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UNIVERSITY OF WASHINGTON Department of Economics Economics 200 Scott Problem Set 4. Competitive Firm Behavior Economic Profit: 1. Undeterred by the statistics on the mortality rates of small businesses (more than half go out of business in 18 months), a young chef opens his own restaurant. To do so, he quit his own job at $8,000 per year, cashed in $20,000 worth of savings bonds yielding 5% to provide capital for the business, and took over a store building owned by his wife which had previously been rented out at $500 per month. His expenses during the first year amounted to $50,000 for food, $15,000 for extra help, and $2,000 for gas, electricity, etc. His total receipts for the first year are $78,000. Assume he is a profit maximizer and derives no particular satisfaction from being his own boss, etc. Would you advise the young chef to stay in business? Competition: 2. A purely competitive case: Output TFC 0 1 2 3 4 5 6 7 8 9 10 $300 300 300 300 300 300 300 300 300 300 300 $ TVC TC AFC AVC ATC MC 0 100 150 210 290 400 540 720 950 1,240 1,600 $ 300 400 450 510 590 700 840 1,020 1,250 1,540 1,900 $ 300 150 100 75 60 50 43 38 33 30 $ 100 75 70 73 80 90 103 119 138 160 $ 400 225 170 148 140 140 146 156 171 190 $ 100 50 60 80 110 140 180 230 290 360 Assume that a purely competitive firm has the schedule of costs given in the table above. Economics 200 Problem Set 4 2-1. 0 1 2 3 4 5 6 7 8 9 10 2-3. Scott Complete the table below showing the total revenue and total profit of the firm at each level of output the firm might produce, assuming market prices of $55, $120, and $200. Output 2-2. 2 Market Price = $55 Market Price = $120 Market Price = $200 Revenue Revenue Revenue $ Profit $ $ Profit $ $ Profit $ Indicate what output the firm would produce and what its profits would be at a: a. Price of $55: output of and profit of . b. Price of $120: output of and profit of . c. Price of $200: output of and profit of . Complete the supply schedule of a firm in the table below and indicate what the profit of the firm will be at each price. Price $360 290 230 180 140 110 80 60 Quantity Supplied Profit $ Economics 200 Problem Set 4 2-4. 3 Scott If there are 100 firms in the industry and all have the same cost schedule: a. Complete the market supply schedule in the table below. Quantity Demanded Price 400 500 600 700 800 900 1,000 b. Quantity Supplied $360 290 230 180 140 110 80 Using the demand schedule given in part a: (1) What will the market price of the product be? $ (2) What quantity will the individual firm produce? (3) How large will the firm’s profit be? $ (4) Will firms tend to enter or leave the industry in the long run? Why? 2-5. If the total costs assumed for the individual firm in problem 1 were long-run total costs and if the industry were a constant-cost industry: a. What would be the market price of the product in the long run? $ b. What output would each firm produce when the industry is in long-run equilibrium? c. Approximately how many firms will there be in the industry in the long run, given the present demand for the product? d. If the following were the market demand schedule for the product, how many firms would there be in the long run in the industry? Price $ 360 290 230 180 140 110 80 Quantity Demanded 500 600 700 800 900 1,000 1,100 Economics 200 Problem Set 4 e. 4 Scott On the graph below, draw the long-run supply curve of this industry. Then draw a long-run supply curve for an increasing-cost industry. Label them CC and IC. P Q 3. Cost Minimization. The diagram below, with intercepts 250 and 100 for the straightline, uses the standard notation and depicts the cost-minimizing use of factors of production for a profit-maximizing firm. The price of labor is $5. K 250 K* L* 100 L Economics 200 Problem Set 4 5 Scott a. What is the numerical value of the firm’s total cost? Explain. b. What is the numerical value of the price of capital? Explain. c. Given cost minimization, what is the marginal rate of technical substitution (give general definition and numerical value for the cost-minimizing combination of K and L)? Explain. 4. Factor Substitution. Use isoquants and isocost curves to show: (a) If capital and labor are perfect complements, factor intensity (the ratio of capital goods to labor) is insensitive to changes in relative factor prices. (b) If capital and labor a perfect substitutes, changing relative factor prices can cause dramatic shifts from exclusive use of one factor of production to the other. 5. Analysis of a Lump-Sum Tax in Competitive Markets. The market for good X is in a competitive long-run equilibrium for an industry with a unique size of firm that minimizes unit (i.e., average) cost. Then, the government imposes a “lump-sum tax.” A lump-sum tax requires each firm in the market to pay a specified amount just for being in business. No matter what the firm’s output or profit, it is now required to pay this new lump-sum tax. Such a tax is sometimes called a franchise fee. Analyze what happens in the market and to the typical firm in both the short run and the long run. What happens to output and price in the short run – for the market and for the typical firm? What happens to output and price in the long run – for the market and for the typical firm? Explain, illustrating your answer with the customary diagrams for supply and demand in the market and for the typical firm’s cost and demand conditions. 6. LR and SR Costs, Isoquants and Isocosts. Draw the long-run average cost of a firm as the envelope of a few short-run average cost schedules (see p. 143 of your text and your notes from lecture). “Talk through” the intuition, using isoquant-isocost diagrams to illustrate your reasoning. 7. Marginal Product of Labor, Marginal Revenue Product of Labor, and Labor Demand. Using diagrams, explain the equivalence between the condition “price equals marginal cost” and the condition “wage equals marginal revenue product of labor” in the short run. Refer to your notes and to pages 182-183 in the text. Note that your text calls marginal revenue produce the value of marginal product. How will an increase in the price of a good affect the demand for labor used in the production of that good in the short-run?