Question

For the following 5 questions, use the simple Solow model where

For all questions assume the rate of depreciation on capital, δ=0.04. Use the other parameters given to answer the question, with the noted abbreviations:

Share of income paid to capital, α

Rate of savings, s

Rate of population growth, n

1.

For the following parameter values determine the steady-state consumption

=.5

=.2

=.02

2.

For the following parameter values determine the steady-state k*

α=.5

s=.1

n=.03

3.

For the following parameter values determine the steady-state y*

α=.5

s=.3

n=.02

4.

For the following parameter values determine the rental rate paid to capital at the steady-state y*

α=.6

s=.3

n=.01

5.

For the following parameter values determine the wage at the steady-state y*

α=.4

s=.2

n=0

Answer 1

At steady-state, sk^* = (δ+n)k^*

k* = [s/(δ+n)]^(1/1-)

y* = [s/(δ+n)]^(/1-)

c* = (1-s)/[(s/δ+n)]

1. Given the values, steady-state consumption, c* = (1-0.2)/[(0.2/0.04+0.02)] = 0.24

2. steady-state capital, k* = [0.1/(0.04+0.03)]^1/0.5 = 100/49 = 2.04

3. steady-state income, y* = [0.3/(0.04+0.02)]^0.6/0.4 =  5^3/2 = 11.18

4. The real rental price of capital equals the marginal product of capital (MPK) in the steady state. And MPK = (δ+n) = (0.04 + 0.01) = 0.05.