Question

(a) Consider the production function,

q = 100K²L^1.5

Calculate the marginal product of labor, MP_L, and the marginal product of capital,MP_K.

(c) Suppose that in the short run, the level of capital is fixed at K = 15. Write out the total product of labor curve. What is the marginal product of labor when L = 100?

(d) Now consider two input combinations, (K = 5, L = 100) and (K = 20, L = 25). Which of the two input combinations lies on the higher Isoquant curve?

Answer 1

a)

q = 100K²L^1.5

MPL = dq/dL = 150K²L^0.5

MPK = dq/dK = 200KL^1.5

c)

K = 15

Total product = q = 100 x 15² x L^1.5 = 22500L^1.5

MPL = 150K²L^0.5 = 150 x (15)² x 100^0.5 = 337500

d)

K = 5 , L = 100

q1 = 100 x 5² x 100^1.5 = 2500000

K = 20, L = 25

q2 = 100 x 20² x 25^1.5 = 5000000

Therefore, the second combination would lie on the higher isoquant curve (higher 'q')