Question

Questlon 3 1 pts Suppose real output grew in Sparta by 4% from 456 BCE to 455 BCE. Over the same period, land stock grew by 1% and labor supply grew by 2%. Suppose 80% of income accrued to labor. Find the rate of total factor productivity growth (i.e. the "Solow Residual").

Answer 1

In our case, total production is given by

Y=AK^.2L^.8

since 80% of income is accrued to labor, rest 20% is to capital. If production in 456BCE is given by

Y=AK^.2L^.8, then based on the information given, production in 455BCE is

1.04Y=A(1+x)(1.01K)^.2(1.02L)^.8

Where x is the growth in new total factor productivity for 455BCE

1.04Y=(1+x)*1.002*1.016AK^.2L^.8

1.04Y=(1+x)*1.002*1.016Y

1.04=(1+x)*1.002*1.016

Solving for x, we get

x=.0216

Hence, in percentage terms, the total factor productivity grew by 2.16%