Question

Consider the following production function using capital (K) and labor (L) as inputs. Y = 10.K0.5L0.5. The marginal product of labor is (MPL=) 5.K0.5/L0.5, and marginal product of capital (MPK) = 5.L0.5/K0.5.a. If K = 100 and L=100 what is the level of output Y?b. If labor increases to 110 while K=100, what is the level of output?c. If labor increases to 110 while K=100, what is the marginal product of labor?d. If labor increases to 120 while K=100, what is the marginal product of labor?e. What happens to marginal product of labor when labor increases while capital remains unchanged?f.Estimate Marginal Products of Capital in the above cases of (c) and (d) using equation given in the question.g. When labor increases from 100 to 110 and then to 120 while the level of capital does not change, what happens to Marginal Product of Capital?

Answer 1

(a)

Production function is as follows -

Y = 10 * K^0.5 * L^0.5

K = 100

L = 100

Calculate Y -

Y = 10 * K^0.5 * L^0.5

Y = 10 * (100)^0.5 * (100)^0.5

Y = 10 * 10 * 10 = 1,000

The level of output is 1,000 units.

(b)

Production function is as follows -

Y = 10 * K^0.5 * L^0.5

K = 100

L = 110

Calculate Y -

Y = 10 * K^0.5 * L^0.5

Y = 10 * (100)^0.5 * (110)^0.5

Y = 10 * 10 * 10.48 = 1,048

The level of output is 1,048 units.

(c)

Marginal product of labor is as follows -

MPL = (5 * K^0.5)/L^0.5

K = 100

L = 110

MPL = (5 * K^0.5)/L^0.5 = (5 * 100^0.5)/110^0.5 = (5*10)/10.48 = 50/10.48 = 4.77

The marginal product of labor is 4.77

(d)

Marginal product of labor is as follows -

MPL = (5 * K^0.5)/L^0.5

K = 100

L = 120

MPL = (5 * K^0.5)/L^0.5 = (5 * 100^0.5)/120^0.5 = (5*10)/10.95 = 50/10.95 = 4.56

The marginal product of labor is 4.56

(e)

The marginal product of labor is decreasing when labor increases while capital remains unchanged.