$1.($Lemons$)$ Suppose there are two types of used cars: peaches and lemons. A peach, if it is known to be a peach, is

worth $$3000$ to a buyer and $$2500$ to a seller. $($We will assume that the supply of cars is fixed and the supply of

possible buyers is infinite$).$ A lemon, on the other hand, is worth $$2000$ to a buyer and $$1000$ to the seller. There

are twice as many lemons as peaches.

a$)$ What would be the prices for lemons and peaches if there was perfect information? Explain. $($Note the number

of buyers when answering this.$)$

b$)$ What would be the price of a used car if neither buyer nor seller knew whether a particular car was a peach or

a lemon and all agents are risk neutral? $($If agents are risk neutral, then their utility is the expected value of the

car they buy minus the price paid.

c$)$ Assume buyers can$$t tell at all if a car is a peach or a lemon, but the sellers do know. Which sellers would want

to sell at the prices calculated in part b$?$ What would happen to the market price for used cars and how many

peaches would be offered?

d$)$ Now assume there are two peaches to every lemon and as in part c$,$ buyers can$$t tell at all if a car is a peach or

a lemon, but the sellers do know. Which would be the market price for used cars and how many peaches would

be offered?