a. A firm has the production function q = ln L+12L^2- 10L^3. Find the average product...
a. A firm has the production function q = ln L+12L^2- 10L^3. Find the average product of labor, the marginal product of labor.
b. Consider the following short-run production function: q = 6L^22 – 1/3L^3. At what level of L do diminishing marginal returns begin? At what level of L do diminishing returns begin?
Homework Answers
a. A firm has the production function q = ln L+12L^2- 10L^3.
APL = q/L = InL/L + 12L - 10L^2
MPL = dq/dL = 1/L + 24L - 30L^2
b. A firm has a short-run production function: q = 6L^2 – 1/3L^3.
There are diminishing marginal returns after the level of labor when MPL reaches a maximum.
MPL = dq/dL = 12L - L^2
Now MPL is maximum when MPL'(L) = 0
12 - 2L = 0
L = 6
After 6th unit of labor, there are diminishing returns to labor.
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