9. Consider a second-hand car market with two kinds of cars:

Kind A cars work fine with probability 9/10 and break down with probability

1/10

Type B cars work fine with probability 1/2 and break down with probability

1/2.

Other than the difference in the probability of break down, kinds A and B cars

are identical. Each seller knows the type of their own car, but this information

is not available to the buyers. The buyers only know that 1/2 the cars are type

A and 1/2 are type B.

Sellers value a car that works fine at 800, while buyers value a car that works

fine at 1000. Both sellers and buyers have a zero value for a car that breaks

down. Both sellers and buyers are risk-neutral.

There are many sellers and even more buyers, and you can assume that in any

transaction the seller gets all the surplus.

(a) Given that quality is observable to sellers but not to buyers, which type(s)

of car(s) would be traded and at what price(s)? Is the market outcome

efficient?

[Hint: Note that the value of a kind A car to a buyer is (9/10)1000 = 900.

Similarly derive other values.]

(b) Suppose any seller can offer a guarantee, which is a contract that promises

to pay the buyer R if the car breaks down (no payment is made if the car

does not break down).

Find the range of values of R for which there is a separating equilibrium

in which kind A cars sell with a guarantee and type B cars sell without a

guarantee.

(c) Suppose the government forces all sellers to offer a guarantee that promises

a refund of 1100 if the car breaks down. Would such a policy promote

efficiency? Explain your answer.