Question

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

QD= 160,000 - 2000PandQS= 40,000 + 2000P

whereQDis the quantity demanded in 100-pound lots,QSis the quantity supplied in 100-pound lots, andP 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 = 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.

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

c. Explain why the answers you calculated in parts(a) and (b) differ.

Short answer

1. The price would be $30 per 100-pound lot, and the quantity would be 100,000 lots.

2. The socially efficient output would be 62,500 lots, and the price$48.75 per lot.

3. The quantity and price declined in part b since the costs were involved.

Step-by-step solution

Explanation for part (a)

Find the equilibrium price and output under competitive conditions by equating the demand and supply:

$$\begin{gathered} \text{160000 - 2000P = 40000 + 2000P} \\ \text{120000 = 4000P} \\ \text{P = 30} \\ \text{Q = 160000 - 2000}\left(\text{30}\right) \\ \text{= 100,000} \end{gathered}$$

Therefore, the equilibrium output would be 100,000 lots, and the price will be $30 per 100-pound lot.

Explanation for part (b)

To find a socially efficient solution, consider the external costs, which are given by MEC = 0.0006Qs, as well as the private costs.

The private cost can be derived using the supply equation Qs = 40000 + 2000P.

Thus, P=0.0005Qs-20, which is equal to MC

Therefore, the socially efficient cost will be equal to:

$$\begin{gathered} \text{MSC = MC + MEC} \\ \text{= 0.0005Qs - 20 + 0.0006Qs} \\ \text{= 0.0011QS - 20} \end{gathered}$$

Solve the demand curve for the price. The result will be:

P = 80 - 0.0005Q

This is the marginal benefit. Equating the marginal benefit and marginal social cost, you will get the socially efficient solution:

$$\begin{gathered} \text{0.0011Q - 20 = 0.0005Q - 80} \\ \text{Q = 62,500} \\ \text{P = 0.0011(62,500) - 20} \\ \text{= 48.75} \end{gathered}$$

Thus, the socially efficient price and output are $48.75 and 62,500.

Explanation of part (c)

The answers in part (a) and (b) differs since the socially efficient levels will be where the marginal cost and marginal benefits are equal; therefore, you need to include the external cost while calculating the answer for part b. In contrast, for part (a), only private costs are included.