Question

CONSIDER THE FOLLOWING SHORT RUN PRODUCTION FUNCTION Q=6L2-0.4L3

a. find the value of L that maximizes out put

b find the value of L that maximizes MARGINAL PRODUCT

c. find the value of l that maximizes average product

Answer 1

a) To maximize the output we have to solve the equation:

$Q'=(6L²-0.4L³)'= 0$

$12L-1.2L²=0$

$L(12-1.2L)=0$

$L1=0$

$L2=10$

b)$MP=12L-1.2L².$ To maximize we have to calculate: MP'=0, so

$12-2.4L=0$

$L=5.$

c)$AP=6L-0.4L²$ To maximize we have to calculate AP'=0, so

$6-0.8L=0$

$L=7.5$