Your firm’s average cost curve is given as 𝐴𝐶 = 2𝑄*2 − 8𝑄 + 26

Question

Your firm’s average cost curve is given as 𝐴𝐶 = 2𝑄² − 8𝑄 + 26

a) Differenciate this average cost function

b) You have been asked to advise the company on minimising costs. Using your answer to the previous section find the level of output at which average cost is at a minimum.

Answer 1

AC = 2q^2 -2q +26

AC' = 4q -2 =0

q =2/4 = 1/2 when AC is minimum

TC = 2q^3 -2q^2 +26q

TC'=MC= 6q^2 -4q +26

MC =AC, marginal cost =average cost when average cost is at a minimum

6q^2 -4q +26 =2q^2 -2q +26

4q^2 -2q=0

2q(2q -1) =0

2q-1 = 0

q = 1/2 when AC is minimum