Question

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

Y = AK^{a}L^{1-}^{a}

- 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: _________

- 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^{a}L^{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

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