Question

Given the total cost function TC = 18q ² + 4q + 16,200 (a) Find marginal cost (MC) and average coat (AC) as functions of q (b) Show that when MC < AC, AC is falling, and when MC > AC, AC is rising​

Answer 1

Answer:

(a) The marginal cost funaction can be found as follows:

MC=\dfrac{dTC}{dQ}=36q+4.MC=

dQ

dTC

=36q+4.

The average cost can be found as follows:

AC=\dfrac{TC}{q}=18q+4+\dfrac{16200}{q}.AC=

q

TC

=18q+4+

q

16200.

(b) If MC < AC, then AC is falling until MC = AC. Let's equate MC and AC:

36q+4=18q+4+\dfrac{16200}{q},36q+4=18q+4+

q

16200

,

18q^2-16200=0,18q

2

−16200=0,

q=30.q=30.

If q>30q>30, MC>AC, therefore, AC is rising.