Imagine that you are perusing a copy of the Auto Trader magazine in search of a used car. Suppose that there are 50 cars offered for sale and 50 buyers interested in a used car purchase. You know that sellers of "Lemons" (bad quality cars) would be willing to accept $4000 and that buyers would be willing to pay up to $4,500 for a "Lemon". Furthermore, sellers of "Cherries" (good quality cars) would be willing to accept $6000 and that buyers would be willing to pay up to $7000 for a "Cherry".

Assume the form of buyers' guesses about the value of the average car in this market is;

(willingness to pay for "Lemons") + (1 - ) (willingness to pay for "Cherries") = value of the average car.

where = proportion of "Lemons" in the market and (1 - ) = the proportion of "Cherries" in the market.

a) How many "Lemons" can exist in this market before the market fails (i.e. no "Cherries" will be offered for sale)?