Question

Suppose there are 50 sellers of cars in a used car market who know the quality of their car. Of these 50 sellers, 25 own plums. Each owner of a plum is willing to sell her car as long as she receives at least $4000 for it. The remaining sellers own lemons, which each would be willing to sell for at least $2000. There are also 50 potential buyers.

a) Suppose that each buyer is willing to pay up to $5500 for a plum and up to $3500 for a lemon. If quality is not observable by buyers, would this lead to market failure in this used car market? Explain why or why not. (5 marks)

b) Suppose instead that each buyer is willing to pay up to $5000 for a plum and up to $3000 for a lemon. If quality is not observable by buyers, could signaling bring about efficiency this market? If so, explain how. If not, explain why not. (5 marks)

Answer 1

a) For the buyer, the expected value of the car will be

1/2×5500+1/2×3500 = 2750 + 1750= 4500

This value is greater than the value that the owner of plum is willing to sell the car. So it makes negotiation possible for all sellers. Thus, gains from trade is received by all sellers. Ultimately, there is no room for market failure.

b) In this case, the expected value of the car will be

1/2×5000+1/2×3000 = 4000

This value is equal to the value that the owner of the plum is willing to sell the car. The owner of lemons will gain from trade whereas the owner of plum will be able to trade only if there is proper market signalling. There by the sellers of plum can participate in trade only by proper market signalling, that their product is a plum not a lemon