Chapter 5 Externalities Problems and Solutions

Chapter 5 Externalities Problems and Solutions
Jonathan Gruber Public Finance and Public Policy Aaron S. Yelowitz - Copyright 2005 © Worth Publishers

Introduction Externalities arise whenever the actions of one party make another party worse or better off, yet the first party neither bears the costs nor receives the benefits of doing so. As we will see, this represents a market failure for which government action could be appropriate and improve welfare.

Introduction Externalities can be negative or positive:
Acid rain, global warming, pollution, or a neighbor’s loud music are all negative externalities. Research and development or asking good questions in class are positive externalities.

Introduction Consider global warming, a negative externality. Many scientists believe this warming trend is caused by human activity, namely the use of fossil fuels. These fuels, such as coal, oil, natural gas, and gasoline produce carbon dioxide that in turn traps heat from the sun in the earth’s atmosphere. Figure 1 shows the trend in warming over the last century.

This table shows the global temperature during the 20th century.
Figure 1 There has been a distinct trend upward in temperature

Introduction Although this warming trend has negative effects overall on society, the distributional consequences vary. In much of the United States, warmer temperatures will improve agricultural output and quality of life. In Bangladesh, which is near sea-level, much of the country will be flooded by rising sea levels. If you’re wondering why you should care about Bangladesh, then you have identified the market failure that arises from externalities. From your private perspective, you shouldn’t!

EXTERNALITY THEORY Externalities can either be negative or positive, and they can also arise on the supply side (production externalities) or the demand side (consumption externalities). A negative production externality is when a firm’s production reduces the well-being of others who are not compensated by the firm. A negative consumption externality is when an individual’s consumption reduces the well-being of others who are not compensated by the individual. The basic concepts in positive externalities mirror those in negative externalities.

Economics of Negative Production Externalities
To understand the case of negative production externalities, consider the following example: A profit-maximizing steel firm, as a by-product of its production, dumps sludge into a river. The fishermen downstream are harmed by this activity, as the fish die and their profits fall. This is a negative production externalities because: Fishermen downstream are adversely affected. And they are not compensated for this harm. Figure 2 illustrates each party’s incentives in this situation.

The yellow triangle is the consumer and producer surplus at Q1.
SMC = PMC + MD Price of steel S=PMC The steel firm sets PMB=PMC to find its privately optimal profit maximizing output, Q1. The yellow triangle is the consumer and producer surplus at Q1. The socially optimal level of production is at Q2, the intersection of SMC and SMB. The steel firm overproduces from society’s viewpoint. p2 This framework does not capture the harm done to the fishery, however. The marginal damage curve (MD) represents the fishery’s harm per unit. The red triangle is the deadweight loss from the private production level. The social marginal cost is the sum of PMC and MD, and represents the cost to society. p1 MD D = PMB = SMB Q2 Q1 QSTEEL Figure 2 Negative Production Externalities

The steel firm’s privately optimal production solves: This yields a quantity of steel Q1 at a price of P1.

The steel firm’s emits pollution causing damage to the fishery. This is represented by the marginal damage curve. Ideally, the fishery prefers: This would yield zero steel production, which is obviously not in the steel firm’s best interests.

The social marginal cost accounts for both the direct costs to the steel firm and the indirect harm to the fishery: We find the socially optimal quantity of steel Q2 at a price of P2, by solving:

The socially optimal quantity entails less production of steel. By doing so, the steel firm would be worse off but the fishery would be better off. Graphically, this triangle in between the PMB and PMC curves from Q2 to Q1. The damage to the fishery is reduced as well. Graphically, this is the area under the MD curve from Q2 to Q1.

The deadweight loss from the original production level Q1 is graphically illustrated as the triangle in between the SMC and SMB curves from Q2 to Q1. Note that the SMB equals the PMB curve in this case.

Negative Consumption Externalities
We now move on to negative consumption externalities. Consider the following example: A person at a restaurant smokes cigarettes. That smoking has a negative effect on your enjoyment of the restaurant meal. In this case, the consumption of a good reduces the well-being of someone else. Figure 3 illustrates each party’s incentives in the presence of a negative consumption externality.

This framework does not capture the harm done to non-smokers, however.
Price of cigarettes S=PMC=SMC The smoker sets PMB=PMC to find his privately optimal quantity of cigarettes, Q1. The yellow triangle is the surplus to the smokers (and producers) at Q1. This framework does not capture the harm done to non-smokers, however. The MD curve represents the nonsmoker’s harm per pack of cigarettes. The social marginal benefit is the difference between PMB and MD. The red triangle is the deadweight loss from the private production level. p1 The socially optimal level of smoking is at Q2, the intersection of SMC and SMB. The smoker consumes too many cigarettes from society’s viewpoint. MD p2 D=PMB SMB=PMB-MD Q2 Q1 QCIGARETTES Figure 3 Negative Consumption Externalities

The smoker’s privately optimal quantity solves: This yields a quantity of cigarettes Q1 at a price of P1. The surplus is the same as before.

The smoker’s consumption causes damage to the other restaurant patrons. They would prefer: This would yield zero cigarette smoking, which is detrimental to the smoker.

The social marginal benefit accounts for both the direct benefit to the smoker and the indirect harm to the other patrons: We find the socially optimal quantity of cigarettes Q2 at a price of P2, by solving:

The socially optimal quantity entails less smoking. By doing so, the cigarette smoker is worse off, but the other patrons are better off. The surplus to the smoker (and tobacco companies) falls. Graphically, this is the triangle in between the PMB and PMC curves from Q2 to Q1. The harm to other restaurant patrons is reduced as well. Graphically, this is the area under the MD curve from Q2 to Q1.

The deadweight loss from the original consumption level Q1 is illustrated graphically as the triangle in between the SMC and SMB curves from Q2 to Q1. Note that the SMC equals the PMC curve in this case.

The Externality of SUVs
Application Consider a real-life example: the use of sport utility vehicles (SUVs). They create three sorts of externalities: Environmental externalities: They consume a lot of gasoline and create more pollution. Wear and tear on roads: SUV drivers do not bear the costs that result from their vehicles. Safety externalities: When SUVs are in accidents, the other drivers are often more severely injured.

Positive Externalities
Positive externalities can occur in production or consumption. A positive production externality is when a firm’s production increases the well-being of others, but the firm is not compensated by those others. Research and development is a production externality. A positive consumption externality is when an individual’s consumption increases the well-being of others, but the individual is not compensated by those others. Nice landscaping could be a consumption externality.

Let’s consider positive production externalities. Consider the following example: A policeman buys donuts near your home. As a consequence, the neighbors are safer because of the policeman’s continued presence. In this case, the production of donuts increases the well-being of the neighbors. Figure 4 illustrates each party’s incentives in the presence of a positive production externality.

The yellow triangle is the consumer and producer surplus at Q1.
Price of donuts S = PMC The yellow triangle is the consumer and producer surplus at Q1. The donut shop sets PMB = PMC to find its privately optimal profit maximizing output, Q1. The external marginal benefit (EMB) represents the neighbor’s benefit. This framework does not capture the benefit to the neighbors, however. The red triangle is the deadweight loss from the private production level. The donut shop underproduces from society’s viewpoint. The socially optimal level of donuts is at Q2, the intersection of SMC and SMB. SMC = PMC -EMB p1 EMB p2 The social marginal cost subtracts EMB from PMC. D = PMB = SMB Q1 Q2 QDONUTS Figure 4 Positive Production Externalities

The donut shop’s privately optimal production solves: This yields a quantity of donuts Q1 at a price of P1.

The shop creates positive externalities to the neighbors through the presence of police. This is represented by the external marginal benefit. Ideally, the neighbors prefer: This would yield much more donut production, which is obviously not in shop’s best interests.

The social marginal cost accounts for both the direct costs to the donut shop and the indirect benefit to the neighbors: We find the socially optimal quantity of donuts Q2 at a price of P2, by solving:

The socially optimal quantity entails more production of donuts. By doing so, the donut shop would be worse off but the neighbors would be better off. The consumer and producer surplus fall. Graphically, this triangle is between the PMC and PMB curves from Q1 to Q2. The benefit to the neighbors is increased as well. It goes up. Graphically, this is the area under the EMB curve from Q1 to Q2.

The deadweight loss from the original donut production level Q1 is graphically illustrated by the triangle in between the SMB and SMC curves from Q1 to Q2. Note that the SMB equals the PMB curve in this case.

Finally, there can be positive consumption externalities. A neighbor’s improved landscape is a good example of this. The graphical analysis is similar to negative consumption externalities, except that the SMB curve shifts outward, not inward.

The theory shows that when a negative externality is present, the private market will produce too much of the good, creating deadweight loss. When a positive externality is present, the private market produces too little of the good, again creating deadweight loss.

The Solution (Coase Theorem)
The Coase Theorem: When there are well-defined property rights and costless bargaining, then negotiations between the parties will bring about the socially efficient level. Thus, the role of government intervention may be very limited—that of simply enforcing property rights.

Consider the Coase Theorem in the context of the negative production externality example from before. Give the fishermen property rights over the amount of steel production. Figure 5 illustrates this scenario.

While the fishery suffers only a modest amount of damage.
SMC = PMC + MD Price of steel This bargaining process will continue until the socially efficient level. S = PMC The gain to society is this area, the difference between (PMB -PMC) and MD for the first unit. The gain to society is this area, the difference between (PMB -PMC) and MD for the second unit. p2 The reason is because any steel production makes the fishery worse off. If the fishery had property rights, it would initially impose zero steel production. p1 MD Thus, it is possible for the steel firm to “bribe” the fishery in order to produce the first unit. But there is room to bargain. The steel firm gets a lot of surplus from the first unit. While the fishery suffers only a modest amount of damage. Thus, it is possible for the steel firm to “bribe” the fishery in order to produce the next unit. While the fishery suffers the same damage as from the first unit. There is still room to bargain. The steel firm gets a bit less surplus from the second unit. D = PMB SMB 1 2 Q2 Q1 QSTEEL Figure 5 Negative Production Externalities and Bargaining

The Solution (Coase theorem)
Through a process of bargaining, the steel firm will bribe the fishery to arrive at Q2, the socially optimal level. After that point, the MD exceeds (PMB - PMC), so the steel firm cannot come up with a large enough bribe to expand production further.

Another implication of the Coase Theorem is that the efficient solution does not depend on which party is assigned the property rights, as long as someone is assigned them. The direction in which the bribes go does depend on the assignment, however. Now, let’s give the property rights to the steel firm over the amount of steel production. Figure 6 illustrates this scenario.

This level of production maximizes the consumer and producer surplus.
SMC = PMC + MD Price of steel S = PMC This bargaining process will continue until the socially efficient level. The gain to society is this area, the difference between MD and (PMB -PMC) by cutting another unit. The gain to society is this area, the difference between MD and (PMB-PMC) by cutting back 1 unit. This level of production maximizes the consumer and producer surplus. If the steel firm had property rights, it would initially choose Q1. p2 While the steel firm suffers a larger loss in profits. While the steel firm suffers only a modest loss in profits. p1 MD Thus, it is possible for the fishery to “bribe” the steel firm to cut back another unit. The fishery gets the same surplus as cutting back from the first unit. The fishery gets a lot of surplus from cutting back steel production by one unit. Thus, it is possible for the fishery to “bribe” the steel firm to cut back. D=PMB=SMB Q2 Q1 QSTEEL Figure 6 Negative Production Externalities and Bargaining

Figure 6 shows that even though the bargaining process is somewhat different, the socially efficient quantity of Q2 is achieved.

Problems with Coasian Solutions
There are several problems with the Coase Theorem, however. The assignment problem The holdout problem The free rider problem Transaction costs and negotiating problems

The “assignment problem” relates to two issues: It can be difficult to truly assign blame. It is hard to value the marginal damage in reality.

The “holdout problem” arises when the property rights in question are held by more than one party. The shared property rights give each party power over all others. This could lead to a breakdown in negotiations.

The “free rider” problem is that when an investment has a personal cost but a common benefit, individuals will underinvest. For example, if the steel firm were assigned property rights and you are the last (of many) fishermen to pay, the bribe is larger than the marginal damage to you personally.

Finally, it is hard to negotiate when there are large numbers of individuals on one or both sides.

In summary, the Coase Theorem is provocative, but perhaps not terribly relevant to many of the most pressing environmental problems.

PUBLIC-SECTOR REMEDIES FOR EXTERNALITIES
Coasian solutions are insufficient to deal with large scale externalities. Public policy makes use of three types of remedies to address negative externalities: Corrective taxation Subsidies Regulation

Corrective Taxation The government can impose a “Pigouvian” tax on the steel firm, which lower its output and reduces deadweight loss. If the per-unit tax equals the marginal damage at the socially optimal quantity, the firm will cut back to that point. Figure 7 illustrates such a tax.

The socially optimal level of production, Q2, then maximizes profits.
SMC=PMC+MD Price of steel S=PMC+tax S=PMC The socially optimal level of production, Q2, then maximizes profits. p2 The steel firm initially produces at Q1, the intersection of PMC and PMB. Imposing a tax equal to the MD shifts the PMC curve such that it equals SMC. Imposing a tax shifts the PMC curve upward and reduces steel production. p1 D = PMB = SMB Q2 Q1 QSTEEL Figure 7 Pigouvian Tax

Corrective Taxation The Pigouvian tax essentially shifts the private marginal cost. The firm cuts back output, which is a good thing when there is a negative externality.

Corrective Taxation The steel firm’s privately optimal production solves: When the tax equals MD, this becomes: But this last equation is simply the one used to determine the efficient level of production.

Subsidies The government can impose a “Pigouvian” subsidy on producers of positive externalities, which increases its output. If the subsidy equals the external marginal benefit at the socially optimal quantity, the firm will increase production to that point. Figure 8 illustrates such a subsidy.

The donut shop initially chooses Q1, maximizing its profits.
Price of donuts S = PMC The donut shop initially chooses Q1, maximizing its profits. Providing a subsidy shifts the PMC curve downward. Providing a subsidy equal to EMB shifts the PMC curve downward to SMC. The socially optimal level of donuts, Q2, is achieved by such a subsidy. SMC=PMC-EMB p1 p2 D = PMB = SMB Q1 Q2 QDONUTS Figure 8 Pigouvian Subsidy

Subsidies The subsidy also shifts the private marginal cost.
The firm cuts expand output, which is a good thing when there is a positive externality.

Subsidies The donut shop’s production solves:
When the subsidy equals EMB, this becomes: But this last equation is simply the one used to determine the efficient level of production.

Regulation Finally, the government can impose quantity regulation, rather than relying on the price mechanism. For example, return to the steel firm in Figure 9.

Yet the government could simply require it to produce no more than Q2.
SMC = PMC + MD Price of steel S = PMC p2 Yet the government could simply require it to produce no more than Q2. The firm has an incentive to produce Q1. p1 D = PMB = SMB Q2 Q1 QSTEEL Figure 9 Quantity Regulation

Regulation In an ideal world, Pigouvian taxation and quantity regulation give identical policy outcomes. In practice, there are complications that may make taxes a more effective means of addressing externalities.

DISTINCTIONS BETWEEN THE PRICE AND QUANTITY APPROACHES TO ADDRESSING EXTERNALITIES
The key goal is, for any reduction in pollution, to find the least-cost means of achieving that reduction. One approach could simply be to reduce output. Another approach would be to adopt pollution-reduction technology.

The models we have relied on so far have examined reductions in output. Thus, we will modify this. Our basic model now examines pollution reduction, rather than say, steel production. Figure 10 illustrates its features.

Since it pays for the pollution reduction, the SMC is the same as PMC.
While it faces increasing marginal costs from reducing its pollution level. PR Pollution reduction has a price associated with it. S=PMC=SMC S=PMC The optimal level of pollution reduction is therefore R*. While the benefit of pollution reduction is zero the firm, society benefits by MD. MD = SMB The steel firm’s private marginal benefit from pollution reduction is zero. Thus, the x-axis also measures pollution levels as we move toward the origin. At some level of pollution reduction, the firm has achieved full pollution reduction. The good that is being created is “pollution reduction.” Such an action maximizes its profits. On its own, the steel company would set QR=0 and QSteel=Q1. D = PMB R* RFull QR PFull P* More pollution Figure 10 Model of Pollution Reduction

As Figure 10 shows, the private market outcome is zero pollution reduction, while the socially efficient level is higher. In the figure, the optimal tax would simply be MD– the firm would reduce pollution levels to R*, because its MC is less than the tax up until that point, but no further. Quantity regulation is even simpler–just mandate pollution reduction of R*.

Assume now there are two firms, with different technologies for reducing pollution. Assume firm “A” is more efficient than firm “B” at such reduction. Figure 11 illustrates the situation.

Firm B has relatively inefficient pollution reduction technology.
PR Firm B has relatively inefficient pollution reduction technology. While Firm A’s is more efficient. PMCB To get the total marginal cost, we sum horizontally. For any given output level, PMCB>PMCA. PMCA S = PMCA + PMCB = SMC Efficient regulation is where the marginal cost of pollution reduction for each firm equals SMB. PMCB Quantity regulation in this way is clearly inefficient, since Firm B is “worse” at reducing pollution. If, instead, we got more reduction from Firm A, we could lower the total social cost. The SMB curve is the same as before. The efficient level of pollution reduction is the same as before. PMCA MD=SMB Quantity regulation could involve equal reductions in pollution by both firms, such that R1 + R2 = R*. Imposing a Pigouvian tax equal to MD induces these levels of output. RB RA,RB RA R* QR Figure 11 Two Firms Emit Pollution

Figure 11 shows that price regulation through taxes is more efficient than is quantity regulation. A final option is quantity regulation with tradable permits. Idea is to: Issue permits that allow firms to pollute And allow firms to trade the permits

As in the previous figure, initially the permits might be assigned as quantity regulation was assigned. This means that initially RA = RB. But now Firm B has an interest in buying some of Firm A’s permits, since reducing its emissions costs PMCB (>PMCA). Both sides could be made better off by Firm A selling a permit to Firm B, and then Firm A simply reducing its pollution level. This trading process continue until PMCB=PMCA.

Finally, the government may not always know with certainty how costly it is for a firm to reduce its pollution levels. Figure 12 shows the case when the social marginal benefit is “locally flat.”

But it is possible for the firm’s costs to be PMC2. PR PMC2
In addition, imagine that the government’s best guess of costs is PMC1. But it is possible for the firm’s costs to be PMC2. PR PMC2 Suppose the true costs are PMC2. Then there is large deadweight loss. PMC1 This results in a much smaller DWL, and much less pollution reduction. If, instead, the government levied a tax, it would equal MD at QR = R1. This could be the case for global warming, for example. First, assume the SMB is downward sloping, but fairly flat. MD = SMB Regulation mandates R1. R3 R1 RFull QR PFull More pollution Figure 12 Model with Uncertainty and Locally Flat Benefits

Figure 13 shows the case when the social marginal benefit is “locally steep.”

But it is possible for the firm’s costs to be PMC2. PR PMC2
In addition, imagine that the government’s best guess of costs is PMC1. But it is possible for the firm’s costs to be PMC2. PR PMC2 Suppose the true costs are PMC2. Then there is small deadweight loss. PMC1 This results in a larger DWL, and much less pollution reduction. If, instead, the government levied a tax, it would equal MD at QR = R1. First, assume the SMB is downward sloping, and fairly steep. This could be the case for nuclear leakage, for example. Regulation mandates R1. MD = SMB R3 R1 RFull QR PFull More pollution Figure 13 Model with Uncertainty and Locally Steep Benefits

These figures show the implications for choice of quantity regulation versus corrective taxes. The key issue is whether the government wants to get the amount of pollution reduction correct, or to minimize firm costs. Quantity regulation assures the desired level of pollution reduction. When it is important to get the right level (such as with nuclear leakage), this instrument works well. However, corrective taxation protects firms against large cost overruns.

Recap of Externalities: Problems and Solutions
Externality theory Private-sector solutions Public-sector solutions Distinctions between price and quantity approaches to addressing externalities

Chapter 5 Externalities Problems and Solutions

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