Question

1. Consider Solow’s growth model with the following production function:

Y = AK^aL^1-a

1. What is the steady state level of per capita income and capital if A = 50, savings rate is 0.08, the depreciation rate is 0.02 and the population growth rate is 0.02? a is 0.50.

Work:

Steady state level of per capita income: _________

Stead state level of per capita capital: _________

1. If the savings rate increases to 0.10, what will be the new steady state level of per capita income and capital?

Work: (4 points)

Steady state level of per capita income: _________

Steady state level of per capita capital: _________

Answer 1

a) We have the production function Y = AK^aL^1-a for which the per capita production function is y = Ak^a

At the steady state, the law of motion suggests

k/y = s/(d + n)

k/50k^0.5 = 0.08/(0.02 + 0.02)

k^0.5 = 100

k = 10000 and so y = 50(10000)^0.5 = 5000

Steady state level of per capita income is 5000 and Stead state level of per capita capital is 10000

b) Now with changed information we have

k/y = s/(d + n)

k/50k^0.5 = 0.10/(0.02 + 0.02)

k^0.5 = 125

k = 15625 and so y = 50(15625)^0.5 = 6250

Steady state level of per capita income is 6250 and Stead state level of per capita capital is 15625