Question

The market for paper in Scranton, PA, is perfectly competitive. It has the demand function: ?? = 60 − ?

There are 10 firms in the market. Each firm has a marginal cost of: ?? = 2?


a. Determine the competitive equilibrium levels of price and output in this market. (5 pts)


b. There is currently no attempt to regulate the dumping of effluent into streams and rivers by the paper mills. As a result, dumping is widespread. Each firm incurs a marginal external cost of: ??? = 0.5?

Determine the socially efficient levels of price and output in this market. (5 pts)


c. Assuming consumers do not bear the cost of the pollution, calculate the difference in consumer surplus between your answers in parts (a) and (b). (5 pts)

Answer 1

Solution —Demand function Q= 60—P or P=60—Q

MC of each firm = 2Q

a....... At the competitive equilibrium, P= MR=MC

or P = MC or 60—Q = 2Q or 3Q=60 or Q=20

equilibrium price P = 60—20 =40

Thus equilibrium price, P =40 and equilibrium market quantity QM=20×10 =200 (there are 10 firms)

b.... Marginal social cost =marginal Private costs +marginal external costs = 2Q+0.5Q = 2.5Q

Now, on a socially optimal equilibrium

Marginal Private benefits (MR)= P = Marginal social cost

or P = MSC or 60—Q = 2.5Q or 3.5 Q = 60 =17 (approximately)

SO socially optimal price, P =60—17 =43

so, socially optimal market output, QM = 17×10 =170

C......Consumer surplus in the free market

CS = (1/2)(Pi—Pa))Q (Pi — intended price, the maximum price one can pay,fromdemandfunction, here 60 , Pa —actual price =40

CS =( 1/2 )(60—40)200 =$2000

CS at Socially efficient output

CS =( 1/2)×(60—43)170 = 1445

Thus the difference in the consumer surplus =2000—1445=555