Question

# Suppose an economy described by the Solow model is in a steady state with population growth...

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?

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