Question

A perfectly competitive firm faces total cost of product as follows: TC = 0.1q2 + 10 + 50. a. If market price is $20/unit, find the output rate at which firm's profit is maximized. b. Find the firm's shut-down point. c. Find the firm's short-run supply function (express output q as a function of market price P). d. If there are 100 identical firms (have the same cost of production) in the market, determine market supply function.

Answer 1

a) Use P = MC

20 = 0.2q + 10

10 = 0.2q

q = 10/0.2 = 50 units

Hence profit maximizing output is 50 units

b) Shut down point is minimum AVC

AVC = 0.1q + 10

Minimum AVC is $10 (when q is 0)

Hence any price below $10 will result in no production so shut down point is $10 per unit

c) It is P = MC (beginning from P = 10)

P = 0.2q + 10

P - 10 = 0.2q

q = 5P - 50

Supply function of 1 firm is q = 5P - 50

d) Market supply is Qs = 100q = 100*(5P - 50)

Hence it is given by Qs = 500P - 5000