars all sell for the same price. In Autolandia, the quality of cars is uniformly distributed with sellers valuing the cars from $0 to $1,000 and buyers valuing the cars from $100 to $1,100 (buyers value each individual car at $100 more than the sellers). For example, consider a market with 1,001 cars. There will be one worth $0 to a seller/$100 to a buyer, one worth $1 to a seller/$101 to a buyer, etc. up to one worth $1,000 to a seller/$1,100 to a buyer.

a) If neither the buyer nor the seller knows the quality of a car, will any cars sell? If so, at what price?

b) If only the seller knows the quality of the car, what will the buyer think is the true value of a car with price p to the seller of that car? How much would a buyer value the average car for sale at price p? Give a numerical example.

c) In the version of the market where only the seller knows the true quality of the car, what will be the equilibrium price?

d) What percentage of the total number of cars get sold?