Consider the following application of monopolistic competition in trade. Firms in an industry

face monopolistic competition and the (residual) demand function facing a firm is:

where Q is the quantity of output demanded, S is the total output of the industry, n is the number of

firms in the industry, b is a positive constant term representing the responsiveness of a firm's sales to

its price, P is the price charged by the firm itself, and P¯ is the average price charged by firms in this

industry. Firms are small, so each firm treats P¯ as given ( a firm does not think its own pricing strategy

changes P¯).

Each firm faces the same residual demand curve. They also have the same fixed cost F. Firm i faces a

constant marginal cost ci .

(a). Please write down the total cost function, average cost function, and marginal cost

function of firm i when it produces Q units of output.

(b). Draw a diagram where the firm's price is on the y-axis, and output is on the x-axis. Please

draw the residual demand curve, marginal revenue, and marginal cost curves on that diagram.

(c). Consider the short-run optimal output and price choice for firm i. Write the optimal

output level Qi , corresponding price Pi , firm profit Ⅱi as functions of marginal cost ci , S, n, b, and

P¯.

(d). Let's start with the scenario where firms are symmetric. That is, all firms face the same

marginal cost, ci = c where i = 1, 2, ...n. In the long run, what is the equilibrium condition that

determines how many firms can stay in this industry? What is each firm's profit in the long run?
 

 

Transcribed Image Text:

xS=0 -bx (P-P) xS=0 -bx (P-P)

Answer rating: 100% (QA)

a The total cost function of firm i when it produces Q units of output is given by Total cost Fixed cost Variable cost F ci Q The average cost functio... View the full answer