Non-linear pricing . Suppose there are two types of customers: Type A has utility 12q -p. Type B has utility 5q-p, where q is an index of quality and p is the price of a unit of quality.

There are three times as many Type B customers as there are Type A customers. The total number of consumers is 400. The marginal cost of serving each customer is 4q. This implies that the total variable cost of serving a customer is 2q-2.  There is also a fixed cost equal to F.

If the firm cannot distinguish type B from type A cusomters, would it want to operate

if F = 1000?