Given the production function: q= 72x+15x2-x3 where Q= output and x= input
a.What is the Marginal Product (MP) when X = 8?
b. What is the Average Product (AP) when X = 6?
c. At what value of X will Q be at its maximum?
d. At what value of X will Diminishing Returns set in?
Marginal Product is the first derivative of the production function. Thus taking the first order derivative we get:
MP = 72 + 30x -3x2
At x = 8:
MP = 72 + 30x8 - ...
The solution answers several questions related to marginal product analysis.