Consider the used car market with equal number of good and bad cars. There are t

Question

Consider the used car market with equal number of good and bad cars. There are two buyers and two sellers. The buyers are willing to pay $ 10,000 for a good car and $5000 for a bad car. A seller with a good car is willing to sell their car for $8000. The seller with a bad car is willing to sell their car for $4000. However, the buyers do not know which seller has a good car. Derive the average a buyer is willing to pay for a used car. Show whether the seller with a good car is willing to sell this car at the price in a. Show whether the outcome in b. is Pareto Efficient (Allocation).

Explanation / Answer

Buyer’s willingness to pay:

For a good car = $10000

For a bad car = $5000

Sellers’s willingness to sell:

A good car for = $8000

A bad car for = $4000

In case there exist perfect information with the buyers as well as sellers then, each of the buyers and sellers earn surplus over what they are willing to pay and get.

(a) When the buyer does not have perfect information as to the quality of the car, he decides to pay an average price for the used car. That price is:

Average price = Prob of good car * 10000 + Prob of bad car * 5000

Here there is equal probability for each, therefore:

= 0.5 * 10000 + 0.5 * 5000

= $7500

(b) The average price is lower than what the sellers are willing to get for a good used car, so at this price only bad car will be sold.

(c) A pareto efficient allocation is the one in which no one can be made better off without making someone else worse off. In our answer in part (b), the solution is clearly not pareto efficient. This is because mutually advantageous trade is still possible. For a good car the buyer is willing to pay 10000 and seller is willing to get 8000, so negotiation can leave each with a better outcome. Similarly, for a bad car buyer is willing to pay 5000 while the seller is ready to accept 4000, so here also advantageous trade possibility exist by changing allocation.

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