Question

Question 4 (20 points) A firm has the following short-run production function as follows: Q = 15L +18L2-0.5L, where Q = total products per period and L = number of workers employed per period. 4.1) (3 points) Derive the marginal product of labor (MPL). At what number of workers (L) does the law of diminishing returns begin? MPL = f(L) = Law of diminishing return begins when L = workers. .

Please answer the two sub-parts

Answer 1

4.1)

MP_L = dQ/dL = 15 + 36L - 1.5L²

Law of diminishing returns become when MP_L=0

So, 15+36L-1.5L² = 0

=> L = 24.41

4.2)

AP_L = Q/L = 15+18L-0.5L²

When AP_L is maximum, d(AP_L)/dL = 0

=> 18 - L=0

=> L=18

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