For a simple graph of a production function with Q on the y-axis and L on the x-axis, which of the following statements is true?
A)The slope of the production function at a specific point equals the marginal product of labor whereas the average slope of the production function equals the average product of labor.
B)The average product of labor is equal to the slope of the ray from the origin to the apex of the production function for all values of L.
C)The slope of the production function at a specific point equals the marginal product of labor whereas the slope between the origin and a specific point on the production function equals the average product of labor.
D)The average product of labor is never equal to the slope of the ray from the origin to the apex of the production function.

Question

Quizplus · Accepted Answer

The slope of the production function at a specific point represents the marginal product of labor, which is the additional output produced by adding one more unit of labor. The slope between the origin and a specific point on the production function represents the average product of labor, which is the total output divided by the number of units of labor used. Therefore, statement C is true. Statement A is partially correct because the slope of the production function at a specific point equals the marginal product of labor, but the average slope of the production function does not necessarily equal the average product of labor. Statement B is incorrect because the slope of the ray from the origin to the apex of the production function represents the marginal rate of technical substitution, not the average product of labor. Statement D is incorrect because statement C is true; the average product of labor can be equal to the slope between the origin and a specific point on the production function. The slope of the production function at a specific point equals the marginal product of labor, which is the additional output produced when one more unit of labor is added. The slope between the origin and a specific point on the production function represents the average product of labor, which is the total output produced divided by the total amount of labor used. Therefore, C is the correct statement. A is incorrect because the average slope of the production function would represent the average product of labor and not the slope. B is incorrect because the slope of the ray from the origin to the apex would not necessarily be equal to the average product of labor for all values of L. D is also incorrect because there are certain points on the production function where the slope of the ray from the origin to that point would be equal to the average product of labor.

For a Simple Graph of a Production Function with Q