Question

The market for paper in a particular region has the supply and demand curves: QD = 160,000 - 2,000P QS = 40,000 + 2,000P, where Q is measured in hundred-pound lots, and P is price per hundred-pound lot. 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. The marginal external cost associated with the paper production is given by the expression: MEC = 0.0002Q.

a. Calculate the competitive price and output, assuming that no attempt is made to monitor or regulate the dumping of effluent.
b. Determine the socially optimal levels for price and output.

Answer 1

a. Competitive price and output is determined at the intersection of QD and QS.
So, QD = QS
This implies, 160,000 - 2,000P = 40,000 + 2,000P
So, 2,000P + 2,000P = 160,000 - 40,000
So, 4,000P = 120,000
So, P = 120,000/4,000 = 30
Thus, P = 30 and Q = 160,000 - 2,000P = 160,000 - 2,000(30) = 160,000 - 60,000 = 100,000
So, competitive price is 30 and output is 100,000

b. Socially optimal level is determined at the intersection of demand and socially optimal supply.
Socially optimal supply = supply + MEC
QS = 40,000 + 2,000P
So, 2000P = Q - 40,000
So, P = Q/2000 - 40,000/2000 = 0.0005Q - 20
So, Socially optimal supply = 0.0005Q - 20 + 0.0002Q = 0.0007Q - 20

And, QD = 160,000 - 2000P
So, 2000P = 160,000 - Q
So, P = 160,000/2000 - Q/2000= 80 - 0.0005Q
Thus, P = 80 - 0.0005Q

Now equating demand and socially optimal supply, we get,
80 - 0.0005Q = 0.0007Q - 20
So, 0.0007Q + 0.0005Q = 80 + 20
0.0012Q = 100
So, Q = 100/0.0012 = 83,333.33
And P = 80 - 0.0005*(83,333.33) = 80 - 41.66 = 38.34
Thus, socially optimal levels for price and output is 38.34 and 83,333.33 respectively.