# For what values of K will the monopolist choose to make and sell only high quality cars?

A monopoly auto manufacturer produces cars and can choose the quality of the car produced. Let x be a measure of quality, and assume that the marginal cost of a unit of quality is constant and equal to 1. There are two types of consumers that are potentially in the car market. Consumers of type A have inverse demand function pA(x) = 7 − x, and consumers of type B have inverse demand function pB(x) = 5 − x. There are equal numbers of each type of consumer. Question: Suppose demand by type As pA(x) = K − x, for some number K. For what values of K will the monopolist choose to make and sell only high quality cars? What is the deadweight loss in these situations?

Answer: As the quality of cars sold to B types is reduced to zero, the marginal loss on each of them is 4 (the distance between 5 and 1 on the vertical axis). It would be optimal to reduce quality this far if the marginal gain on A types was at least this large. This would happen as long as K ≥ 9. In this situation, B types would lose all of their potential consumer surplus, so the deadweight loss would be 8 for each one, or 800 in total.