Question

Suppose a country’s production function has three factors of production: K—capital, L—the number of workers, and H—human capital. The production function is Y = (K^0.3)(L^0.4)(H^0.3). (a) What is the marginal product of labor? How does human capital affect the MPL?

(b) What is the marginal product of human capital? How does human capital affect the MPH?

c) What share of total income is paid to labor? What share of total income is paid to human capital?

(d) What share of total income would workers appear to receive?

(e) An unskilled worker earns the MPL, whereas a skilled worker earns the MPL plus the MPH. Using your above answers, find the ratio of the skilled wage to the unskilled wage. How does human capital affect this ratio? Explain.

Answer 1

a)Marginal Product of labour= ∆Y/∆L= 0.4K​​​0.3L-0.6H0.3

As human capital (H) increases, Marginal Product of Labour increases and vice versa.

b) Marginal Product of human capital=∆Y/∆H=0.3K0.30.3 L​​​​​0.4H-0.7

As human capital Increases, Marginal Product of Human Capital (MPH) Decreases and vice versa.

c) Share of total income paid to labour= 40%

Share of total income paid to human capital= 30%

d) Workers receive income on account of their labour and human capital. Thus share of total income recieved by workers= Share of total income paid to Labour+ Share of total income paid to human capital= 40+30= 70%

e) Ratio of skilled wage to Unskilled wage=( MPL+ MPH)/MPL= (0.4K​​​0.3L-0.6H0.3 + 0.3K0.3 L​​​​​0.4H-0.7)/(0.4K​​​0.3L-0.6H0.3)= 1+ 0.75= 1.75.

Ratio is constant. Changes in human capital doesn't have any Effect on this ratio.