Suppose that there are two types of customers, High and Low, served by a monopolist. High types have utility uH (x, P) = 2V} P, while low types have utility uL (x. P] = \\E P, where x is the quantity of the good consumed, and P is the total {not per unit) amount paid. Fraction q of the population has High type, and fraction l-q has Low type. The monopolist has constant marginal cost c and no xed cost. 3) Suppose consumer types are observable. Find the monopolist's rstbest quantity and price for each type. Now suppose consumer types are not observable. b) Suppose the monopolist wants both types to buy but must offer the same bundle to everyone. What quantity and price does it pick? 0) Explain why the rst best is not achievable. (1) Suppose q = 0.2 and c = 1. Give an example of a pricing scheme that yields a higher expected prot than the answer to part b