Consider the following production function using capital (K) and labor (L) as in
ID: 1150566 • Letter: C
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?
Explanation / Answer
(a)
Production function is as follows -
Y = 10 * K0.5 * L0.5
K = 100
L = 100
Calculate Y -
Y = 10 * K0.5 * L0.5
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 * K0.5 * L0.5
K = 100
L = 110
Calculate Y -
Y = 10 * K0.5 * L0.5
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 * K0.5)/L0.5
K = 100
L = 110
MPL = (5 * K0.5)/L0.5 = (5 * 1000.5)/1100.5 = (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 * K0.5)/L0.5
K = 100
L = 120
MPL = (5 * K0.5)/L0.5 = (5 * 1000.5)/1200.5 = (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.