In the Deep Creek Mining Company example described 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 owns a piece of equipment having a 500-bhp rating
Consider the following short-run production function (where L = variable input, Q = output):
Q= 10L-0.5L^2
Suppose the 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.
8. Based on the production function parameter estimates reported in Table 7.4:
Which industry (or industries) appears to exhibit decreasing returns to scale? (Ignore the issue of statistical significance.)
9. Consider the following Cobb-Douglas production function for the bus transportation system in a particular city:
Q=aL^B1F^B2K^B3
Where L= labor input in worker hours
F= fuel input in gallons
K = capital input in number of buses
Q= output measured in millions of bus miles
Suppose that the 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
Howard Bowen is a large scale cotton farmer. The land and machinery he owns has a current value of $4 million. Bowen 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. Bowen 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 farmer or a local manufacturer, 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.)
4. From you knowledge of the relationships among the various cost functions, complete the following table.
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 plant. A single, centrally located facility, with a production capacities of 8,000, 6,000, and 4,000 units per year, would have fixed costs of $475,000, $425,000 and $400,000, 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.