Question

A firm in a competitive industry has a total cost function of TC = 0.2 Q2 – 5Q + 30, whosecorresponding marginal cost curve is MC=0.4Q – 5. If the firm faces a price of 6,
a)what quantity should it sell? (10 points)

b)What profit does the firm make at this price? (10 points)

c)Should the firm shut down? (10 points)

Answer 1

Answer:

Consider the following calculations

Explanation:

TC=0.2Q2 - 5Q + 30,

MC=0.4Q - 5.

Equilibrium condition

MC=P

0.4Q - 5 = 6

0.4Q = 11

Q = 11/.4

=27.5

Profit = TR - TC

        =27.5*6 - .2(27.5)2 -5(27.5)+30

       =165 -756.25 -137.5 +30

       = - 698.5

Firm is incurring loss

Firm will continue to produce as long as it is able to recover AVC

AVC =0.2Q -5

=0.2(27.5) -5

=5.5 -5

=0.5

Hence firm will continue to produce