Consider the following production function? Y = A×K^a×L^1?a.
If a = 0.3, and over the past year total factor productivity (TFP) grew 2.3 percent, capital grew 2 percent, and output grew 5 percent, what was the growth rate of labor?

Question

Quizplus · Accepted Answer

Using the production function, we can write the growth rate of output (Y) as the sum of the growth rates of TFP, K, and L:

%ΔY = %ΔA + a(%ΔK) + (1-a)(%ΔL)

Plugging in the given values, we get:

5% = 2.3% + 0.3(2%) + 0.7(%ΔL)

Solving for %ΔL, we get:

%ΔL = (5% - 2.3% - 0.6%)/0.7 = 2.1%/0.7 = 3%

Therefore, the growth rate of labor was 3 percent.

Consider the Following Production Function? Y = A×Ka×L1?a

Consider the Following Production Function? Y = A×K^a×L^1?a