NAME: INTERMEDIATE MICROECONOMIC THEORY FALL 2006 ECONOMICS 300/012 Section I: Multiple Choice (4 points each) Identify the choice that best completes the statement or answers the question. 1. The marginal rate of technical substitution of labor for capital measures a. the amount by which capital input can be reduced while holding quantity produced constant when one more unit of labor is used. b. the amount by which labor input can be reduced while holding quantity produced constant when one more unit of capital is used. c. the ratio of total labor to total capital. d. the ratio of total capital to total labor. 2. Suppose the production function for good q is given by q = 3K + 2L where K and L are capital and labor inputs. Consider three statements about this function: I. The function exhibits constant returns to scale. II. The function exhibits diminishing marginal productivities to all inputs. III. The function has a constant rate of technical substitution. Which of these statements is true? a. All of them. d. I and III but not II. b. None of them. e. only I. c. I and II but not III. 3. When the isocost line is tangent to the isoquant, then a. MRTS = w/r. b. the firm is producing that level of output at minimum cost. c. the last dollar spent on capital yields as much extra output as the last dollar spent on labor. d. All of the above. 4. Suppose cows (Q) can be fed corn-based feed (C) or soybean-based feed (S) such that the production function is Q = 5C + 10S. If the price of corn feed is $4 and it is on the horizontal axis, and the price of soybean feed is $5 and it lies on the vertical axis, what is the expansion path? a. C = ½ S c. the horizontal axis b. S = ½ C d. the vertical axis
5. Suppose that a lamp manufacturer is currently producing 1,000 lamps. At this level of output, the MP L = 50 and MP K = 200. The rental rate on capital is $20, and the wage rate is $10. The manufacturer a. is currently minimizing the cost of producing 1,000 lamps per month. b. can reduce the cost of producing 1,000 lamps by using more labor and less capital. c. can reduce the cost of producing 1,000 lamps by using less labor and more capital. 6. A firm has a production function q = 3KL. The wage rate is $9 and the rental rate on capital is $12. In the short-run the firm s capital is fixed at K = 3. The firm s short-run total cost is a. STC = q + 36 c. STC = q + 27 b. STC = 3q + 36 d. STC = (4/3)q + 27 7. If a firm is a price taker, then its marginal revenue will always equal a. price. c. one. b. total cost. d. zero. 8. The short-run market supply curve is a. the horizontal summation of each firm s short-run supply curve. b. the vertical summation of each firm s short-run supply curve. c. the horizontal summation of each firm s short-run average cost curve. d. the vertical summation of each firm s short-run average cost curve. 9. Under perfect competition, if an industry is characterized by positive economic profits in the short run a. firms will leave the market in the long run and the short-run supply curve will shift outward. b. firms will enter the market in the long run and the short-run supply curve will shift outward. c. firms will enter the market in the long run and the short-run supply curve will shift inward. d. firms will leave the market in the long run and the short-run supply curve will shift inward. 10. If the market for hula-hoops is characterized by a very inelastic supply curve and a very elastic demand curve, an inward shift in the supply curve would be reflected primarily in the form of a. higher prices. c. lower prices. b. higher output. d. lower output. Page 2 of 6
Section II: Essay Problems Give clear, well-written answers to the questions below. Use graphs if appropriate. Please make sure your graphs are legible and label all parts of the graph (e.g., axes, lines, etc.). You will not receive full credit if the graphs are illegible. 1. (10 points) Assume that a firm has the following production function: q = f(k,l). Draw a set of isoquants that are consistent with the properties of decreasing marginal product for both inputs and decreasing returns to scale. Explain why the isoquants in your diagram are consistent with these two properties. Page 3 of 6
2. (10 points) Assume that a firm has the following production function: q = f(k,l). Capital is fixed in the short-run, and the firm s short-run cost function is STC = 15 + 30q. a. What is the equation for the firm s short-run cost function if the government imposes a $5 per unit specific tax? Does it affect variable or fixed cost? Explain. b. What is the equation for the short-run average cost if the government imposes a $25 lump sum tax instead of the unit-specific tax? By how much did the average cost change? Explain. Page 4 of 6
3. (20 points) Suppose a firm operating in a perfectly competitive industry has the following short-run total cost function: STC = 100 + 4q 2 and short-run marginal cost function: SMC = 8q. a. What is the minimum price necessary for the firm to earn a positive economic profit? b. Below what price will the firm shut down in the short run? c. Assume that the market price is $80. What is the profit-maximizing level of output for this firm? d. What are the short-run profits for the firm? e. Show the level of profits in a graph, including the relevant revenue and cost curves. Page 5 of 6
4. (20 points) Assume that there is a perfectly competitive constant-cost industry. Suppose that each firm minimizes its long-run average cost at an output of 20 units and at an average cost of $4/unit. Market demand is given by Q D = 2000 100P. a. What is the long-run equilibrium price? b. How many firms will operate in this market in the LR equilibrium? Show your work. c. Draw a graph of the long-run equilibrium price and quantity for each firm, including LRAC, MC, and MR. d. Draw a graph of the long-run market supply curve. e. What is the definition of a constant-cost industry? Page 6 of 6