Question

Suppose an economy described by the Solow model is in a steady
state with population growth *n* of 1.8 percent per year and
techno- logical progress *g* of 1.8 percent per year.Total
output and total capital grow at 3.6 percent per year. Suppose
further that the capital share of output is 1/3. If you used the
growth- accounting equation to divide output growth into three
sources—capital, labor, and total factor productivity—how much
would you attribute to each source?

Answer #1

If we use the growth- accounting equation, we have

∆Y/Y = a*∆K/K + (1 - a)*∆N/N + ∆A/A

Growth rate of output = capital share x growth rate of capital + labor share x growth rate of labor + growth rate of TFP

3.6% = (1/3)*3.6% + (2/3)*1.8% + ∆A/A

∆A/A = 3.6% - 2.4% = 1.2%

This gives us the growth rate of TFP.

Hence, the contribution of capital is (1/3)*3.6% =1.2 percent annually, contribution of labor is (2/3)*1.8% = 1.2 percent and total factor productivity growth is also 1.2 percent

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Production Function: y=50K^0.4 (LE)^0.6
Depreciation rate: S
Population growth rate: n
Technological growth rate:g
Savings rate: s
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