Economy

Chapter 5: Answers to Questions and Problems

1.

a. When K = 16 and L = 16, [pic]. Thus, APL = Q/L = 16/16 = 1. When K = 16 and L = 81, [pic]. Thus, APL = 24/81 = 8/27.

b. The marginal product of labor is [pic]. When L = 16, [pic]. When L = 81, [pic]. Thus, as the number of units of labor hired increases, the marginal product of labor decreases [pic], holding the level of capital fixed.

c. We must equate the value marginal product of labor equal to the wage and solve for L. Here, [pic]. Setting this equal to the wage of $25 gives [pic]. Solving for L, the optimal quantity of labor is L = 16.

2. See Table 5-1.

[pic]

Table 5-1

a. Labor is the fixed input while capital is the variable input.

b. Fixed costs are 20($15) = $300.

c. To produce 475 units in the least-cost manner requires 6 units of capital, which cost $75 each. Thus, variable costs are ($75)(6) = $450.

d. Using the VMPK = r rule, K = 5 maximizes profits.

e. The maximum profits are [pic].

f. There are increasing marginal returns when K is between 0 and 3.

g. There are decreasing marginal returns when K is between 3 and 11.

h. There are negative marginal returns when K is greater than 7.

3. The law of diminishing marginal returns is the decline in marginal productivity experienced when input usage increases, holding all other inputs constant. In contrast, the law of diminishing marginal rate of technical substitution is a property of a production function stating that as less of one input is used, increasing amounts of another input must be employed to produce the same level of output.

4.

a. FC = 50.

b. [pic].

c. [pic].

d. [pic].

e. [pic].

f. [pic].

g. [pic].

5. Since [pic], the firm is not using the cost minimizing combination of labor and capital. To minimize costs, the firm should use more labor and less capital since the marginal product per dollar spent is greater...