Write down the total cost function

Assignment Help Macroeconomics

Reference no: EM133339908

Case: 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 ?i 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?

(e). Suppose now firms have different marginal costs. However, firms can only find out about their marginal cost after they pay fixed cost F and enter the market. Firm i decides if it wants to stay in the market or exit upon observing its marginal cost ci . What is the cut-off marginal cost c ∗ that makes a firm indifferent between exiting or staying in the market?

Reference no: EM133339908

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