Question

In a used cars market, there are many car sellers with even larger number of car buyers. A car priced at 800 is considered high quality to the seller, a car at 200 is considered low quality to the seller. To a buyer, for any quality of a car, the value to the buyer is x times the value to the sellers. x>1. Sellers have information about the quality of their own car, whereas buyers know 2/3 of cars are low quality and the remainder being high quality. Agents are risk-neutral. For which values of x will sellers sell their cars?

Answer 1

Answer :-

According to the buyers known information, 2/3 of the cars are low quality, then obviously the remaining 1/3 of them are high quality, {(1-(2/3)}

and they value the low quality cars at 200x (x times its value to seller) and high quality cars at 800m (x times its value to seller), They will be wiling to pay the expected value for a car ;

Expected value of a car to the buyer ;

EV = 200x × (2/3)+800x × (1/3) = 1200x/3 =

For all sellers to sell all the used cars, this expected value of the car that the customer is willing to pay 400x should be greater than or equal to 800(since the seller values high quality car at 800, he will sell these only if the customer is willing to pay more than 800 for all the cars) The values of x for which the expected value for the customer is higher than 800 is ;

400x>= 800x

Therefore, x>=2

Thus if x is greater than or equal to 2, then all sellers will sell their used cars.