Question

Cosider the following short run production:

Q=6L²-0.4L³

a. Find the value of L that maximize out put.

b. Find the value of L maximizes marginal product.

c. Find the value of L that maximizes average product.

Answer 1

a. The value of L that maximizes output is:

$Q'(L) = 12L - 1.2L^2 = 0,$

L(10 - L) = 0,

L = 0 (does not fit the conditions), L = 10 units.

b. The value of L that maximizes marginal product is:

$MP'(L) = Q''(L) = 12 - 2.4L = 0,$

2.4L = 12,

L = 5 units.

c. The value of L that maximizes average product is:

$APL'(L) = (Q/L)' = 6 - 0.8L = 0,$

0.8L = 6,

L = 7.5 units.