Question

The market for paper in a particular region in the United States is characterized by the following demand and supply​ curves:

Upper Q Subscript Upper D Baseline equals 155 comma 000 minus 2 comma 000 Upper PQD=155,000−2,000P

and

Upper Q Subscript Upper S Baseline equals 50 comma 000 plus 2 comma 000 Upper PQS=50,000+2,000P

where

QD

is the quantity demanded in​ 100-pound lots,

QS

is the quantity supplied in​ 100-pound lots, and P is the price per​ 100-pound lot. Currently there is no attempt to regulate the dumping of effluent into streams and rivers by the paper mills. As a​ result, dumping is widespread. The marginal external cost​ (MEC) associated with the production of paper is given by the curve

MEC equals 0.0006 Upper Q Subscript Upper SMEC=0.0006QS.

a. Calculate the output and price of paper if it is produced under competitive conditions and no attempt is made to monitor or regulate the dumping of effluent.

​(Enter

your responses rounded to two decimal

places.​)

Without​ regulation, the price is

​$26.2526.25

per​ 100-pound lot, and the quantity is

102500102500

​100-pound lots.

b. Determine the socially efficient price and output of paper.

​(Enter

your responses rounded to two decimal

places.​)

The socially efficient price is

ans-

per​ 100-pound lot, and the socially efficient quantity is

ans-

​100-pound lots.

Answer 1

a. Under competitive conditions, QD = QS
So, 155,000−2,000P = 50,000+2,000P
So, 2000P + 2000P = 155,000 - 50,000
So, 4000P = 105,000
So, P = 105,000/4000
So, P = 26.25

Q = 50,000+2,000P = 50,000+2,000(26.25) = 50,000 + 52,500
So, Q = 102,500

b. QS = 50,000+2,000P
So, 2000P = Q - 50,000
So, P = (Q/2000) - (50,000/2000) = 0.0005Q - 25

So, MSC = P + SMEC = 0.0005Q - 25 + 0.0006Q = 0.0011Q - 25

QD = 155,000−2,000P
So, 2000P = 155,000 - Q
So, P = (155,000/2000) - (Q/2000)
So, P = 77.5 - 0.0005Q

At equilibrium, P = MSC
So, 77.5 - 0.0005Q = 0.0011Q - 25
So, 0.0011Q + 0.0005Q = 77.5 + 25
So, 0.0016Q = 102.5
So, Q = 102.5/0.0016
So, Q = 64,062.5

P = 77.5 - 0.0005Q = 77.5 - 0.0005(64,062.5) = 77.5 - 32.03125 = 45.47
Thus, P = 45.47