Question

Request you to answer this microeconomics question ASAP:

Consider a market for used cars. There are many sellers and even more buyers. A seller values a high quality car at 800 and a low quality car at 200. For any quality, the value to buyers is m times the value to sellers, where m > 1. All agents are risk-neutral. Sellers know the quality of their own car, but buyers only know that 2/3 of the cars are low quality and the remaining 1/3 of them are high quality. For what values of m do all sellers sell their used cars?

Answer 1

3. If the buyers know that 2/3rd of the cars are low quality and remaining 1/3rd of them are high quality, and they value the low quality cars at 200m (m times its value to seller) and high quality cars at 800m (m 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= 200m*2/3 + 800m*1/3 = 1200m/3 = 400m

For all sellers to sell all the used cars, this expected value of the car that the customer is willing to pay 400m 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 m for which the expected value for the customer is higher than 800 is

400m >= 800

m >= 2

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

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