Question

Consider an economy in which production function is characterized by the following neoclassical function. Suppose, again tat it has a saving rate of 0.1, a population growth rate of 0.02, and average depreciation rate of 0.03

Y= K^0.6 N^0.4

1. Given the neoclassical production function, what is the labor share of income?
2. Given the neoclassical production function, what is the capital share of income? 
3. What is the value of the steady-state value of capital-labor ratio or k?
4. What is the value of the steady-state value of per-capita output or y

Answer 1

Solution:

1.). Y = K^0.6N^0.4

Labor = N

MP_N = $\frac{\partial Y} {\partial N}$ = 0.6K^-0.4N^0.4

Labor share of income = $\frac{0.6N^{0.4} }{K^{0.4}}$

 

2.). Y = K^0.6N^0.4

Capital = K

MP_K = $\frac{\partial Y} {\partial K}$ = 0.4K^0.6N^-0.6

Capital share of income = $\frac{0.4K^{0.6} }{N^{0.6}}$