Homework #4 Microeconomics (I), Fall 2010 Due day:

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1 組別 姓名與學號 Homework #4 Microeconomics (I), Fall 2010 Due day: Part I. Multiple Choices: 60% (5% each) Please fill your answers in below blanks, only one answer for each question C C B A A D C A D B B A 1. Economic costs of an input include: A) only implicit costs. B) only explicit costs. C) both implicit and explicit costs. D) whatever management wishes to report to the shareholders. 2. Sarah earns $40,000 per year working for a large corporation. She is thinking of quitting this job to work full time in her own business. She will invest her savings of $50,000 (which currently has an annual 10% rate of return) into the business. Her annual opportunity cost of this new business is: A) $0 B) $40,000 C) $45,000 D) $90, Which of the following will cause the marginal cost curve of making cigarettes to shift? A) A $5 million penalty charged to each cigarette maker. B) A $1 per pack tax on cigarettes. C) A $1 million advertising campaign by the American Cancer Society. 4. The slope of the isocost line tells the firm how much: A) capital must be reduced to keep total cost constant when hiring one more unit of labor. 1

2 B) capital must be increased to keep total cost constant when hiring one more unit of labor. C) more expensive a unit of capital costs relative a unit of labor. D) the isocost curve will shift outward if the firm wishes to produce more. 5. The long run average cost curve may initially slope downward due to: A) economies of scale. B) decreasing average fixed costs. C) increasing marginal returns. 6. Learning by doing will result in: A) an upward-sloping long-run average cost curve. B) a larger long-run marginal cost than long-run average cost. C) a rotation in the isocost curves. D) lower long-run costs than short-run costs. 7. Economists define a market to be competitive when the firms: A) spend large amounts of money on advertising to lure customers away from the competition. B) watch each other's behavior closely. C) are price takers. 8. There are 10 identical internet service providers (ISPs) in a city serving a market demand with an elasticity of The elasticity of supply for each firm is 3.0. The elasticity of demand faced by an individual ISP provider is: A) -42 B) -15 C) -1.5 D) -27 2

3 9. The above figure shows the cost curves for a competitive firm. If the firm is to operate in the short run, price must exceed: A) $15. B) $11. C) $10. D) $5. 10.Long-run market supply curves are upward sloping if: A) firms are identical. B) the number of firms is restricted in the long run. C) input prices fall as the industry expands. 11.Suppose that for each firm in the competitive market for potatoes, long-run average cost is minimized at $0.2 per pound when 500 pounds are grown. The demand for potatoes is Q = 10,000/p. If the long-run supply curve is horizontal, then how many firms will this industry sustain in the long run? A) 0 B) 100 C) 50,000 D) There is not enough information to answer. 12.If firms in a competitive market are not identical, then an increase in cost will: A) push the most inefficient firms out of the market. B) push the most efficient firms out of the market. 3

4 C) shift marginal cost to the right. D) Need more information. Part II. Problems: 40% 1. A firm produces output according to the following function: q = f (L, K) = L 1/2 K 1/3 The cost of labor is $9 and the rental cost of capital is $4. a) With the given prices, use the Lagrangian method to compute the optimal (cost-minimizing) capital to labor ratio (K/L) for the firm (5%) b) Suppose the firm wishes to produce 72 units of output. How much capital and how much labor does the firm employ? (4%) c) What is the total cost of producing 72 units of output? (3%) d) Suppose that the firm suddenly decides to double the quantity of output (from 72 to 144 units) but only has a day to complete the order. Therefore, in that time, the amount of capital is fixed but labors are not. How much will it cost to produce 144 units of output? (10%) ANS: a) The Lagrangian is: = 9L + 4K + λ[q L 1/2 K 1/3 ] The first order conditions are L = 9 (λ/2)l -1/2 K 1/3 = 0 K = 4 (λ/3)l 1/2 K -2/3 = 0 λ = q L 1/2 K 1/3 = 0 Combining the first two of these conditions: K/L = 3/2 b) The result from (a) is that K = 3L/2. Substitute into the production function q = L 1/2 K 1/3, with q=72: 72 L 1/2 (3L/2) 1/3 =0 Solve to get L=144 and K=216. c) The total cost is wl + rk = 9(144) + 4(216) = 2,160. d) Using K=216, the production function indicates that: 144 = L 1/2 (216) 1/3 Solve for L=576. The total cost will be $9*579 + $4*216 = $6,048 4

5 2. Lelu runs a firm that sells multipasses to intergalactic cruises. Her short-run cost function is given by C(q) = q q +144 a) If the market price is $75/pass, how many units will Lelu produce? (4%) b) At what price will Lelu earn zero profits? (4%) c) If the price is equal to the level you found in (b), will Lelu shut down? If so, explain. If not, below what price will she shut down? (10%) ANS: a) Profit = Revenue Cost = 75q - C(q) = 75q - q 2-25q Max profit => d(profit)/dq=0 75-2q - 25 = 0 q = 25. b) Profit= 0 when p=ac=mc: AC = q /q = 2q + 25 = MC Solve the equation, and get q=12. AC(12) = MC(12)=49. So profit equals zero when p=$49. c) No, Lelu will shut down when the price is below the minimum of the AVC (where AVC=MC) AVC = q+25 Minimum occurs when q=0 and so the shut down price is p=$25. 5