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Intermediate Microeconomic Analysis Signature: (Econ 173) Printed name: Drake University, Fall 2001 William M. Boal ID number:
MIDTERM EXAMINATION #3 VERSION A
“Firms and Competition”
October 29, 2001
INSTRUCTIONS: This exam is closed-book, closed-notes, but calculators may be used. Point values for each question are noted in brackets.
I. MULTIPLE CHOICE: Circle the one best answer to each question. Feel free to use margins or the back page for scratch work. [3 pts each—90 pts total]
The next two questions refer to the following information. Suppose package delivery services are produced using only labor, with the following production function: q = x 2/3^ , where q = number of packages delivered and x = number of workers.
(1) The formula for the marginal product of workers is a. (2/3). b. (2/3) x -1/^. c. (2/3) x 2/^. d. x. e. None of the above.
(2) The formula for the elasticity of output with respect to labor input is a. (2/3). b. (2/3) x -1/^. c. (2/3) x 2/^. d. x. e. None of the above.
(3) Which of the following production functions does not show diminishing returns to labor (x 2 )? a. q = 5 x 1 1/2^ x 2 1/^.
b. q = 5 x 1 + x 2. c. q = 5 x 1 1/2^ + x 2 1/^. d. q = 5 x 1 + x 2 + 4(x 1 x 2 )1/^. e. No exceptions—all show diminishing returns to labor.
(4) The production function q = (x 1 -1^ + x 2 -1^ )-1^ yields the following formula for the marginal rate of substitution in production of input 2 for input 1 (that is, the slope of the isoquant with input 1 on the vertical axis and input 2 on the horizontal axis): a. x 1 /x 2. b. (x 1 /x 2 )1/^. c. (x 1 /x 2 )^2. d. -1. e. None of the above.
(5) The production function q = x 1 2/3^ x 2 2/ shows a. increasing returns to scale. b. constant returns to scale. c. decreasing returns to scale. d. cannot be determined from the information given.
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The next three questions refer to the following information. A certain kind of machine can produce 12 parts per hour if it is operated by 3 workers. Fewer workers cannot operate the machine and extra workers contribute nothing. Let x 1 denote the number of machines in use of this type. Let x 2 denote the number of workers assigned to operate these machines.
(6) The equation for the firm’s expansion path is a. x 1 = 3 x 2. b. x 1 = (1/3) x 2. c. 12 = x 1 + 3 x 2. d. 1 = 3. e. None of the above.
(7) The firm’s isoquants are a. downward-sloping straight lines. b. downward-sloping smooth curves. c. L-shaped. d. upward-sloping. e. None of the above.
(8) The formula for the firm’s production function is a. q = x 1 + 3 x 2. b. q = min{12x 1 , 4x 2 }. c. q = 12 x 1 x 23. d. q = 12 x 1 + 4 x 2. e. None of the above.
The next three questions refer to the following information. The elasticity of output with respect to labor for the US economy as a whole is about 2/3. The elasticity of output with respect to capital is about 1/3. Suppose labor input increases by 3% and capital input increases by 9%.
(9) Without any technical change, one would expect output to increase by a. 3%. b. 5%. c. 7%.
d. 9%. e. 12%.
(10) If in fact output increased by 8%, then the Solow residual (that is, the increase in multifactor productivity) was a. 1%. b. 2%. c. 3% d. 4%. e. 5%
(11) Suppose the formula for a firm’s marginal rate of substitution in production of input 2 for input 1 (that is, the slope of the isoquant with input 1 on the vertical axis and input 2 on the horizontal axis) is 2x 1 /x 2. Suppose also that the price of input #1 is $30 and the price of input #2 is $20. Which input combination might this firm possibly use? a. x 1 = 5 and x 2 = 15. b. x 1 = 20 and x 2 = 30. c. x 1 = 10 and x 2 = 20. d. x 1 = 10 and x 2 = 10. e. All of the above.
The next four questions refer to the following information. Suppose a firm’s total cost function is given by TC(q) = 0.05 q 3 – 6 q 2 + 250 q.
(12) The firm’s average cost function is a. AC(q) = 0.05 q 2 – 6q + 250. b. AC(q) = 0.15 q 2 – 12 q + 250. c. AC(q) = 0.15 q – 6. d. AC(q) = 0.05 q 3 – 6 q 2 + 250 q. e. None of the above.
(13) The firm’s marginal cost function is a. MC(q) = 0.05 q 2 – 6q + 250. b. MC(q) = 0.15 q 2 – 12 q + 250. c. MC(q) = 0.15 q – 6. d. MC(q) = 0.05 q 3 – 6 q 2 + 250 q. e. None of the above.
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(21) In the long run, if an industry enjoys free exit and entry of firms, price equals a. marginal cost. b. average cost. c. both marginal and average cost. d. neither marginal cost nor average cost. e. total cost.
(22) Suppose that in a certain industry, costs for each firm tend to rise as more firms enter the industry, and fall when firms leave the industry. In this case, the long-run supply curve a. slopes up (positive slope). b. slopes down (negative slope). c. is horizontal (zero slope). d. is vertical (infinite slope). e. Cannot be determined from the information given.
(23) Suppose the demand for broccoli were suddenly but permanently to shift to the right due to a permanent change in eating habits. One should expect price to a. rise in the short run but fall back in the long run. b. fall in the short run but rebound in the long run. c. rise in the short run and rise further in the long run. d. fall in the short run and fall further in the long run. e. remain constant in the short and long run.
The next five questions refer to the market in the graph below. Suppose a tax of $3 per unit is placed on this market.
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(24) What is the total price that demanders will have to pay, including the tax? a. $2. b. $3. c. $4. d. $5. e. $6. f. $7. g. $8.
(25) What is the net price that suppliers will receive, excluding the tax? a. $2. b. $3. c. $4. d. $5. e. $6. f. $7. g. $8.
(26) As a result of the tax, consumer surplus will a. increase by $25. b. increase by $50. c. decrease by $25. d. decrease by $50. e. None of the above.
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(27) As a result of the tax, producer surplus will a. increase by $25. b. increase by $50. c. decrease by $25. d. decrease by $50. e. None of the above.
(28) The deadweight loss from the tax will be a. $3. b. $5. c. $10. d. $15. e. $30.
The next two questions refer to the following graph, which shows domestic supply and demand for a particular good. Suppose this market is opened to international trade and the world price turns out to be $4.
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(29) As a result of international trade, a. consumer surplus and producer surplus each increase. b. consumer surplus and producer surplus each decrease. c. consumer surplus increases but producer surplus decreases. d. consumer surplus decreases but producer surplus increases. e. consumer and producer surplus remain unchanged.
(30) As a result of international trade, total social welfare in this country a. decreases by $100. b. decreases by $200. c. decreases by $300. d. increases by $100. e. increases by $200. f. increases by $300. g. remains unchanged.
