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:
Labor input L (NO. of workers Total product TPL(=Q) Marginal Product MPL Average Product APL
b. Plot the (i) total product, (ii) marginal product, and (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 to be L squared)
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.
9. Consider the following Cobb-Douglas production function for the bus transportation system in a particular city:
Where L=labor input in workers hours
F=fuel input in gallons
K=capital input in number of buses
Q=output measured in millions of bus miles
Suppose 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.
b. Suppose that labor input (worker hours) is increased by 2 percent next year (with the other inputs held constant). Determine the approximate percentage change in output.
c. Suppose that capital input (number of buses) is decreased by 3 percent next year (when certain older...