Suppose that the economy grows by 3 percent, total factor productivity grows by 2 percent, and the labor force grows by 2 percent. If labor contributes 40 percent to real GDP, then the stock of capital must have risen by 0.33 percent.

Question

Quizplus · Accepted Answer

The production function is Y = AK^aL^(1-a), where Y is real GDP, A is total factor productivity, K is the stock of capital, and L is the labor force. If the economy grows by 3 percent, then Y/Y-1 = 1.03. If total factor productivity grows by 2 percent, then A/A-1 = 1.02. If the labor force grows by 2 percent, then L/L-1 = 1.02. If labor contributes 40 percent to real GDP, then a = 0.4. Substituting these values into the production function, we get:1.03 = 1.02K^0.4 * 1.02^0.61.03 = 1.0404K^0.4K^0.4 = 1.03/1.0404K^0.4 = 0.9903K = 0.9903^(1/0.4)K = 1.0033Therefore, the stock of capital must have risen by 0.33 percent.

Suppose That the Economy Grows by 3 Percent, Total Factor