Question

You are a manager in a perfectly competitive market. The price in your market is $35. Your total cost curve is C(Q) = 10 + 2Q + .5Q^2.

a. What level of output should you produce in the short run?
b. What price should you charge in the short run?
c. Will you make any profits in the short run?
d. What will happen in the long run?
e. How would your answer change if your costs were C(Q) = 80 + 5Q + 30Q^2?

Answer 1

You are a manager in a perfectly competitive market. The price in your market is $35. Your total cost curve is C(Q) = 10 + 2Q + .5Q^2.

ATC=C/Q = 10/Q + 2 +0.5Q

a. What level of output should you produce in the short run?

P=MC(dTC/dQ=2+Q)

35= 2+Q

Q=33

b. What price should you charge in the short run?
The price should be $35

c. Will you make any profits in the short run?

ATC at Q = 33 = 10/33 + 2 +0.5*33

Profits = (P-ATC)*Q = (35-18.8)*33 = 534.6
d. What will happen in the long run?

In the long run, new firms will enter into the industry and supply will go up leading to fall in the market price to the extent that there is zero economic profits earned by all the firms in the market.