Exercise 2 (Multiple Products) Consider an industry in which a unique firm pro- duces two goods, A and B. The cost function of this firm is C(qA, qB) = F + qA + 2qB.

The demand function of each product is Di(pi) = 1/pi for i = A, B.

1. Find the competitive and the monopoly prices. Find firm profits in each case (Hint: Show that the revenue of a monopolist is independent of the price and, thus, profits are higher the fewer units are sold). 2. Compute the Ramsey price when the firm is constrained to earn a profit of at least 0 and no subsidy is possible. 3. Write the optimal prices in terms of F. Show that when F = 0 and F = 2 the Ramsey prices coincide with the competitive and the monopoly price, respectively. Why aren't there Ramsey prices for F > 2?