Assignment:
For each question, please show the necessary derivation (if applicable) and highlight the answer. Limit your answers within 5 pages. No cover sheet is required.
Q1: At a management luncheon, two managers were overheard arguing about the following statement: "A manager should never hire another worker if the new person causes diminishing returns." Is this statement correct? If so, why? If not, explain why not.
Q2: Suppose that a firm is currently employing 20 workers, the only variable input, at a wage rate of $250. The average physical product of labor is 25, the last worker added 10 units to total output, and total fixed cost is $5,000
a. What is marginal cost?
b. What is average variable cost?
c. What is the average total cost?
d. At the current output rate, is average variable cost increasing, constant, or decreasing?
Is average total cost increasing, constant, or decreasing? (Hint: Check the graph of short-run cost curves)
Q3: The Largo Publishing House uses 400 printers and 200 printing presses to produce books. A printer's wage rate is $20, and the price of a printing press is $5,000. The last printer added 8 books to total output, while the last press added 2,500 books to total output. Is the publishing house making the optimal input choice? Why or why not? If not, how should the manager of Largo Publishing House adjust input usage?
Q4: Gamma Corporation, one of the firms that retains you as a financial analyst, is considering buying out Beta Corporation, a small anufacturing firm that is now barely operating at a profit. You recommend the buyout because you believe that new management could substantially reduce production costs, and thereby increase profit to a quite attractive level. You collect the following product information in order to convince the CEO at Gamma Corporation that Beta is indeed operating inefficiently:
MPL = 25 PL =$20
MPK = 15 PK =$15
Explain how these data provide evidence of inefficiency. How could the new manager of Beta Corporation improve efficiency?
Q5: Ross Perot added his memorable "insight" to the debate over the North American Free Trade Agreement (NAFTA) when he warned that passage of NAFTA would create a "giant sucking sound" as U. S. employers shipped jobs to Mexico, where wages are lower than wages in the United States. As it turned out, many U. S. firms chose not to produce in Mexico despite the much lower wages there. Explain why it may not be economically efficient to move production to foreign countries, even ones with substantially lower wages.
Q6: You are planning to estimate a short- run production function for your firm, and you have collected the following data on labor usage (L) and output (Q):
Labor usage (L) Output (Q)
3 1
7 2
9 3
11 5
17 8
17 10
20 15
24 18
26 22
28 21
30 23
a. Please key in the data into MS Excel for regression analysis. Estimate your firm's short-run production function. Do the parameter estimates have the appropriate algebraic signs? Are they statistically significant at the 5 percent level? (Hint: Run the production function as Q = AL3 +BL2 )
b. At what point do you estimate marginal product (MP) begins to fall?
c. Calculate estimates of average products (AP) and marginal products (MP) when the firm employs 20 workers.
d. When the firm employs 20 workers, is short-run marginal cost (MC) rising or falling? How can you tell?
Q7: The chief economist for Argus Corporation, a large appliance manufacturer, estimated the firm's short- run cost function for vacuum cleaners using an average variable cost function of the form
AVC = a + bQ + cQ2
where AVC dollars per vacuum cleaner and Q number of vacuum cleaners produced each month. Total fixed cost each month is $180,000. The following results were obtained:
DEPENDENT VARIABLE: AVC R-SQUARE F-RATIO P-VALUE ON F
OBSERVATIONS: 19 0.7360 39.428 0.0001
PARAMETER STANDARD
VARIABLE ESTIMATE ERROR T-RATIO P-VALUE
INTERCEPT 191.93 54.65 3.512 0.0029
Q -0.0305 0.00789 23.866 0.0014
Q2 0.0000024 0.00000098 2.449 0.0262
a. Are the parameter estimates (a, b and c) statistically significant at the 1 percent level of significance?
b. Do the results indicate that the average variable cost curve is U-shaped? How do you know?
c. If Argus Corporation produces 8,000 vacuum cleaners per month, what is the estimated marginal costs?
d. If Argus Corporation produces 8,000 vacuum cleaners per month, and sell all of them in the market at price of $200 each. How much will be the total profit (i.e. total revenue - total costs)?