A firms total cost function is: TC = 500 + 150q - 20q2 + q3 what is the dollar value at the minimum of the average variable cost (avc) curve? $50?

the correct answer is $150

Explanation:

TC=500 + 150q - 20q^2 + q^3

AVC = (150Q-20Q^2+Q^3) / Q

=150-20Q+Q^2

When AVC is at its minimum means that the marginal cost (CM) is igual to AVC, so we could consider this analysis:

CM = d (TC) / dq = 150-40Q+3Q^2

CM=AVC

150-40Q+3Q^2=150-20Q+Q^2

Join similar terms:

150-150-40Q+20Q+3Q^2-Q^2=0

0-20Q+2Q^2=0

Q (-20+2Q) = 0

Q_1=0 y Q_2=20/2=10

with q_1 with q_2

150-40*0+3*0=150-20*0+0 150-40*10+3*10^2=150-20*10+10^2

$150=$150 150-400+300 = 150-200+100

$50 = $ 50

We have two solution if we assume that q=0 like the minimum then the results is $150.

f we assume that q=10 like the minimum then the results is $50.