Question

Question 3: Suppose buyers will pay $2000 for a good car (a 'plum') and $1000 for a bad car (a 'lemon'). All cars acquired by the sellers are lemons which they acquire for $1200 each. They can then choose to have mechanics fix the cars up – turning them from lemons to plums - for $300 each. Buyers cannot tell the difference between lemons and plums until after the purchase, and are riskneutral (i.e., will pay their expected valuation).

1. Explain why in equilibrium, no transactions are made.

2. Suppose the used car salesmen can commit to having the mechanics repair a q-fraction of the cars. (Once such an arrangement is made, they are committed to it.) For what values of q will the equilibrium still lead to no transactions, and for which values of q will transactions take place?

Answer 1

1. In equilibrium, no transactions are made as the buyers expected valuation will be 1000$ since all the cars are lemons. Since they will only be willing to pay 1000$, and the sellers themselves acquired the car by paying 1200$, they will be at a loss by selling the car for 1000$. Hence there will be no transactions taking place in this situation.

2. Now, if the used car salesmen can commit to having the mechanics repair a fraction of the cars, the valuation of the customers (Expected valuation) Of the car will increase as there will now be a fraction of cars that are worth 2000$ to them.

Suppose a fraction of cars q is repaired by the salesman.

Expected valuation of the customer = 1000(1-q) + 2000q (1-q fraction of cars is lemon and q cars are plum)

Price according to salesman = 1200(1-q) + 1500q (Since he bought 1-q fraction of cars for 1200$ and spent 1500$ on q fraction of cars)

At the value of q for which both of these are equal, transactions will start taking place, below this no transactions will take place as the expected valuation of the customer will be lower than the price the salesman will be willing to accept.

1000-1000q+2000q = 1200-1200q+1500q

1000+1000q = 1200+300q

700q = 200

q=200/700 =. 0.2857142

Thus when at least 28.57% of cars are repaired by the salesman and become plums, transactions will start taking place.

Hope it’s clear. Do ask for any clarifications if required.