Cobb-Douglas Production Function - Assignment Example

Derive an expression for the marginal product of the efficiency unit of labor (EN).
This refers to the change in output resulting from employing one additional unit of labor. It is obtained by differentiating the output function(Y) concerning labor.
The marginal product of the efficiency unit of labor (EN) = dY/d (EN)

= (1-α) (EN) –αKα
Suppose that α =1/3, show that the share of capital in output is 1/3 and the share of the efficiency unit of labor is 2/3.
α represents the share of capital in the equation therefore α is equal to the share of capital hence α =1/3=share of capital =1/3.
The sum of the share of capital in output and the share of the efficiency of a unit of labor is equal to one.
The share of the efficiency unit of labor is (1-α). If α =1/3 therefore 1-1/3=2/3

Show the derivation of production per effective worker, y ̃=k ̃^α where y ̃=k ̃=K/EN.

Production per effective worker=y ̃=k ̃^α

y ̃= Y/EN= ( K/EN)1/3(EN/EN)2/3
EN/EN=12/3=1
y ̃= (K/EN)1/3 but EN=1, therefore y ̃=k ̃1/3
We have new production function: Y=K^α N^((1-α) )
Derive the per capita capital stock in a steady state.
The steady state refers to a state in which the level of income per worker/capita is growing at rate g(growth rate) instead of being constant. It is the situation in which per capita output is unchanging, implying that k is constant.

MPK= αK(α-1)N(1-α)
APK= K(α-1) N(1-α)
MPK/ APK= αK(α-1)N(1-α)/ K(α-1) N(1-α)
=α
Would you recommend an increase or decrease in investment if the marginal productivity of capital (MPK) in a country is given by (MPK-δ)<r? Explain your reasoning.
I will recommend a decrease in investment since the rate of interest which determines investment in an economy is larger than the marginal productivity of capital. This is an indication that the level of output being produced in the economy is low hence there is nothing to invest in. Read More