Chapter 7
1. In the Deep Creek Mining Company example describes in this chapter (table 7.1) suppose again that labor is the variable input and capital is the fixed input. Specifically, assume that the firm’s own a piece of equipment having a 500-bhp rating.
a. Complete the following table
LABOR INPUT L (NO. OF WORKERS) TOTAL PRODUCT TP l(=Q) MANAGINAL PRODUCT MP l AVERAGE PRODUCT AP l
1 ———- ————- ————
2 ———- ———– ————–
3 ————- ———— ———–
4 ——— ———— ———–
5 ————— ———- ———–
6 ———– ——— ———–
7 ——— ——– ———
8 ——— ——— ——–
9 ——— ———- ————-
10 ———- ——– ———-
b. Plot the (i) total product, (ii) marginal product (iii) average product functions
c. Determine the boundaries of the three stages of production
6. Consider the following short run-production function (where L=variable input, Q=output)
Q=10L-0.5L2
Suppose that output can be sold for $10 per unit. Also assume that the firm can obtain as much of the variable input (L) as it needs at $20 per unit
a. Determine the marginal revenue product function
b. Determine the marginal factor cost function
c. Determine the optimal value of L, given that the objective is to maximize profits
8. Based on the production function parameter estimates reported in Table 7.4
a. Which industry ( or industries) appears to exhibit decreasing returns to scales?
(Ignore the issue of statistical significance)
b. Which industry comes closest to exhibiting constant returns to scales?
c. In which industry will a given percentage increase in capital result in the largest percentage increase in output?
d. In what industry will a given percentage increase in production workers result in the largest percentage increase in output?
9. Consider the following Cobb-Douglas production function for the bus transportation system in a particular city
Q=aLB1FB2KB3
Where L= labor input in workers hours
F= fuel input in gallons
K=Capital input in number of buses
Q= output measure in millions of bus miles
Suppose that parameters (a, B1, B2 and B3) of this model were estimated using annual data for the past 25 years. The following results were obtained
a= 0.0012 B1=0.45 B2=0.20 B3=0.30
a. Determine the (i) labor, ( ii) fuel, (iii) capital input production elasticities.
b. Suppose that labor input (worker hours) is increased by 2 percent next year (with the other input held constant). Determine the approximate percentage change in output
c. Suppose that capital input (number of buses) is decrease by 3 percent next year ( when certain older buses are taken out of service). Assuming that the other input are held constant, determine the approximate percentage changes in output.
d. What type of returns to scale appears to characterize this bus transportation system? (Ignore the issue of statistical significance)
e. Discuss some of the methodological and measurement problems one might encounter in using time –series data to estimate the parameters of this model.
Chapter 8
2. Howard Bowen is a large-scale cotton farmer. The land and machinery he own has a current market value of $4 million. Bowne owes his local bank $3 million. Last year Bowen sold $5 million worth of cotton. His variable operating costs were $4.5 million: accounting depreciation was $40,000, although the actual decline in value of Bowen’s machinery was $60,000 last year. Bowne paid himself a salary of $50,000 which is not considered part of his variable operating costs. Interest on his bank loan was $400,000. If Bowen worked for another famer or a local manufacture, his annual income would be about $30,000. Bowen can invest any funds that would be derived, if the farm were sold, to earn 10 percent annually. (Ignore taxes)
A. Compute Bowen’s accounting profits
4. From your knowledge of the relationships among the various cost functions, complete the following table
Q TC FC VC ATC AFC AVC MC
0 125 — —— —- —— ——- ——
10 —— —- —- —— ——- ——— 5
20 —- —— —— 10.05 —— —— ——
30 —– —- 110 —— —— —— ——
40 255 — —– —— —- —— ——–
50 —- —– —– —— —— 3 ——–
60 —– —– ——- —— —– —– 3
70 —— —– —— 5 ——- —– —–
80 —– —- 295 —— —— —— ———
6. The Blair Company’s three assembly plants are located in California, Georgia and New Jersey. Previously the company purchased a major subassembly, which becomes part of the final product, from an outside firm. Blair has decided to manufacture the subassemblies within the company and must now consider whether to rent one centrally located facility. (e.g. in Missouri, where all the subassemblies would be manufactured)or to rent three separate facilities each located near one of the assembly plants, where each facility would manufacture only the subassemblies needed for the nearby assembly plants. A single centrally located facility with a production capacity of 18,000 units per year, would have a fixed costs OF $900,000 per year and a variable cost of $250 per unit. Three separate decentralized facilities, with production capacities of 8,000, 6,000 and 4,000 respectively and variable costs per unit of only $225 per unit, owing primarily to the reduction in shipping costs. The current production rate at the three assembly plants are 6,000, 4,500 and 3,000 units respectively
a. Assuming that the current production rate are maintained at the three assembly plants, which alternative should management select?
