Firm A has the following technology: f(x1, x2) = x1x2

The price of input 1 is w1 = 2 and the price of input 2 is w2 = 4. (a) Firm A would like to produce y units of output. What is the conditional factor demand for the two inputs? What is the cost function?

(b) Assume Firm A is a monopolist who can practice third degree price discrimination. The firm faces two types of consumer. The demand function for type 1 is D1(p) = 20 2p and the demand function for type 2 is D2(p) = 30 3p. What of the two types will the monopolist set a higher price? Explain your conclusion with reference to the price elasticity of demand for the two consumers.

(c)Firm A is a monopolist who will practice first degree price discrimination. The inverse demand curve for the good produced by the monopolist is given by p(y) = 20 3y. What is the optimal amount of output? Explain how you found it.

(d) Now suppose there exist another firm, Firm B, identical to Firm A. The two firms compete in an oligopoly market as a pair of Bertrand competitors. What price will the two firms set? Explain the result as the Nash equilibrium of a game between the two firms.

(e) Compare your answers at points c and d. Are consumers better off under first degree price discrimination or under the Bertrand competition?