A firm has $2.5 million in sales, a Lemer index of 0.85, and a marginal cost of $25, and competes against 1000 other firms in its relevant market. 1.a. What price does this firm charge its customers? 1.b. By what factor does this firm mark up its price over marginal cost? Interpret your result. 2. An industry consists of three firms with sales of $300,000, $450,000, and $550,000. 2. a. Calculate the Herfindahl-Hirschman index (HHI). 2. b. Calculate the four-firm concentration ratio (C₁). Problem #4 You are the manager of a monopoly, and your economists have estimated your demand and cost 600 +500 + 202 and the marginal cost is functions as P-250-3Q, the total cost is TC = given by MC 50 +4Q. 1. Enunciate the Formula: MR for Linear Inverse demand. [from your textbook] 2. Use the formula from question 1, to find the marginal revenue MR when the inverse demand is P-250-3Q. 3. What's the principle of the Monopoly Output Rule? [from your textbook] 4. Use the principle enunciated in question 3 to find the output Q that the firm should produce to maximize its profit. = 5. What's the Monopoly Pricing Rule? [from your textbook] 6. Use the Monopoly Pricing Rule from question 5 to find the price P that the firm should charge when maximizing its profit. 7. Determine the firm's total revenue (TR), total cost (TC) and maximum profits (II). 8. Is demand elastic, inelastic, or unit elastic at the profit-maximizing price-quantity combination? Explain your answer! PRINCIPLE Monopoly Output Rule A profit-maximizing monopolist should produce the output QM such that marginal revenue equals marginal cost: MR (QM ) = MC (QM) PRINCIPLE Monopoly Pricing Rule Given the level of output, QM, that maximizes profits, the monopoly price is the price on the demand curve corresponding to the QM units produced: s PM = P(QM) Formula: MR for Linear Inverse Demand. For the linear inverse demand function, P (Q) = a +bQ, marginal revenue is given by MR= a + 2bQ
