1. 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.
A. Complete the following table:
B. Plot the (i) total product, (ii) marginal product, and (iii) average product functions
D. Determine the boundaries of the three stages of production.
Stage 1 0-5 Increasing rate in TPx
Stage 2 5-9 decreasing rate in TPx
Stage 3 9-11 negative rate in TPx
6. Consider the following short-run production function (where L = variable input, Q = ...view middle of the document...
9. Consider the following Cobb-Douglas production function for the bus transportation system in a particular city:
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
A. Determine the (i) labor, (ii) fuel, and (iii) capital input production elasticities.
i) Β1 = .45
(ii) B2 = .20
(iii) B3 = .30.
B. Suppose the labor input (workers hours) is increased by 2 percent next year (with the other inputs held constant). Determine the approximate percentage change in input.
=.45(.02) = 0.009 (9%)
C. Suppose the capital input (number of buses) is decreased by 3 percent next year (when certain older buses are taken out of service). Assume that the other inputs are held constant; determine the approximate percentage change in output.
=.30 (-0.03) = -0.009 (-9%)
D. What type of return to scale appears to characterize this bus transportation system? (ignore the issue of statistical significance)
=.45 + .20 + .30= .95 this would be decrease return scale due to it is under 1 (?)
E. Discuss some of the methodological and measurement problems one might encounter in using time-series date to estimate the parameters of this model.
According to the book the following secular trends, cyclical variations, seasonal effects and random fluctuations could cause issues with this type of model. Say they buy new buses and they are more efficient than the older buses, population changes or the drivers have become more experienced then new drivers.
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...