4. Given the following short-run production function, Q = 1500L + 60L² - L³ where Q is output and L is variable input, find:
a. The point of diminishing marginal returns
b. The point where the elasticity of production is equal to one.
c. The boundary between stage II and stage III
d. Show that marginal product is equal to average product when average product is at its maximum.
The first thing to solve such questions is to write down all the equations:
Q = 1500L + 60L² - L³
Taking the first order derivative we get the Marginal Product
So MPl = 1500 + 120L - 3L²
Also dividing Q by L we get the average product:
APl = 1500 + 60L - L²
The point of diminishing marginal returns start when the slope ...
The solution answers a lot of important questions related to marginal cost analysis.