In the US, the capital share of GDP is about 25 percent, the average annual grow

Question

In the US, the capital share of GDP is about 25 percent, the average annual growth rate of GDP is 4%, the depreciation rate is 5% per year, and the capital-output ratio is estimated to be 3.0. Assuming, a constant returns production function (i.e., Cobb-Douglas) and that the US is in a steady state, answer the following (See page 252 of text for guidance):

a) (1pt) Find the savings rate.

b) (1pt) Find the MPk

c) (1pt) Find the MPk if US moved to the Golden Rule steady state.

d) (1pt) Find the Capital-Output ratio at Golden Rule Steady State.

e) (1pt) Find the saving rate at Golden Rule Steady State.

Explanation / Answer

A)

sy=(n+g+d)k

s=(n+g+d)k/y = (.04+.05)3 =0.27

initial savings rate is 27%.

n+g: annual growth rate of GDP

d: depriciation rate

k/y = capital-output ratio

B)

MPk=a/(K/Y)

MPk= 0.25/3 = 0.083

a= capital share of GDP= 25%

C)

Golden rule steady state: MPk=(n+g+d)

MPk = 0.05+ 0.04 =0.09 OR 9%

D)

Golden rule steady state k/y= a/MPk =0.25/0.09= 2.78

E) Golden rule steady state s=(0.04+0.05)2.78 =0.25 or 25%

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