Question

F. At what level of output does Alison’s average cost curve reach a minimum?

Alison lives in a small town where she plans to hire workers to help her make candy. Her production function for candy is 0.5 94LKO5 She begins producing with K-4. The cost of capital is S50/unit. The wage depends on the amount of workers she employs. Specifically, w(L)-10 + 2L.

Answer 1

K is fixed for the production function so we have q = 4L(4^0.5) = 8L. This implies L = q/8 or 0.125q.

Cost function is C = wL + rK or C = (10 +2L)*L + 50*4

C = (10 + 2*0.125q)0.125q + 200

= 1.25q + 0.03125q^2 + 200

AC = C/q = 1.25 + 0.03125q + 200/q

Minimize AC

dAC/dq = 0

0.03125 = 200/q^2

This gives q = (200/0.03125)^0.5 = 80. Hence when q = 80, AC is minimum