If the production function describing an economy is Y = 100 K^.25L^.75, then the share of output going to labor: A) is 25 percent. B) is 75 percent. C) depends on the quantities of labor and capital. D) depends on the state of technology.

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Quizplus · Accepted Answer

The share of output going to labor is equal to the marginal product of labor times the quantity of labor, divided by total output. The marginal product of labor is equal to the partial derivative of the production function with respect to labor, which is 75 K^.25L^-.25. The quantity of labor is L. Total output is Y = 100 K^.25L^.75. Therefore, the share of output going to labor is:(75 K^.25L^-.25) * L / (100 K^.25L^.75) = 75/100 = 0.75 = 75%

If the Production Function Describing an Economy Is Y =