Microsoft Word - Problem Set 8

Problem:

The market demand for train service is
yd(p) = 4 - p.

The cost function for a firm to provide train service is c(y)=y2 +F,

where F is the fixed costs (e.g., laying and maintaining the tracks).

(a) Show that the firm's marginal cost function is MC(y) = 2y.

(b) Suppose that the firm is a monopolist. Assuming the firm produces a positive level of output, calculate the output and price it sets. Explain why the profit-maximizing price is greater than the monopolist's marginal cost.

(c) In an appropriate diagram, illustrate the monopolist's optimal choice of output level (assuming it produces a positive level of output) and the resulting deadweight loss. On the diagram, point out that the monopolist's price exceeds its marginal cost.

(d) In an appropriate diagram, illustrate why a perfectly competitive firm optimally chooses an output level such that price equals marginal cost (as long as it produces a positive level of output).

(e) Even though doing so is not profit-maximizing, assume that the firm chooses an output level such that price equals marginal cost (and produces a positive level of output)-thereby mimicking what the outcome would be if the market were perfectly competitive. Find the output level and the price in this case.

(f) With reference to an appropriate diagram, explain why the increase in consumers' surplus going from the monopoly market structure to a single firm charging the competitive price from part (e) is:   ∫(4-p)dp, where integral is from 8/3 to 3.