Question

A firm sells its product in a perfectly competitive market where other firms

sell an identical product at a price of $120 per unit. The firm's total cost is c(q) = 2500 + q2.

(a) How much output should the firm produce in the short-run?

(b) If all the other competitors in the market have the same cost function, what

would you expect to happen to the price of the output in the long-run? Explain

your answer clearly and, if you believe the current output price is not stable

in the long run, determine the long-run equilibrium price.

(c) Assume now that the current market price for the output is $100 per unit, and

the government decides to tax producers at a rate of $5 per unit of output

produced. What will be the short-run consequence of this taxation? What is

likely to happen in the long-run if the tax is maintained?

Answer 1

A) = MC=2Q

Firm Profit Maximizing quantity is at ,p=MC

120=2q

Q=120/2=60

B)AC=2500/q. +q

At Q=60

AC=2500/60 +60=101.67

So P>AC ,it means firms are earning positive profit.so In long run new firm will enter the market and reduce equilibrium price .,so that all firms earn normal Profit.

Long run Equilibrium price at P=MC=minimum AC.

AC=MC

2500/q+q=2q

Q2=2500

Q=50

P=AC=MC=2500/50 +50=100( long run equilibrium price)

C)New C=2500+q2+5q

MC=2q+5

So Increase in MC will decrease supply and which results in Increases in equilibrium price in short run .

In long run equilibrium price will be

AC=2500/q +q +5

AC=MC

2500/q +q+5=2q+5

Q=50

Minimum AC=2500/50+50+5=105( new long run equilibrium price)