Externalities draft for EOLSSDavid A. StarrettEconomic Externalities

by David A. Starrett

The concept of externality has played a central role in the economic theory of resource allocation. The idea behind the concept is simple to state: An externality exists when the actions of a specified group of economic agents have significant economic repercussions on agents outside the group. However, there are considerable difficulties in making this concept precise, mostly having to do with the operational meaning of significant. To illustrate the difficulty, note that virtually every economic action you take has some impact on some other agent. If I buy an orange, the seller has more money and less oranges, and there are similar repercussions for every market transaction. Yet these situations are not ones that any economist would identify as externality producing. To qualify as externality, there must be an involuntary element in the repercussions and an associated distortion in economic incentives. Clearly, this extra requirement eliminates market transactions for which participation is strictly voluntary. However, what is left is still somewhat amorphous and we find it important to define externality precisely as an analytic concept.

Many definitions have been suggested for this concept but it is difficult to give a precise one that covers adequately all of the various examples that have emerged in applications. Indeed, here we find it necessary to divide the concept into at least two subcategories with separate definitions: Direct Externalities and Indirect Externalities. We will discuss these categories separately though later we will see that the line between them is not always distinct.

I Direct Externalities

We will say that a direct externality exists whenever a choice variable of one agent (or decision-making group) enters into the direct objective function of some other agent(s). Clearly, when there is an externality in this sense, the associated choice made will have involuntary impacts on the affected agent(s). This definition encompasses many of the best known examples. In the case of air pollution, the smoke put into the air by a factory helps to determine ambient air quality, a variable that enters into the utility functions of resident consumers. In the case of road congestion, one drivers decision to enter a crowded highway affects average traffic speed which in turn affects the utility of other users. The externality of the commons also fits within this definition. When many ranchers graze their cattle on a piece of open land, the decision by one rancher to add to his herd will lower the amount of forage available to others, which in turn lowers the productivity (and hence profits) of other ranchers. We discuss first this class of externality and its implications for economic allocation. Later we will argue that the concept needs to be generalized somewhat to include other situations that generate similar outcome characteristics.

1. Externalities and inefficiency

As suggested above, there is a general presumption that externalities are a bad thing in that when they are present and not dealt with in a centralized way, the resulting allocations are going to be economically inefficient. We can see now that this is generally true for the definition just given. Suppose agents behave toward each other in a decentralized Nash waythat is each makes his own decisions taking as given the behavior of other agents. Suppose further that we are in a general situation in which payoffs of the various agents depend on actions they all take. Let ai stand for the (vector) of decision variables available to agent i. To the extent that agents face constraints, we assume that they can be solved for a dependent set as functions of some independent subset, and that ai represents the independent subset. The matrix of all actions will be simply denoted a (without a superscript). Further, the notation (ai,b-i) will mean the configuration in which agent i plays from configuration a whereas everyone else plays from b. Let Pi (a) stand for the objective function of agent i. Now a* will be an equilibrium outcome for the group if each finds it best to use her * decision as long as she expects everyone else to do so as well; that is:

for all i, Pi(a*) $ Pi(ai,a*-i), for all feasible choices ai.

We now argue that equilibrium in this context will generically be nonoptimal from the point of view of the group as a whole. This conclusion will hold no matter how we choose to weight individual payoffs in defining the group objective. Suppose we assign weights wj and consider the social objective W(a) = 3j wj Pj (ai). Thinking of ai as one dimensional, we can define its marginal social benefit and marginal private benefit as

MSBi(a) = 3j wj MPj / Mai,

MPBi (a) = MPi / Mai.

Now, by the definition of equliibrium (a*), MPBi(a*) = 0 so

MSBi(a) = 3ji wj MPj / Mai.

Thus, as long as the interdependences are generic, we expect to find the MSBs not equal to zero at equilibrium so the group can be made better off through marginal changes in private choice variables. Further, we can measure the marginal external cost of choice ai as MSBi(a) - MPBi(a). We will see how this measure is represented in a number of concrete examples below.

2. Internalizing externalities through markets.This section is drawn largely from Starrett (1988)

Direct externalities are often linked to collective properties of the commodities or services through which they are conveyed and there are strong reasons why this should be so. When goods that we generally think of as private in nature generate real externalities, there is a quite natural way in which institutions will arise that effectively eliminate the associated externality. We illustrate with the example of physical garbage. Suppose that there are no enforced regulations on the disposal of household garbage. Then, ignoring the possibility of altruistic behavior, we would expect everyone to dump theirs on someone else. And of course this situation involves a direct externality since my decision to dump on you affects your utility. We model this as follows: Let aghi be the amount of garbage dumped by h on i. Then, the consumption of garbage by agent h is 3i agih. We assume that each agent cares only about his final allocation of garbage and not at all about the allocation to others. Thus, agent hs utility may be represented by a function defined on net consumption:

Uh = Uh (3i aghi - zg h, ch),

where zgh, represents his fixed endowment of garbage and ch is net consumption of private goods. Each maximizes subject to a standard budget constraint p ch = 0, and a garbage constraint: 3i aghi = zgh. Obviously in a Nash equilibrium where the dumping policies of others are taken as given, each agent will want to dump all of her own on someone else, and it does not matter who.

Except by chance (that is, generically), we know the decentralized equilibrium will not be efficient. This happens here as long as different people have different tolerances for garbage (here measured as the marginal rate of substitution [MRSac]-- the rate at which a consumer must be compensated with consumption to be willing to accept an extra unit of garbage) so that we can find a pair of agents (h.,i) for which

(Here, agent h has a lower tolerance for garbage than agent i.) The outcome is inefficient since agent i can give some amounts of both consumption and garbage to agent h in such a way as to make them both better off.

But now suppose that society establishes and enforces a property right whereby I cannot dump on you without your permission. Then, persons with isolated sites have incentives to offer dumping services for compensation from those with comparatively high disutility. Indeed, if agent i is able to set the terms of an arrangement with agent h, she will collect the first unit of garbage for a fee equal to MRSach and enjoy the full surplus: MRSach - MRSaci. More generally, both parties are winners as long as the price is set between their relative disutilities, so economic efficiency is improved. Further, we would expect such trades to continue until all differences in tolerance are eliminated (thus establishing a common collection price). As long as none of the parties involved have enough power to influence the market clearing price, the outcome will be an efficient allocation of garbage. Letting Pg represent this price, agent h will choose her net consumption vectors to

Max Uh(cgh, ch), subject to p ch + Pg cgh = 0.

Stated in this form, the price of garbage will be negative, but otherwise we find ourselves in a classical framework where competitive equilibrium is Pareto efficient. Each agent will equate her tolerance rate to the price ratio in market equilibrium.

Here, markets succeed in internalizing the externality created when I dump garbage on you without your permission. Not only has the private property right promoted efficient allocation but it has done so automatically, without the need for interference except for the enforcement of the right. This is the major virtue of the invisible hand. It is easy to see that the example generalizes to other commodities such as apples, oranges, computers, etc. where ownership rights can be unambiguously assigned to individuals. And, at least in capitalist societies, this is done so that markets are used to allocate these resources and any potential externalities they might otherwise generate are internalized.

3. Externalities and collective goods

Consequently, externality conveying items must have some features that make the assignment of private property rights impossible or undesirable. The biggest impediment to internalizing externalities through the market is nonappropriabilitynamely the difficulty or impossibility of enforcing a private property right. A pure example of such an item is clean air. It is not possible to assign an individual the right to clean air over his property since there is no practical way to prevent that air from mingling with dirty air coming from elsewhere. Other resources with similar character include fish in the ocean, greenhouse gas concentrations and lake water quality. Even when a property right can be enforced it still might not be desirable if the costs of enforcement are too high. For example, grazing land can be treated as private property only at the cost of building fences or walls. When the density of use is sufficiently small, the benefits of efficiency may not be worth this cost so we may prefer open access whereby the land is treated as a collective resource.

If private property rights are not assigned, the associated resource necessarily takes on a public character, by which we mean that any individuals decision to use or degrade the item necessarily has repercussions on others, thereby generating a direct externality as defined above. We see, now that the examples of externality given at the outset (pollution, congestion and commons) indeed all stem from a public character in the conveying item. In such situations, the social benefit from individual consumption is necessarily different from the private benefit, the difference measuring the marginal social cost of the externality. Efficient management of such resources requires some type of collective action.

Even when exclusion is costlessly possible, it may not always be desirable from an efficiency standpoint. This happens for resources that have an element of nonrivalry. A resource possesses some degree of nonrivalry if my use of it does not completely exclude your use. As an example of pure nonrivalry, consider radio or television signals. My use of the signal to obtain reception does not in any way preclude your using the same signal. In this case, we can if we like exclude at a finite cost (through the use of scramblers) but it is inefficient to do so; once the signal is sent (and the associated costs sunk) the greatest benefit will be derived from allowing all potential users free access. Another commodity with nearly the same character is information. Once it is produced the costs of dissemination are minimal so that efficient management would dictate free access. Notice that if we do choose not to exclude then the associated commodity takes on the same public character as we identify with the inherently nonappropriable goods so that as before, private decision-making will necessarily generate direct externalities. Goods, services and resources that are either nonappropriable or nonrival we label as collectiveitems in this class cannot be efficiently allocated privately without generating costly externalities. The extreme examples in this class possess both properties. National defense and biodiversity are cases in point. In both cases, it is not possible to exclude citizens from the benefits nor is their a cost of allowing additional users (or enjoyers). Economic or environmental resources for which appropriability is either impossible or undesirable are sometimes referred to as commons and the associated management difficulties as the problem of the commons.

4. Market allocation of collective goods

As suggested above Collectiveness does not entirely preclude the use of markets but does imply that if employed they will be inefficient at best. There are two ways in which markets might be used in this contextwe can exclude and force agents to pay for use or we can allow agents to contract for use but not exclude. As an example of the first type we may use patents to exclude potential users from free access to information as a way of providing incentives for the production of such information. But we would be even better off if we could provide those incentives in another way, since the patent royalty will deter agents whose potential benefit, though positive, falls short of the royalty. In this situation there is an allocative inefficiency but no direct externality as defined above. The inefficiency here results from an error of omission (failure to provide something useful) rather than one of co-mission that would generate a direct externality.As an example of the second type, suppose we sell community safety through the market. That is we allow citizens individually to purchase police time for patrolling the town streets. It is possible that there would be some purchases on this market but we argue that these will be lower than desirable for the overall social good; when any particular citizen purchases police time, most of the benefits go to others (referred to as free riders in the literature) who will benefit equally from the police presence (a direct externality). Here (in contrast to the case of privately divisible goods such as bread or steel) the private benefit from purchase is much lower than the social benefit. The difference reflects the marginal direct external benefit conferred on others when one agent contracts for community protection. Since market price can only reflect the private benefit, police protection will be underprovided in this case compared to the first best.See Oakland (1987), and Inman (1987) for further discussion of market provision of collective goods.

Thus, we see that when the resource in question is collective in nature we will have to assign at least some of the rights collectively if we seek to achieve optimal management. If decision-making rights are assigned to a smaller group, their decisions will necessarily generate inefficiencies, sometimes conveyed by direct externalities.

5. Correction for Externality

In situations where the decision collective is not exactly commensurate with the affected group, we expect externalitiesnamely some of the costs or benefits of action will fall on outsiders (as in our example of police protection). Whenever this happens, we expect incentives to be distorted in the same kinds of ways we saw they were when private rights are assigned to collective resources. However, in these situations we may be able to use market like instruments to restore correct incentives. The standard method of correction for externality is to impose a tax per unit at the rate of external costs (or subsidy for external benefits). For example, since the burning of coal contributes to air pollution and global warming, a tax should be added to the price paid by users to producers of coal, the tax being equal to marginal social damages from these effects. In this way the price paid by users will reflect both the private costs of production and the social externality costs; then each user will equate the marginal benefit from use with the full marginal social cost, thereby generating a socially optimal use level.

This reasoning can be used to justify a variety of green taxes in situations where externalities damaging to the environment (from private decisions) can be identified. Of course, to reach the first best, we must be able to identify and measure the marginal external damage and monitor and enforce the volume of emissions so as to set appropriate tax rates and collect corresponding tax revenues. And agents have incentives not to reveal their true preferences if they know that their answers will be linked to tax rates that influence behavior. For example, one would be tempted to overstate aversion to air pollution if one thought the answers given would have any affect on further lowering pollution (through raising the tax rate). We will return to the measurement problem later.

Even in situations where free rider externalities make it impossible to determine and/or enforce first best conservation principles, there are a variety of second best policies available that will be better than doing nothing. For example, a method widely used in the United States involves the setting of environmental standardsthat is in the case of air pollution from the burning of coal, each polluter can be assigned a quota. As long as we are certain that the unregulated level of pollution is too high, a social improvement can be achieved by assigning quotas in such a way that the total emissions are reduced.

However, it has long been recognized that we can do even better than this by assigning initial rights to pollute (that correspond to the quotas above) and then allowing trade. An example of this method is the use of emission permits to regulate the atmospheric concentration of So2. Unless we can correctly measure peoples disutility from smog we may not be able to determine the optimal concentration. However, whatever concentration is chosen, we can use tradeable permits as a vehicle for achieving that level in a least cost manner.

Let us see how this might work for the case of So2. First we would need to identify the region to be regulated and all the sources of emissions in this region. Further we must have a monitoring system in place that enables the regulator to verify levels of emissions. Next, we assign property rights by giving an initial allocation of permits (rights to emit a pound (or ton) of So2 into the atmosphere) to each emitter. Then they can be allowed to buy additional permits or sell some of their allocation on a permit market. Just as in the case of the garbage example discussed at the outset, if different emitters have different opportunity costs of emissions, there will be trades on this market (with high cost emitters purchasing from those with lower costs) and in equilibrium total emissions will be achieved at least opportunity cost. And if we observe voluntary trades taking place, we can be sure that the emissions market is Pareto superior to the simple setting of standards. Further, note that the information requirements are the same. In both cases, we must be able to monitor the levels of emissions, but nothing else.

It is worth pointing out that aside from distributional considerations the outcome achieved by a permit market can also be achieved through the use of an externality tax. Any equilibrium permit price could have been imposed as a tax rate and thereby achieve roughly the same total emissions level with the same degree of efficiency. However, now the informational requirements for the two schemes are different. In a permit scheme, the total quantity is specified and the marginal valuation is revealed by the equilibrium permit price, whereas in a tax scheme, the price is specified and total emissions revealed through choice.

This distinction takes on extra significance in a world of uncertainty. When there is uncertainty in economic production relationships, if quantity is specified, this uncertainty will show up in random variation in the associated price, whereas if price is specified there will be random variation in the corresponding quantity. Thus, in this situation, there may be a preference between these two methods depending on which uncertainty is more costly.See Weitzman (1974).

II Indirect externalities

In addition to direct externalities, there are situations in which private action has real repercussions on outsiders well being yet the transmission mechanism is more indirect. The issues here are subtle and somewhat controversial. Indeed, there is a strong tradition in benefit cost analysis, recommending that various indirect effects of projects should not be counted in the benefit/cost calculus, thereby implying that such effects do not generate significant externalities. The relevant indirect effects include price changes in related markets, increased sales, profits or employment in related industries and changes in tax collections or subsidy payments. We examine a few of these cases with the aim of identifying if and under what circumstances there might be significant externalities.

The essence of the argument against externality in all these cases is that the effects involve pure transfers. For example, in the case of employment, when it goes up in one sector of the economy, either people work more (thereby giving up leisure) or employment goes down elsewhere. In either case it is argued that the value of extra employment in the related sector is offset by the value of lost leisure or employment elsewhere. Similarly if sales go up in a related sector either production resources have been bid away from some other sector (where sales go down by a commensurate amount) or resources are drawn out of the leisure activity whereby the opportunity cost of leisure is lost.

Note, however, that these arguments rely on the perfect workings of the associated markets. Only if the labor market functions perfectly will it be true that the value of the marginal product of labor will be the same in all uses, and also equal to the marginal value of leisure. When these equalities fail to hold for any reason, the argument that external effects are a pure transfer also fails. Thus, we see that there is still a place for significant indirect externalities whenever there is a market failure and this is the position we will take and explore here. Indeed, we will argue that each potential source of market failure generates an associated indirect externality.

1. Externalities through price change

When the market variable involved is a price the externality involved frequently is referred to as pecuniary. The cost shows up indirectly as an effect on an agents indirect objective functionfor the consumer, the indirect objective is the utility derived from optimal behavior in markets; for the firm it is the profit so derived.We will use a more mathematical formulation of these functions in the next section. For example, an effective decision by OPEC to cut back on the production of oil will raise the price of gasoline which will lower the achieved utility of all users. Note that pecuniary externalities are purely distributive in natureone side of the market gains while the other side loses an equal amount. If the price of oil goes up by a dollar, a consumer that consumes c will have $c less income to spend on other things, whereas a firm that produces y will have $y more profit. Since supply must equal demand in equilibrium these amounts exactly cancel in the aggregate.

However, there are still a way in which a pure price change may generate a significant externality. Market outcomes are only first best if we are able to optimize on the distribution of income by guaranteeing that the marginal welfare of a dollar is the same for all citizens. If lump sum transfers (transfers made independent of the recipients behavior) are possible then this condition can be achieved by making such transfers from those with low welfare weights to those with higner ones until equality is established. However, such transfers are difficult (some would say impossible) to arrange in a democratic society and instead we rely on taxes based on items such as income earned or purchases made. These taxes introduce distortions in incentives (here to work or consume) so do not provide a cost free way of equalizing weights. When we fail to meet the equalizing condition, then the cancellation noted above does not translate to the social welfare function. For example, if the users of gasoline are considered more deserving (have a higher marginal welfare of a dollar) than the owners of oil firms, then the losses to users from a price increase count more in welfare terms than the gains to owners so that on balance there is a marginal welfare loss and therefore a marginal external cost. The issue of equity in distribution is a controversial one and naturally involves a value judgement. There is no way to prove that one person is more or less deserving at the margin than another. Distributional externalities of the type just discussed only emerge if we judge as a society that differences do exist at the margin.

2. Externalities through market activity levels

When could there be a significant externality associated with a change (say increase) in some market activity level? In analogy with the case of price, this can only happen if there is some reason why the benefits of the extra activity are different from the opportunity cost of obtaining that extra activity. Such an imbalance can occur in at least three ways (in addition to the equity consideration just discussed): there may be impediments to market clearing, supply (or demand) may be forthcoming at conditions other than those of perfect competition, or the market may be subject to an ad valorem tax.

The first of these situations is most often associated with employment benefits. Suppose that the labor market does not clear in that some agents would be willing to work at something less than the going wage but are unable to find work. That is, in the status quo their marginal utility of leisure (MU/Ml) is less than the wage w. Then, if some private decision generates extra employment elsewhere (*l) and that worker is hired, the extra value of marginal product (w*l) exceeds the lost opportunity cost of time ([MU/Ml]*l) so there is a net marginal external benefit of [w - MU/Ml]*l. Generalizing from this case, we can see that there can be external effects through any market that does not clear. The size of the marginal externality will be measured by the gap between the marginal valuation of the associated commodity by buyer and seller.

There will be a similar second best externality in monopolized markets. A monopoly restricts supply to a point where the price charged (p) exceeds the marginal cost of production (MC) so that the value of an extra unit to buyers exceeds the opportunity cost of production to sellers. Consequently, when an outside action stimulates activity by an amount (*x) in this market, it will generate a marginal external benefit of size ([p - MC]*x. For example, if computer operating systems are monopolized then an innovation that stimulates demand for a complementary good (say computers) will generate such an external benefit.

When the market variable affected involves the indirect tax system, we refer to the associated externality as fiscal. If the tax is an ad valorem commodity tax at rate (t) this tax introduces the same type of gap between marginal value to purchaser and supplier as in the previous two examples. Namely the price paid by buyers will exceed that received by sellers by the amount of this unit tax. Consequently when activity is stimulated in such a market by an amount (*y), there will be a marginal external benefit of size (t*y). For example, when the tax is a local sales tax, the decision of one community to expand will bid residents away from other communities and marginally lowers the tax base in those communities. Here the externality imposed is negative (the change in tax base is negative): residents in the affected communities will be required to pay marginally higher local taxes in order to maintain the same level of public services.

III Measuring Externalities

How are we to determine the correct costs or benefits attributable to externalities? As we have seen, in the case of indirect externalities, these are generally revealed as long as we can identify the external impacts on associated markets. Similarly, we can quantify the externality of the grazing commons by measuring the loss in productivity from reduced forage when extra livestock are introduced. However, for many direct externalities (such as air pollution) there is no similar natural measure. We will discuss briefly a variety of methods have been proposed for obtaining the correct measures.

Perhaps the most natural procedure (known by the name contingent valuation) involves designing surveys in such a way as to elicit information on preferences directly. For example, we can ask people how much they would be willing to pay for a specified reduction in the amount of air pollution. This method has been increasingly popular recently, but experience with it is mixed at best. It is clear that responses are quite sensitive to the way in which questions are asked. Furthermore, research has shown that responses tend to be biased in a number of ways.

Part of the difficulty with contingent valuation may be that when questions are strictly hypothetical, respondents do not think very hard about them and consequently do not give the more accurate answers they would if money were on the line. It would seem that we might do better by providing real incentives. Indeed, this is the main reason economists prefer to rely on so called revealed preference methods. These are methods wherein agents reveal their preference through actions taken in real choice situations. This can be done through mechanism design or hedonic identification.

1. Mechanism design

There is a long literature on the design of mechanisms that provide incentives for participants to truthfully reveal preferences. These typically involve the sending of messages (such as marginal preference valuations) and a schedule of monetary payments as a function of messages sent, with the understanding that the associated allocation decision will be a known function of messages and payments. The best known success story here is the second price auction for allocating a single item. In this scheme, people bid for the item and it is sold to the highest bidder for the second highest bid price. This mechanism is efficient in that it induces bidders to bid their true valuations (thus revealing their true preferences) and therefore guarantees that the item is sold to the person who values it most.

Unfortunately however, the class of allocation problems for which efficient mechanisms can be constructed is quite limited. And even when such mechanisms do exist, they are generally too complicated to implement from a practical point of view. For example, in the best known mechanism for revealing the valuation of a collective good (such as clean air), agents must send in their willingness to pay schedules and then they receive a tax or transfer based on the amounts reported by the other agents. Even if such a scheme could be made practical, it still only works perfectly under quite restrictive assumptions on the structure of preferences.

2. Hedonic identification

Aside from hypothetical surveys and direct mechanisms, the only way to learn something about private preferences is to infer it from behavior observed in some natural context, typically behavior on related private goods markets. For example, one can presumably learn something about the value of clean air by observing differences in rents on clean versus dirty sites. Or one can learn about the value of job safety by observing the differences in wages between safe and risky jobs. These procedures of indirect revelation are known as hedonic methods and there is a large literature on their theoretical foundations as well as attempts at empirical implementation. Again, the areas of success are limited. The class of public items for which hedonic methods are amenable is limited and even when available, the practitioner generally faces problems of identification. For example, in the case of clean air, land rents vary across locations for many reasons other than ambient air quality (view, convenient access to shops, work, etc) and the method works only if one can identify which parts of the rent difference are due to which cause. We can illustrate these difficulties by looking more closely at this example.

Suppose individuals choose locations in a city by comparing rental cost with resulting transport cost and quality of amenities. Assume for the moment that amenities are measured by air quality alone which is represented at location s as "(s). Further assume that rent and transport cost at location s are given by r(s) and N(s) respectively. Conditional on being at location s, an agent chooses private consumption through standard utility maximization:

Maxc,l U["(s),c,l] subject to c + r(s)l + N(s) = m,

where c stands for a Hicksian aggregate of nonland consumption, l for land, and m for income. Assuming that we can think of the location choice as a continuous variable, the consumers choice of s will reveal the marginal value of air quality. To see this, form the Lagrangian:

L = U["(s),c,l] - 8[c + r(s)l + N(s)]

and look at the first order condition for choice of s:

[MU/M"] d"/ds = 8[dN/ds + l(s)dr/ds].

Monetizing the utility unit by dividing by the marginal utility of income, we obtain for the marginal value of air quality:

.

Presumably, we can observe the residential density [l(s)] and the rent gradient [r(s)] from market data. Thus, assuming the air quality and transport cost gradients can be identified from engineering and environmental studies, we can measure the marginal value of air quality.

Hedonic methods of this type whereby the value of externalities or public goods are inferred from related market choices have the advantage over contingent valuation in that they are based on revealed preference rather than hypothetical choices. Unfortunately, however, their range of applicability is quite limited. Identification is only possible if there is some intermediate choice variable that does not enter utility directly. Location played that role in the example abovenote that if the consumer cares about location per se, the method breaks down since it will not be possible to separate location preference from air quality preference.

However, even when exact hedonic identification is not possible, we may be able to use information revealed by choice to put upper or lower bounds on marginal valuations. For example, in the case of congestion, we can measure the extra time required to make a commute trip that it causes and then compute the value of this time to the commuter on the basis of her wage. Generally this will understate the true external cost imposed since it ignores the frustration and anxiety of driving in heavy traffic, so it will be a lower bound. Similarly the costs of treating respiratory ailments caused by air pollution will be a lower bound to its true cost. Such upper and lower bounds can be valuable at least in helping us avoid bad mistakes. For example if we are able to show that a particular pollution cleanup project would be desirable even when the only benefits counted are the cost of respiratory illnesses, then the project clearly should be accepted.

Bibliography

The survey of externality topics given in this paper merely skims the surface of a very large subject. The reader should consult references below for more in depth coverage of indicated topics.

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Baumol, W. and W. Oates (1988), The Theory of Environmental Policy, Cambridge University Press, New York. This book goes into considerable detail on the theory of collective goods and externalities and the institutional arrangements that have been created to deal with them.

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