If a production function is given by the equation Q = 12X + 10X2 – X3,

If a production function is given by the equation Q = 12X + 10X2 – X3, where Q = Output and X = Input, then calculate the equations for

a. average product
b. marginal product
c. point of diminishing average returns
d. point of diminishing marginal returns

ANSWER

a. AP = Q/X, or 12 + 10X – X2
b. MP = dQ/dX, or 12 + 20X – 3X2
c. DAR occurs where AP at a maximum, or dAP/dX = 0, or 10 – 2X = 0, X = 5
d. DMR occurs where MP at a maximum, or dMP/dX = 0, or 20 – 6X = 0, X = 3.33