Question

Consider the cost function C= 40 + 3Q 2Q^2 + 1/2Q^3 . i) At Q = 4, what is the firm’s average fixed cost? ii) At Q = 4, what is the firm’s marginal cost? iii) If the firm optimally produces Q = 4, and P = 35-aQ, what does a have to be? iv) Which Q minimizes the firm’s average variable cost? v) What is the firm’s minimum average variable cost?99

Answer 1

Solution:

I think there must be omiting error in the equation. I am considering it as Cost function C= 40 + 3Q - 2Q^2 + 1/2Q^3.

i) Given the cost function is C= 40 +3Q -2Q² + 1/2 Q³ . We can identify fixed cost from the cost function

Fixed cost = 40

Average fixed cost at Q= 4

AFC= 40/4= 10

ii) Given Q=4

MC= Chnage in TC/ Change in quantity= 3- 4Q + 3/2 Q²= 3- 4x4+3/2x16 = 3- 16+ 24= 11

iii) GIven P= 35-aQ

A firm will produce optimally on that point of quantity where the difference between price and marginal cost will be maximum

So, we can write

max(P-C)xQ=0

Substituting the value

(35-a4- 11)4=0

24-a4=0

a=24/4=6

iv) Average variable cost= Variable cost/ quantity= (3Q -2Q² + 1/2 Q³)/Q = 3-2Q+ Q²/2

Minimum ATC= Change in ATC/ Change in Q= -2+ 2Q/2=0

-2+Q=0 so, Q=2

v) Minimum avaerage variable cost is at Q=2

So, AVC= 3-2Q+ Q²/2 = 3-2x2+2^2/2= 3-4+2= 1