$\text { Consider the following production function }$Y = A×K^a×L^1?a. If a = 0.3, and over the past year total factor productivity grew 2.3 percent, capital grew 2 percent, and labor grew 3 percent, what was the growth rate of output?

Question

Quizplus · Accepted Answer

Using the Cobb-Douglas production function, Y = A×Ka×L1−a, where a = 0.3. 
Over the past year, total factor productivity (A) grew by 2.3 percent, capital (K) grew by 2 percent, and labor (L) grew by 3 percent. 
To find the growth rate of output, we need to plug in the growth rates into the production function: 
Y2/Y1 = (A2/A1) × (K2/K1)a × (L2/L1)^(1-a) 
Y2/Y1 = (1.023) × (1.02)^0.3 × (1.03)^0.7 
Y2/Y1 = 1.05 
Thus the growth rate of output is 5 percent.

Consider the following production function \text { Consider the following production function } Consider the following production function Y = A×Ka×L1?a

$\text { Consider the following production function }$ Y = A×K^a×L^1?a