4 20 total points Suppose in the short run a perfectly compe

4. (20 total points) Suppose in the short run a perfectly competitive
firm has variable cost = 3q2, and MC = 6q where q is the quantity of
output produced. Also, the firm has fixed cost F = 3000.
a) (8 points) If the market price of the product is 180, how much
output should the firm produce in order to maximize profit?
b) (6 points) How much profit will this firm make?
c) (6 points) Given your answer to b), what will happen to the market
price as we move from the short run to the long run?

Solution

Answer : a ) Given, MC = 6q ; Price ( P ) = 180

At equilibrium condition in competitive market P = MC

=> 180 = 6q => q = 30.

Therefore, the firm produces 30 units to maximize it\'s profit.

b ) TR ( Total Revenue ) = p*q = 180 * 30 = 5400;

TC ( Total Cost ) = Variable Cost + Fixed Cost

= 3q² + 3000 = 3 ( 30 )² + 3000 = 5700.

Profit = TR - TC = 5400 - 5700 = - 300.

Therefore, the firm faces loss here , i.e., firm earns zero profit.

c) As firms faces loss in short run time period, many firms exit from the market. As a result market supply decrease which lead to price rise in long run time period.