Consider two competitive economies that have the same quantities of labor (L = 400) and capital (K = 400), and the same technology (A = 100).
The economies of the countries are described by the following Cobb—Douglas production functions:
North Economy: Y = A L^.3 K^.7
South Economy: Y = A L^.7 K^.3
a. In North Economy, what is the labor's share of income? What is the capital's share of income?
b. Calculate the output for both economies.
c. Calculate the marginal product of labor for both economies.
d. Calculate the real wage for both economies.
e. Calculate the marginal product of capital for both economies.
f. Calculate the real rental rate for both economies.
For North Economy:
For South Economy:
A=100, L=400 and K=400
(a) Labor and capital share of income for north economy:
Labor Share of Income=L*MPL
Labor share of income=L*0.3*A*L^(-0.7)*K^0.7
Labor share of income=L*0.3*AL^0.3 K^0.7
Labor share of income=0.3*100*〖400〗^0.3*〖400〗^0.7=12,000
Capital share of ...
This solution contains a detailed explanation of how to calculate share of income, output and marginal product of labor.