# The production function for a firm is q = −0.6L3 + 18L2K

The production function for a firm is

q = −0.6L+ 18L2K + 10L,

where q is the amount of output, L is the number of labor hours per week, and K is the amount of capital. The wage is \$100 and the rental rate is \$800 per time period.

a. Using Excel, calculate the total short-run output, q(L), for L = 0, 1, 2, …, 20, given that capital is fixed in the short run at K̅ = 1. Also, calculate the average product of labor, APL, and the marginal product of labor, MPL. (You can estimate the MPL for L = 2 as q(2) −q(1), and so on for other levels of L.)

b. For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost, AC; and the marginal cost, MC. Using Excel, draw the AVC, AC, and MC curves in a diagram.

c. For each quantity of labor in (a), calculate w/APL and w/MPL and show that they equal AVC and MC, respectively. Explain why these relationships hold.

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