Exercise 1 (Distortionary Taxation) Consider the cost function C(q) = cq + F, and the two demands 1. q(p) = 1 p

2. q(p) = p^ with > 1. Suppose that a regulator wants to set the price for the product that maximizes social welfare. The regulator can offer a subsidy T to the firm so that it breaks even. This subsidy comes with a social cost arising from distortionary taxation of T, where 0. 1. Find the optimal price for each of the two demand functions. 2. Show that when = 0 the optimal price coincides with the competitive one and when goes to infinity the price converges to the monopoly one.