Question

# The production function for a firm is Q = −0.6L 3 + 18L 2K + 10L...

The production function for a firm is Q = −0.6L 3 + 18L 2K + 10L where Q is the amount of output, L is the number of labor hours per week, and K is the amount of capital.

(a)Use Excel to calculate the total short run output Q(L) for L = 0, 1, 2...20, given that capital is fixed in the short run at K = 1.

(b) Use Excel to calculate the total long run output Q(L) for L = 0, 1, 2...20 and K = 0, 1, 2.......20. (Note: You can use one formula to perform all calculations in this question).

(c) Suppose firm currently employs one unit of labor and one unit of capital. Use the matrix generated in part (b) to determine the returns to scale for this production function. Suppose that the wage is \$100, the rental rate is \$800 per time period and the capital is fixed at K = 1

(d) For each quantity of labor in part (a), calculate the average product of labor (APL), marginal product of labor (MPL), total variable cost (T V C), total cost (T C), average variable cost (AV C), average total cost (AT C) and marginal cost (MC).

(e) For each quantity of labor in part (a), calculate w/APL and w/MPL, and confirm that they equal AV C and MC, respectively. Explain why these relationships hold.  