Question

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?

Answer 1

Answer:

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.