Question

A firm operates in a perfectly competitive market where the market price is p=$200. The firm’s total cost of production is given by the following equation: TC(q) = 250 + 10q² + 20q, where q is the quantity supplied. When this firm maximizes profit, what is the optimal quantity to produce in the short run and what will happen in the long run?

a) q=0 (shut-down) both in the long run and in the short run

b) q=9 in the short run and in the long run some firms will exit

c) q=9 in the short run and in the long run new firms will enter

d) q=0 in the short run and q=9 in the long run

e) None of the above.

Answer 1

c) q=9 in the short run and in the long run new firms will enter

(In the short run, optimal quantity is determined where P = MC
MC = d(TC)/dq = 2(10q) + 20 = 20q + 20
So, P = MC gives,
200 = 20q + 20
So, 20q = 200 - 20 = 180
So, q = 180/20
So, q = 9
Profit = TR - TC = P*q - (250 + 10q2 + 20q) = (200*9) - 250 - 10(9)2 - 20(9) = 1800 - 250 - 810 - 180 = 560
So, due to positive profits, firms will enter in the long run.)