High-Quality and Low-Quality Versions of Some Good.

There are two types of consumer. TypeA has utility given by 12q - p. Type B has utility given by 5q - p, where q is a numerical index of quality and p is the price of one unit of the good. There are three times as many Type B as there are TypeA. The total number of consumers is 400. The marginal cost of serving each individual consumer's purchase is 4q. This means the total variable cost of serving a consumer is 2q². If the consumer's utility goes negative, the consumer will not buy from you and go somewhere else. If utility is non-negative, the consumer will buy one unit of the good. Given that the firm cannot distinguish the two types of consumer but can provide a menu of the product of two different qualities at two different prices. What would be the quality of the two types of product that it sells, and at what prices?