Suppose the slope of a short-run production function is given by 2/L^0.5. Which of the following statements is (are) TRUE?

I. The marginal product of the fifth worker is 0.20.
II. The production function exhibits increasing marginal returns.
III. The marginal product of the sixteenth worker is 0.50.
IV. The production function's slope eventually changes from positive to negative as the firm produces more and more.

Question

Quizplus · Accepted Answer

The marginal product of the nth worker is given by the slope of the production function at that point. The slope of the production function is given by 2/L^0.5, so the marginal product of the nth worker is 2/L^0.5.I. The marginal product of the fifth worker is 2/5^0.5 = 0.20.II. The production function exhibits decreasing marginal returns, not increasing marginal returns.III. The marginal product of the sixteenth worker is 2/16^0.5 = 0.50.IV. The production function's slope is always positive, so it never changes from positive to negative.

Suppose the Slope of a Short-Run Production Function Is Given