There are two types of consumers: one half of consumers are type 1 (low type) and the other half are type 2 (high type). Type 1's demand curve is q1 = 8 P, while type 2's demand is given by q2 = 12 P. Consider a monopolist selling its product to these consumers. Assume that the marginal cost is equal to zero.

1.1. Suppose that the firm can charge only one price, P, for each unit.

(1) (5 point) What is the market demand, Q? (Note: Q should be equal to q1 + q2.)

(2) (10 point) What should be P that maximizes the monopoly's profit? For the profit- maximizing P, will both types of consumers purchase the product, or only high type con- sumers purchase?

(3) (5 point) Given the price in (2), what is the resulting social surplus?