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The production function for a firm is

q = −0.6L^{3 }+ 18L^{2}K + 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, AP_{L}, and the marginal product of labor, MP_{L}. (You can estimate the MP_{L} 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/AP_{L} and w/MP_{L} and show that they equal AVC and MC, respectively. Explain why these relationships hold.

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