Question

Two countries are described by the neoclassical production function. The first country however has a savings rate of 40% and a population rate of 1%, while the second has a savings rate of 10% and a population growth rate of 3%. Both countries experience technological progress at 2% and capital depreciation at 5% yearly

a.) Solve for the ratio of the steady-state income per effective worker in both countries

b.) If capitals share in output in both countries is 1/3, how much higher will income per effective worker be in the first economy compared to the second

Answer 1

A)

In case of Solow model,

Change in capital per worker is given by

In steady state,

So,

Put

or

and we know

So, steady state steady state income per effective worker is given by

  

For country 1

s=0.40, n=0.01 and and g=0.02

For country 2

s=0.10, n=0.03 and and g=0.02

So,

b)

If , then