Suppose that the demand curve is P = 10 - Q and the costs of production are C = q2 + 9. The marginal cost function is MC = 2q.

(a) Find minimum efficient scale.

(b) For what range of output is this technology a natural monopoly?

(c) What are the second-best-where P = AC and the market clears-price and output?

(d) Could an entrant profitability enter by undercutting the incumbent? How?

(e) Suppose that an entrant enters and produces at minimum efficient scale. Then the residual demand for the incumbent firm (I ) is P I = 10 - qmes - q I . What is the profit-maximizing output for the incumbent if its fixed costs are sunk? If its fixed costs are variable?

(f) For the case where the incumbent's fixed costs are variable, determine the change in total surplus from entry. [Hint: For both this part and

(g), assume that qe = qmes .]

(g) For the case where the incumbent's fixed costs are sunk, determine the change in total surplus in both the short and long run.

(h) Is entry socially beneficial in this case? Is this natural monopoly sustainable?