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

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

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

The average cost can be found as follows:

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

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

$$36q+4=18q+4+\dfrac{16200}{q},$$ $$18q^2-16200=0,$$ $$q=30.$$

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