Suppose a price searching firm faces a demand curve given by Q = 30.5P, and has an average cost curve given by AC = 8.

a. Find the equations for the marginal revenue curve and the marginal cost curve.

b. Find the profit maximizing level of output and the profit maximizing price. At this combination, what is the level of firm profit? What is the level of deadweight loss?

c. Now suppose the marginal cost curve becomes MC = Q 5. What is the new profit maximizing price and quantity?

d. Using the new marginal cost function in (c), suppose now the government imposes a $10 per unit subsidy on the firm. What is the elasticity of demand at the new profit maximizing level of output?

e. Still assuming that the true marginal cost is given by MC=Q-5, does the firm produce the socially optimal level of output in part (d)? Explain.