In a small Asian country,it is estimated that changing the level of capital from $8 million to $12 million will increase real GDP from $5 million to $6 million.If the number of hours worked in the labor force does not change,what does this information tell you about the slope of the per-worker production function in this range?
A)The slope is -4.
B)The slope is 1/4.
C)The slope is 4.
D)The slope is 8.

Question

Quizplus · Accepted Answer

The per-worker production function can be written as Y/L = f(K/L), where Y is real GDP, L is the number of hours worked by labor, and K is the level of capital.

Using the information given, we can find the marginal product of capital (MPK) as:
MPK = (ΔY/ΔK)/(ΔL/ΔK) = [(6-5)/(12-8)]/(L/L) = 0.25/L

This means that for every additional unit of capital, real GDP will increase by an average of 0.25 units, holding labor constant. Therefore, the slope of the per-worker production function in this range is 0.25, or 1/4.

In a Small Asian Country,it Is Estimated That Changing the Level