Selected Readings

nality cost (i.e., MSCf = MPCf + MECf).The vertical distance between the MPCf and MSCf curves is the marginal externality cost of producing the good.If the externality cost of the firm depicted in Figure 15.6 is typical of all firms in the industry,then the MSCi curve in Figure 15.7 lies above the MPCi curve.

The socially efficient level of output occurs when each firm in the industry incurs the full costs of producing the product.This is illustrated in Figure 15.7 at the output level Q1 i,where the MSCi curve intersects the industry demand curve, DD.The socially efficient price is P1.It is apparent from Figures 15.6 and 15.7 that when firms ignore externality costs,there is an inefficiently high level of production.The oversupply of the product is illustrated in Figure 15.7 as the distance Q0 i –Q1 i.The welfare cost to society is also illustrated in Figure 15.7.This cost is given by the shaded area FGE, which measures the difference between the marginal social cost and marginal social benefit for each unit of overproduction. Problem 15.2. Suppose that the marginal private cost of producing fertilizer is

Suppose further that the marginal externality cost of the pollution emitted is

Finally,suppose that market demand for fertilizer is given as

a.Find the perfectly competitive price and output level. b.If this industry were dominated by a single firm,what would be the profit-maximizing price and output level? c.Find the socially optimal price and output level.

Solution

a.A perfectly competitive industry will produce at an output level at which marginal private cost equals price, MPC = P.Solving the demand equation for price yields

Substituting MPC Q = 4

MEC Q = 2

Q P = -50 025 .

P Q = -200 4

MPC P =

4 200 4 Q Q = Q* = 25 P* $ = - ( ) = 200 425 100

b.A monopolist maximizes profit by producing at an output level at which marginal private cost equals marginal revenue, MPC = MR.The monopolist’s total revenue equation is

c.The socially optimal level of output occurs at an output level at which marginal social cost equals price, MSC = P.Marginal social cost equals the sum of marginal private and marginal externality costs, MSC = MPC + MEC.Thus,the socially optimal level of output is

TR PQ QQ Q Q = = -( ) = 200 4 200 4 2

MR dTR dQ Q= = -200 8 MPC MR =

4 200 8 Q Q = Q* . = 1667 P* . $ . = - ( ) = 200 41667 13333

MPC MEC P + =

4 2 200 4 Q Q Q + = Q* = 20 P* $ = - ( ) = 200 420 120

COASE THEOREM

The presence of negative externalities is a strong argument in favor of government intervention in the marketplace.In principle,there are at least two ways in which the government can intercede in the market to promote a more socially beneficial outcome.On the one hand,the government can directly involve itself in the market process by,say,requiring producers to directly absorb the cleanup costs of the pollution rather than allowing these costs to be absorbed by witting or unwitting third parties.This approach falls under the general rubric of government regulation.By contrast,the government can try to establish conditions under which the market determines an efficient solution to the externality problem.A theoretical justification for this market approach can be found in the Coase theorem (see Coase,1960).

To understand the rationale underlying the Coase theorem,it will be useful to view negative externalities as the result of a “missing”market. More specifically,the fertilizer plant discussed earlier has unrestricted access to clean water.Because clean water is free,the total cost of producing fertilizer is less than it would be if the firm had to pay for clean water.

Suppose,on the other hand,that there existed a market for clean water and the fertilizer plant had to pay a positive price per unit of clean water used. In general,the market price for a good or service is determined where the marginal private benefit (demand) curve for clean water intersects the marginal private cost (supply) curve.Since clean water is a scarce resource,the firm would undoubtedly have to pay a positive price for clean water.Thus, the firm’s marginal production cost would be higher,its output lower,and the price of fertilizer higher,than would be the case if it obtained clean water for free.

In most cases,however,markets for clean water or clean air do not exist. Why? The reason is that no one “owns”the property (ownership) rights to these resources.Without well-defined property rights,there can be no market for the purchase and sale of,say,clean water,and,therefore,no market price.The result is an inefficient (excessive) use of this clean water. In other words,in the absence of well-defined property rights,there is an incentive for the fertilizer company to “overproduce”and,consequently,to “overpollute.”What this suggests,of course,is that one possible way to solve the problems caused by negative externalities is for the government to assign private property (ownership) rights for these resources.

To see how the assignment of property rights will lead to a socially efficient use of clean water,suppose that the government gives the fertilizer plant ownership of the clean water.The profit-maximizing fertilizer plant will now base its output decisions not only on the market for fertilizer but on the market for clean water as well.More specifically,the fertilizer plant must also consider the possible trade-off of reduced profit from lower fertilizer production and income earned from selling clean water to the downriver brewery.If the increase profits earned from the sale of clean water are greater than the reduced profits from lower fertilizer production,then it will be in the fertilizer company’s best interest to reduce fertilizer output and,consequently,pollution.This situation is illustrated in Figure 15.6.

The maximum amount the brewery is willing to pay the fertilizer company to reduce its level of output,and thus the level of pollutants discharged,is measured by the vertical difference between the MPCf and MSCf curves.The fertilizer company’s lost profit from a reduction in output is the vertical difference between the firm’s marginal revenue (price) and marginal private cost (MPCf ) curves.

Prior to being assigned the property rights to clean water,the fertilizer company maximized its profit by producing at output level Q0 f,where P = MPCf.With ownership of clean water property rights,the fertilizer company should be willing to reduce its output as long as the amount of compensation from the brewery is greater than the loss in profits.Assuming that there are no transaction or bargaining costs,it should be obvious from Figure 15.6 that for any output level less than Q1 f the compensation from the brewery is less than the additional profit from increasing output.Thus,the fertilizer