consider a numbercal example example using the solow growth

consider a numbercal example example using the solow growth model, suppose that F(K,N)=K^0.5N^0.5 with d=0.1,s=0.2,n=0.01,and z=1, and take period to be a year.

a) determine capital per worker, income per capita, and consumption per capita in the steady state.

b) find the golden rule quantity of capital per worker. Is there overinvestment or underinvestment in this economy, relative to golden rule?

Solution

Solutions A:

Capital per worker :

(n+d)k=s zf(k)

Consumption per capita:
c=(1-s)y

Income per capita:
y=zf(k)

Solutions B:

While a higher capital stock implies higher output, this does not mean a higher capital stock is desirable. To sustain a high capital stock, a lot of output will have to be devoted to investment, leaving less available for consumption.

Golden Rule: The capital stock per-worker that maximizes consumption per-worker. In the Solow Growth Model with no population growth and technological progress, this occurs where

=MPK

At steady state, investment is equal to total depreciation because savings is equal to investment.