Question

5. [Marginal Cost] Find the marginal cost (MC) functions for each of the following average cost functions.

(a) AC = 2.5Q+4+ 40/Q .

(b) AC = 200/Q +5?6Q+4Q^2 .

(c) AC = 2Q^2 ?8Q+174.

Answer 1

Marginal cost = extra cost incurred due to producing one additional unit of the good.

MC =

Where TC = total cost of producing the good.

We are given average costs,

Average cost =

SO, TC = AC × Q

(a)

AC = 2.5Q + 4 + 40/Q

SO, TC = 2.5 Q² + 4Q + 40

AND, MC =

= 2.5×2Q + 4

= 5Q+4

(b)

AC = 200/Q + 5 - 6Q + 4Q²

SO, TC = 200 + 5Q - 6Q² + 4Q³

And, MC =

= 5 - 6×2Q + 4×3Q²

= 5 - 12Q + 12Q²

(C)

AC = 2Q²-8Q+174

SO, TC = 2Q³ - 8Q²+174Q

AND, MC =

= 2×3Q²-8×2Q+174

= 6Q² - 16Q +174