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MicroChapter6pset.doc

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Besanko & Braeutigam – Microeconomics, 4 editionSolutions Manual Chapter 6 Perfectly Competitive Markets 1. A firm sells a product in a perfectly competitive market, at a price of $50. The firm has a fixed cost of $30. Fill in the following table and indicate the level of output that maximizes profit. How would the profit-maximizing choice of output change if the fixed cost increased from $40 to $60? More generally, explain how the level of fixed cost affects the choice of output. 2. A bicycle-repair shop charges the competitive market price of $10 per bike repaired. The firm’s short-run total cost is given by STC(Q) = Q /2, and the associated marginal cost curve is SMC(Q) = Q. a) What quantity should the firm produce if it wants to maximize its profit? b) Draw the shop’s total revenue and total cost curves, and graph the total profit function on the same diagram. Using your graph, state (approximately) the profit-maximizing quantity in each case. 3. Dave’s Fresh Catfish is a northern Mississippi farm that operates in the perfectly competitive catfish farming industry. Dave’s short-run total cost curve is 2, where is the number of catfish harvest per month. The corresponding short-run marginal cost curve is . All of the fixed costs are sunk. (a) What is the equation for the average variable cost ( )? (b) What is the minimum level of average variable costs? (c) What is Dave’s short-run supply curve? Copyright © 2011 John Wiley & Sons, Inc. Chapter 8 - 1 Besanko & Braeutigam – Microeconomics, 4 editionSolutions Manual 4. Ron’s Window Washing Service is a small business that operates in the perfectly competitive residential window washing industry in Evanston, Illinois. The short-run total cost of production is STC(Q) = 40+ 10Q + 0.1Q , where Q is the number of windows washed per day. The corresponding short-run marginal cost function is SMC(Q) = 10 + 0.2Q. The prevailing market price is $20 per window. a) How many windows should Ron wash to maximize profit? b) What is Ron’s maximum daily profit? c) Graph SMC, SAC, and the profit-maximizing quantity. On this graph, indicate the maximum daily profit. d) What is Ron’s short-run supply curve, assuming that all of the $40 per day fixed costs are sunk? e) What is Ron’s short-run supply curve, assuming that if he produces zero output, he can rent or sell his fixed assets and therefore avoid all his fixed costs? 5. The oil drilling industry consists of 60 producers, all of whom have an identical short- run total cost curve, STC(Q) = 64 + 2Q , where Q is the monthly output of a firm and $64 is the monthly fixed cost. The corresponding short-run marginal cost curve is SMC(Q) = 4Q. Assume that $32 of the firm’s monthly $64 fixed cost can be avoided if the firm produces zero output in a month. The market demand curve for oil drilling services is D(P) = 400 − 5P, where D(P) is monthly demand at price P. Find the market supply curve in this market, and determine the short-run equilibrium price. 6. There are currently 10 identical firms in the perfectly competitive gadget manufacturing industry. Each firm operates in the short run with a total fixed cost of F and total variable 2 cost of 2Q , where Q is the number of gadgets produced by each firm. The marginal cost for each firm is MC = 4Q. Each firm also has non sunk fixed costs of 128. Each firm would just break even (earn zero economic profit) if the market price were 40. (Note: The equilibrium price is not necessarily 40 when there are 10 firms in the market.) The market demand for gadgets is Q = 18M − 2.5P, where Q is the aMount purchased in the entire market. a) How large are the total fixed costs for each firm? Explain. b) What would be the shutdown price for each firm? Explain. c) Draw a graph of the short-run supply schedule for this firm. Label it clearly. d) What is the equilibrium price when there are 10 firms currently in the market? e) With the cost structure assumed for each firm in this problem, how many firms would be in the market at an equilibrium in which every firm’s economic profits are zero? 7. The wood-pallet market contains many identical firms, each with the short-run total cost function STC(Q) = 400 + 5Q + Q , where Q is the firm’s annual output (and all of the firm’s $400 fixed cost is sunk). The corresponding marginal cost function is SMC(Q) = 5 + 2Q. The market demand curve for this industry is D(P) = 262.5 − P/2, where P is the market price. Each firm in the industry is currently earning zero economic profit. How many firms are in this industry, and what is the market equilibrium price? Copyright © 2011 John Wiley & Sons, Inc. Chapter 8 - 2 Besanko & Braeutigam – Microeconomics, 4 editionSolutions Manual 8. A firm in a competitive industry produces its output in two plants. Its total cost of producing Q uni1s from the first plant is TC = (Q ) 1 and t1e marginal cost at this plant is MC = 2Q . The firm’s total cost of producing Q units from the second plant is TC = 1 2 1 2 2 2(Q 2 ; the marginal cost at this plant is MC = 4Q 2 The p2ice in the market is P. What fraction of the firm’s total supply will be produced at plant 2? 9. A competitive industry consists of 6 type A firms and 4 type B firms. Each firm of type A operates with the supply curve: Each firm of type B operates with the supply curve: a) Suppose the market demand is At the market equilibrium, which firms are producing, and what is the equilibrium price? b) Suppose the market demand is At the market equilibrium, which firms are producing, and what is the equilibrium price? 10. The global propylene industry is perfectly competitive, and 2ach producer has the long-run marginal cost function MC(Q) = 40 − 12Q + Q . The corresponding long-run average
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