Suppose the production function of PowerGuns Co. is given by Q = 25LK where Q is

Question

Suppose the production function of PowerGuns Co. is given by Q = 25LK where Q is the quantity of guns produced in the month, L is the number of workers employed, and K is the number of machines used in the production. The monthly wage rate is $3,000 per worker and the monthly rental rate for a machine is $6,000. Currently PowerGuns Co. employs 25 workers and 40 machines. Assume perfect divisibility of labor and machines. A. What is the current average product of labor for PowerGuns Co.? What is the current marginal product of machines? (Assume 1 unit increase in machines). B. Does PowerGuns

Explanation / Answer

a)The current input mix is L=25 and K=40, so the current output level is Q = 25× 25× 40 = 25000 AP(L) = Q/L = 25000/25 = 1000 To compute the marginal product of machine, we keep the employment of labor constant, L=25, and increase K by 1 unit, so K=41 and compute the new output level, Q = 25× 25 × 41 = 25625 , thereby the marginal product of machine, MP(K) 25625 – 25000 = 625. b)The production function displays increasing returns to scale. For example, if PowerGuns double the employment of both labor and machines, i.e., L=50, K=80, we have the new output level Q = 25×50 ×80 =100000 , which is four times as large as the original output. c)TC = $3000 × 25 + $6000 × 40 = $315,000 AC = TC/Q = $315000/25000 = $12.6 To compute the marginal cost, we solve this equation for the new level of labor employment (K is fixed), 25000 + 1 = 25 × L × 40, we get L = 25.001. So the marginal cost of producing one additional gun is, MC = 0.001 × $3000 = $3.00.

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