A firm\'s short-run cost function for a good is C(a)-30-10q+5q and the market de

Question

A firm's short-run cost function for a good is C(a)-30-10q+5q and the market demand function for the good is q -460-4p where q is output level of the good , is the market quantity demanded for the good and p is the price of the good. The market for the good is currently competitive and there are 100 firms including this firm which produces the good. Moreover, each firm has the same cost function as that of this firm. Find this firm's short-run profit maximizing output level, profit and producer's surplus 1S

Explanation / Answer

c = 30 + 10q + 5q2

MC = 10 + 10q

short run supply function is given by

MC = p

10 + 10q = p

10q = p - 10

q = p/10 - 1

n = 100

so short run market supply qs = nq

= 100(p/10 - 1)

= 10p - 100

so qs = 10p - 100

qd = 460 - 4p  

so qs = qd

10p - 100 = 460 - 4p

10p + 4p = 460 + 100

14p = 560

p = 40

q = 10p - 100

= 10(40) - 100

= 400 - 100

= 300

profit = pq - c

= 40(300) - 30 - 10(300) - 5(300)2

= - 451830

producer surlus = 1/2(40-10)(300)

= 9000

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