Question

Q1 An identical firm in a competitive market has the following cost curve: C(q) = 2q2 + 20q + 32 where q is the number of products sold by each firm. Any entry or exit does not change the input costs in the market. The market demand for the product is given by Q = 280 – 2p, where Q is the total number of products sold in the market. (a) . What is the long-run market supply curve if there is free entry and exit in the market? What are the long-run market equilibrium price and output? What is the total number of firms in the market? (b). Suppose the government awards the operation permits only to 40 firms in the market. What are the individual firm’s supply curve and the market supply curve, respectively? What are the market equilibrium price and output? What is the amount of products sold by each firm? (c) . If a new firm wants to enter the market, it has to buy an operation permit from one of the existing firms. If an existing firm is allowed to sell the operation permit in an open market, what will be the price of a permit?

Answer 1

A) In long run firm earn zero economic profit ,it means price is equal to total average cost.and Marginal cost.

MC=4q+20

AC=2Q+20+32/Q

MC=AC

4Q+20=2Q+20+32/Q

2Q=32/Q

Q^2=16

Q=4{ firm output in long run equilibrium}

MC=4Q+20=4*4+20=36=p=AC

Market output,

Q=280-2*36=280-72=208

Each firm produces same output so,

Number of firm=208/4=52

Market supply curve is sum of individual firm supply curve.

Individual firm supply is Marginal cost ,

MC=4Q+20

P=4Q+20

Q=0.25P -5{ individual supply}

Long run Market supply,

Q=(0.25p-5)*52

Q=13p-260{ long run market supply}

B) Q=0.25p-5{ individual firm supply , unchanged}

Q=(0.25p-5)*40

Q=10p-200 {market supply}

Equilibrium at market supply= market demand

10p-200=280-2p

12p=480

P*=480/12=40

Q*=10*40-200=200

Each firm sold quantity=200/40=5

C)the price of the permit will equal to supernormal profits that firm is earning.

Q=5

Profit =TR-TC=40*5-2*5*5-20*5-32=200-50-100-32=18

So the price of permit will be 18