Question

In an isolated town, there are two distinct markets for cars. Buyers will pay up to $12,000 for a high-quality car or $8,000 for a low-quality car. There are 100 high-quality cars for sale, and the sellers have a minimum acceptable price of $11,000. There are also 100 low-quality cars for sale at a minimum acceptable price of $5,000. The supply of automobiles is perfectly inelastic above the reservation price.

a) If there is perfect information (i.e., the buyer knows what is a high and low quality car as does the seller), how many high-quality and how many low-quality cars will be sold?

b) Suppose that the quality of a car is known to the seller, but not to the buyer. What price will prevail in the marketplace if buyers correctly estimate the chance of acquiring a low-quality car at 50%? What happens to the number of high-quality cars for sale at that price.

c) After sellers make all adjustments, what will the equilibrium price of cars be? What proportion of those cars will be high-quality cars?

d) What happens to your answers to parts a), b), and c) if sellers of high-quality cars have a minimum acceptable price of $9,500 rather than $11,000?

Answer 1

a) When the buyers have perfect knowledge

100 high quality and 100 low quality cars would be sold

b) When the quality is not known to the buyers the expected price would be:

Average price = 12000*1/2 + 8000*1/2 = 10000

c) High quality cars would not be offered for sale by the sellers as the expected price is less than the minimum acceptable price of the sellers

Equilibrium price = Between 5000 and 8000

d) When the sellers have minimum acceptable price of 9500 rather than 11000

part a) does not change

part b) does not change

part c) 100 high quality cars will be offered for sale because the expected price>minimum acceptable price and

100 low quality cars will be offered for sale at 10000

Proportion of high to total cars  = 1/2