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ENVIRONMENTAL AND NATURAL RESOURCE ECONOMICS Part 1: PERFECT COMPETITION, EFFICIENCY AND EXTERNALITIES by Jon D. Harford (Last updated January, 2005) (Note: references to Tietenberg are to his book Environmental and Natural Resource Economics, 7th edition, published by Addison Wesley.

Perfect Competition without Externalities (Tietenberg discusses this type of material in Chapter 2 of his book.) Perfect competition is an ideal form of a market economy which represents a simple starting point for analysis of real world economies. In perfect competition large numbers of buyers and sellers exist in each and every market and no one of them believes he has any influence over price. In addition, there is no uncertainty or imperfection in information and all decision makers are rational. Rationality for consumers means maximizing a well- defined utility function subject to an individual budget constraint, while rationality for each producer means each firm maximizes profits by its choice of inputs and output. For consumers, maximizing utility subject to the budget constraint leads to particular choices of consumption goods for each set of price and budget that the consumer faces. By varying the price of one particular good, other things the same, one can derive a relationship between the quantity of one particular good chosen and its price. This relationship is the individual demand curve of a consumer, a relationship which holds prices of other goods and income constant. Assuming that consumption of a unit of a good X by George affects no one except George, the demand curve of George for good X can be interpreted as reflecting the marginal benefit of units of 2 consumption. Referring to the demand curve in Figure 1a, it is seen that at price of $12, George would buy one unit of the good X. Accordingly, the value to George of the first unit of the good must be at least $12. At a price of $11, George would be willing to buy two units of X. From this we can infer that the second unit of X must be worth at least $11. Continuing in this reasoning it is seen that the third unit of X must be worth at least $10, the fourth unit must be worth $9, and the fifth unit must be worth at least $8. Accordingly, we would argue that the total of five units must be worth at least $(12+11+10+9+8)=$50. The total value of five units of the X good we shall call the total benefits of that consumption. Now suppose George faced a price of $8 for the X good and accordingly paid a total ($8)(5)=$40 to acquire five units. The difference between the amount George spent to acquire the five units and the total benefits of those units would be called his consumer surplus. George's consumer surplus is his net benefits of consuming five units of the good. That is, net benefits are the total benefits minus the total costs (his expenditures) of consuming the five units. We know that this net benefit is at least ($50-$40)=$10. The method of refining this estimate is to take ever smaller increments in the amount of the X good and calculate the highest price associated with acquiring that increment. If one takes this process to its ultimate limit, one finds that the total benefits equal the area under the demand curve up to the quantity consumed. Therefore, we can conclude that the value of consumer surplus is the area between the demand curve and the price line over to the quantity consumed. Marginal benefit is the rate of change of total benefits with respect to a change in the good consumed. An estimate of George's marginal benefit a given unit of X is the highest price at which that unit is purchased. Mathematically, 3

George's marginal benefit of consuming an infinitesimal amount of additional good X is the height of his demand curve. Individual demand curves are added horizontally (quantity addition) to obtain the market demand curve for good X. The total benefit, marginal benefit, and consumer surplus associated with the market demand curve for X are calculated in exactly the same fashion as with the individual demand curve. 4

While benefits come from consuming goods, costs come from producing them. Perfectly competitive firms maximize profits under conditions in which they take input and output prices as constants. In the short run this leads to a choice of output in which marginal cost equals price. In the long run equilibrium marginal cost and average cost both equal price. Thus, at the market output that is supplied for any given level of price it can be said that output is being produced at marginal cost. Of course, the supply curve only reflects private costs. That is, costs which the individual firms see as affecting their profits. Referring to Figure 1b, one sees that one unit of output will be produced when the price is $4, thus indicating that the cost to private producers of the first unit of output is no more than $4. At a price of $5, suppliers are willing to provide two units of the good. This indicates that the second unit of the good costs the firms no more than $5. Iterating, it is seen that the third unit 5 costs no more than $6, and the fourth unit costs no more than $7. If uses the same reasoning, but takes ever smaller increments to output, it is seen that the area under the supply curve up to the amount produced is the total private cost of production. Now suppose that suppliers receive $8 per unit for each of five units for a total of $40. Our method of cost accounting would indicate that the total private cost is no more than ($4+$5+$6+$7+$8)=$30. However, in the long run under perfect competition there must be zero economic profit and firms would therefore have revenues equal to opportunity costs. The difference in the two views of costs is that our estimate of $30 takes the view that part of the "costs" of firms are not costs from society's viewpoint, but economic rents. Economic rents are those payments to factors of production above the minimum necessary to keep them in an industry. In other words, economic rents are that part of the payments to factors such as a bricklayer, that is above his opportunity cost as represented, for example, by the level of wage he could receive by working in another industry. The collection of economic rents received by factors of production in an industry is called the producers' surplus. Producers' surplus is represented by the area between the price line, the supply curve, and the vertical axis, up to the quantity produced. The producers' surplus can be considered the net benefits of production to the supply side, just as consumer surplus can be consider the net benefits of consumption to the demand side of the market. It is one of the remarkable things about perfect competition is that it is perfectly efficient given certain conditions. Some of the conditions for its efficiency are merely the conditions for its existence. These include perfect information by all parties about all prices and products, no uncertainty, that economies of scale disappear at output levels small compared to the market 6

demand at a price that reflects average cost, and that goods have attributes that make private ownership possible. An additional condition for the efficiency of perfect competition is that there are no externalities or third-party effects. Since the subject of environmental economics is basically one of applying the notion of externalities to problems such as pollution and congestion, we will have much more to say about this subject. For now, let us turn to Figure 2 to illustrate how perfect competition produces efficiency under the ideal circumstances indicated. By efficiency, it is simply meant that overall benefits minus costs are maximized. In the Figure, it is seen that output Q* clears the market and that area N is consumer surplus, and area M is producer surplus. The total benefits of the production and consumption of Q* is the sum of producers' and consumer surplus. Now suppose that we consider the costs and benefits of expanding output to Q1. One cannot know how the benefits and costs would fall on various parties without 7 describing the policy that would bring about such and increase in output, but we can know what the effect on net benefits would have to be. Specifically, the increase in benefits associated with greater consumption of the good would be represented by area G, while the increase in production cost associated with the increased output would be (G+H). This implies that net benefits would go down by an amount equal to H. One can perform a similar analysis to demonstrate that a reduction in output would also reduce net benefits because consumption benefits would be decreasing faster than the reduction in production costs. Under the circumstances assumed, no form of government intervention can improve efficiency.

A POLLUTION EXTERNALITY: THE OUTPUT DIMENSION We now consider a situation in which a perfectly competitive industry produces pollution in direct proportion to the amount of output it produces. In other words, it is assumed that the ratio of pollution (Z) to output (Q) is a constant equal to w=(Z/Q). This pollution creates an external cost to society. For example, it z were an air pollutant, the external cost would be manifested in an increased incidence of respiratory ailments in the general population, reduced visibility, and damage to the surfaces of buildings, cars, and clothing. Assuming that pollution is proportional to output makes it legitimate to plot these external costs as a function of output. Since they can be plotted as a function of output, they can be placed within the same type of diagram that we use for supply and demand. We define marginal social cost (MSC) as the sum of marginal private cost (MPC) and the marginal external cost (ME) created by a unit of output. MPC is represented, for reasons we have already discussed, by the supply curve. Since marginal external cost is a cost that is in addition to the private cost for the same unit of output, we derive marginal social cost by the vertical addition of 8

ME and MPC. The result of this vertical addition are combined with the supply and demand curves in Figure 3. The diagram indicates that the private market will yield and equilibrium output of Q0.

However, the efficient level of output will be at Q*, where marginal social cost equals the marginal benefits of the good. Thus, the existence of a pollution externality implies that the unregulated market will produce an excessive level of the good. Given the goal of efficiency, how would a regulatory authority design a policy to achieve the efficient level of output? In the present simple setting of perfect competition and the assumption of an all-wise government, the answer is relatively simple. The private market will internalize the cost of pollution if it is made to pay a price for the pollution equal to its marginal (external)cost. Specifically, the government would set a constant 9 tax of T per unit of output, where T=ME*, and ME* is the level of marginal external cost at the efficient output level. This tax and its effects are illustrated in Figure 3. (Refer also to Figure 4.4 in Tietenberg, 7th edition.) With most supply and demand curves the tax will cause the price that demanders to pay to go up and the price that suppliers receive to go down. In other words, the tax creates a wedge between the supply and demand prices, causing both sides of the market to bear some of the burden of less favorable prices for their sides of the market. This is necessary because output must be reduced and still maintain an equilibrium in the market where neither shortage nor surplus exists. In basic terms, both suppliers and demanders are made worse off by the tax. Those who buy and sell a good are not likely to wish it to be taxed even if there is an externality. Before quantifying losses to suppliers and demanders, we turn to the basic point that there is a net gain from this pollution tax. In Figure 3 the area labeled A represents the net gain to society of imposing the ideal pollution tax. This area is derived by subtracting the loss of benefits from output reduction from Q0 to Q* from the savings in social cost from that same reduction in output. This area represents a dollar number whose relative size may not be especially large in comparison with the taxes collected! You may well wonder if the cost of the tax does not indicate that our calculation of net gain is incorrect and too optimistic. However, the tax collected is not a social cost. It represents a transfer of resources from the private sector to the government. These resources can presumably be returned to the general public in the form of reduced levels of other taxes or increased spending on goods provided by the government. A real social cost of a pollution tax would exist if there were administrative costs of collecting these taxes. In the present analysis we are ignoring 10 such administrative costs, but recognition of such costs would not necessarily argue against the use of pollution taxes, since all taxes have such costs.

The area A+Y1+Y2 represents the reduction in external cost due to the reduction in output from Q0 to Q*. Since the vertical distance between the MSC curve and the Supply curve represents marginal external cost, the area between these two curves over the range of output reduction represents the reduction in external costs. The area (V1+V2) represents tax revenue raised, which is a pure transfer. The areas (V1+Y1) and (V2+Y2) represent the losses of consumer and producer surpluses due to the tax. Subtracting the loss of surpluses from the reduction in external costs and the gain in tax revenue leaves the area A as the net benefit associated with bringing output down to the efficient level. In discussing the uses of the pollution tax, we deliberately did not state that these taxes should be used for compensation of pollution victims. The reason is that under present assumptions, such compensation cannot improve efficiency and might well harm efficiency. Compensation for pollution damage will harm efficiency if such compensation reduces the incentive for individuals to keep the overall costs of pollution to them as small as possible. For example, if someone could live far away from a pollution source and make $50000 a year and have no medical costs or close to the pollution source and make $52000 but pay for $3000 in medical costs to counteract the effects of pollution, then efficiency dictates that the person should live far away from the pollution. However, if the person were compensated for such pollution-related medical costs, he would live near the pollution source. In conclusion, under the present assumptions a tax per unit of output equal to marginal external cost at the efficient level of output with no compensation to victims of pollution will yield an efficient market equilibrium. The tax corrects the essential 11 problem that the free market under-prices the output that creates the pollution. How much of the tax is passed on to consumers and how much is absorbed by suppliers is of no importance as far as the efficiency of the situation is concerned. The important feature is that the tax reduces the output to the efficient level.

WHEN POLLUTION CAN VARY INDEPENDENTLY OF OUTPUT We now consider the issue of pollution under the assumption that pollution can be varied independently of output. This is clearly possible with most types of air and water pollution. Various filtering processes on smokestacks can reduce emissions of air pollutants. Various changes in processes and in-factory systems for recovering wastes can reduce the pollutants going into our waterways. However, all of these reductions in pollution releases, holding output constant, require an extra expenditure of money by the firm or person responsible. To model the situation, consider Figure 4 where the horizontal axis is measured in units of pollution (z), and all curves are drawn holding the firm's output at q0. (See also Figure 15.2 in Tietenberg, 7th edition in reference to the Figures 4 and 5 in these Notes.) Figure 4 has both a right and left vertical axis. The left vertical axis hits the horizontal axis at the point of zero pollution releases. The right vertical axis hits the horizontal axis at a point indicating the level of pollution that the firm would release if it had no financial incentive to restrict its pollution output. This level of pollution is labeled z0, and is the level of pollution which minimizes the cost to the firm of producing a given output. The vertical axes both measure concepts in terms of dollars per unit of pollution. Starting at the right axis and moving left, the level of pollution released is declining. Accordingly, the measure of pollution eliminated is the horizontal distance from the right axis 12 to the level of pollution actually released, which is algebraically

(z0-z). The curve labeled mcz is the marginal cost of pollution reduction curve. Presumably, mcz starts at a zero level at z0, since the cost of pollution control is at a minimum at that point. MCZ rises as one moves from right to left and the amount of pollution reduction is increased. It is generally accepted that for many pollutants the marginal cost of pollution reduction rises extremely rapidly as one approaches one hundred percent elimination, and the mcz curve is drawn to reflect this. The area under the mcz curve from the right axis over to the amount of pollution actual released can be interpreted as the total cost of pollution control. If pollution were reduced to level z*, then the area labeled e would be the total cost of pollution control. The curve md is the marginal damage curve and it is a function of the actual pollution released. The height of this curve indicates the increase in damages to society from one more unit of pollution. At the aggregate level, this curve may be rising, constant, or falling, although a rising curve is likely to be the most common case for the pollution from an industry of firms. Because each firm is a small contributor to the total pollution, md is taken as constant. Since we are discussing the issue currently on the scale of a single firm, it is appropriate to assumed that md is roughly constant. The area under the md curve from the left axis up to the actual level of pollution represents the total damages from pollution released. Within the context of this 13

diagram, efficiency in the choice of pollution, or equivalently, in the choice of pollution control, is characterized by the minimization of the sum of pollution control costs plus pollution damages. In fact, total damages and total external cost are the same concept. However, marginal damage has the units of dollars per unit of pollution, while marginal external cost has the units of dollars per unit of output, so the marginal concepts do not have the same units and one needs separate terms to keep them straight. One may further view marginal damage as a measure of the marginal benefit of getting rid of pollution, and the reduction in pollution damages from eliminating a certain amount of pollution as the benefits of that action. 14

From the viewpoint of the firm the md curve does not matter in any direct sense. The firm will only be induced to engage in pollution control if there is some direct financial incentive to do so. Before deciding on what financial incentive to create, one has to know what one would like to accomplish. From the viewpoint efficiency, the best level of pollution control is given by the release of z* amount of pollution because that is where marginal damage of pollution equals the marginal cost of eliminating pollution (md=mcz). At higher levels of pollution, the cost of getting rid of another unit of pollution is less than the damage it causes; at levels of pollution lower than z*, the cost of eliminating one more unit of pollution is greater than the damage caused by that unit of pollution. A financial incentive to reduce pollution could come in the form of a pollution tax of amount t. For given output (therefore given revenue), the firm will desire to minimize the sum of pollution taxes and pollution control costs, where the pollution control costs are a function of how much pollution is reduced below z0, and the pollution tax costs are going to be t times the amount of pollution still released. The solution to the firm's problem is to eliminate pollution down to the point where the marginal cost of pollution control just equals the rate of tax (t). One can see this by noting that if the cost of getting rid of one more unit of pollution is less than the tax one would have to pay on it, then the firm's overall financial burden is reduced by getting rid of that unit of pollution. On the other hand, if the cost of getting rid of another unit of pollution is greater than the tax on that unit, then the firm will be better of by paying the tax on that unit.

If the tax is set at the level of t*, then the firm will choose to produce pollution at the level of z*, and incur t*z* amount of pollution taxes and an amount equal to area e in control 15 costs. The pollution taxes reflect the size of the remaining damages from the release of z* level of pollution by the firm. The area g is interpretable as the net benefit of inducing the firm to eliminate the release of (z0-z*) amount of pollution. That is, potential damages of (e+g) have been eliminated, while control costs of amount e have been incurred. This diagram can be scaled up to the industry level with only minor changes. The scaling up involves the horizontal addition of pollution levels from all firms, which requires an alteration of the scale on which the horizontal axis is drawn. To reflect the larger scale, capital letters are used for the corresponding concepts previously denoted with small letters. In many cases, this alteration of scale will imply that the aggregate marginal damage (MD) curve should be drawn in an upward sloping fashion. Figure 5 reflects the diagram drawn at an industry scale. The areas G and E are industry level of analogues of areas g and e from 16 17

Figure 4. G represents the net benefits of the efficient level of industry pollution control, while E represents the control costs of all firms. With MD upward sloping, the total pollution tax payments will exceed the area representing total damages form remaining pollution. This latter concept is represented by area R. As with the tax per unit output, there is a presumption that the proceeds of the tax revenue are distributed in a way that is independent of one's behavior or status as victim or polluter. The tax revenue is a transfer of purchasing power to the government for its redirection, and does not represent a social cost. On the other hand, both of these taxes effect output because of the effective upward shift in supply (as viewed from the demand side) caused by the financial burden of these taxes. To relate these two one has to keep in mind that T is a tax per unit of output and t is a tax per unit of pollution. At z* pollution and Q0 output, the tax burden per unit of output would be (t*z*/Q0). As we explore in more detail in the Appendix to this Chapter, the pollution tax, by placing an a burden on extra output because of its association with pollution, not only gives the proper incentives to reduce pollution for a given output level, it also gives the proper incentives for the industry to reduce output to the efficient level. Furthermore, in those cases where the ratio of pollution to output can be varied, the pollution tax is superior in efficiency to the output tax. Other things the same, efficiency will be improved the most the more directly the policy is aimed at discouraging the actual agent of the externality.

THE POLLUTION STANDARD APPROACH (See Tietenberg, 7th edition, pages 348-352 for relevant discussion.) While many economists have long sung the virtues of the pollution tax approach, it has been rarely used in practice. More 18 commonly, regulators are told to set pollution standards on firms. The actual content of these regulations can be complicated for many practical reasons involving difficulties of monitoring and measurement. We will address some of these issues later on. For now we take the simple view that a pollution standard is a limitation on the absolute amount of pollution that a firm may emit in a given period of time. It is also assumed that the regulator can costlessly monitor and enforce such a standard just as it has been assumed that the pollution tax can be costlessly and accurately collected. The theoretical issue at hand is whether such an approach can achieve the efficiency associated with the pollution tax approach. In terms of the ideal model, the answer is basically no. In terms of Figure 4, it is certainly possible to assume that the regulator sets the pollution standard of the firm at the level z* and thereby duplicate the pollution released under the tax approach for a firm producing a given output. However, no taxes are being collected on the remaining pollution. This implies that the costs to the firm do not reflect the damages remaining from the pollution still not eliminated. Therefore, the remaining pollution still creates a truly external cost and the firms' average and marginal costs of output will not reflect all costs to society. Accordingly, the market's equilibrium price for the good will be too low and output will be too high compared with the efficient level. Clearly, efficiency will be improved by the use of pollution standard relative to doing nothing. The reduction in pollution associated with each output level does produce a net benefit. In fact, the extra control costs incurred because of the standard to imply an upward shift in the supply curve and some reduction in equilibrium output. However, the reduction in output is simply too small to attain efficiency because of the absence of a tax to reflect the remaining pollution damage. 19

Some would argue that while a pollution tax may be superior under certain ideal circumstances, in the "real world" the standard approach is better. However, there is at least one practical informational problem that offers an additional argument for the tax approach. One might suppose that the regulator has a reasonably good idea about the MCZ curve for the aggregate of firms, but not very good information regarding the individual mcz curves of firms. All the regulator needs to know to set the pollution tax at the appropriate level is the aggregate MCZ and MD curves. Individual firms responding to that common tax will all equate their individual marginal costs of pollution control to that tax. This is efficient in that the aggregate costs of pollution control will be at the minimum necessary to eliminate a given total of pollution. On the other hand, for a regulator to set a standard for total pollution that can be enforced, it must set standards on individual firms. To achieve the same efficiency as the pollution tax all those standards must be set so that the marginal cost of pollution control is the same for all firms. This is because any differences in the marginal cost of control between two firms implies that the total cost of pollution reduction could be lowered by having the firm with the higher marginal cost reduce pollution one unit less and the lower marginal cost firm reduce pollution by one unit more. However, achieving equal marginal cost of control for all firms using the standard approach requires the regulator to have detailed knowledge of the control cost relationships of each and every firm. Without this knowledge, the regulator is likely to use some rule of thumb for deciding on emission reduction responsibilities. One such rule would be to have all polluters reduce their pollution by X%. While such a rule may sound reasonable, it is not likely to lead to the reduction of pollution at the least total cost. In fact, such a percentage reduction rule requires that the regulator 20 be able to properly choose base levels from which to measure pollution reduction as well as measure actual pollution itself. Another practical consideration favoring the use of pollution taxes is that the revenue raised can be used to substitute for revenue from taxes that cause inefficient distortions in behavior. An important example of a tax causing undesirable changes in behavior is the income tax. The income tax is applied to earnings in the market, but not to the real income created when one does chores for one's self such as washing the car, repairing one's home, or cooking one's meals. Nor does the income tax system count the value of leisure as income. This means that the income tax encourages the substitution of non-market work and leisure for efforts which create market income. Such substitution effects create a burden of taxation that is in excess of the direct burden as measured by the taxes raised. The pollution tax creates net benefits because of the changes in behavior that it creates. If the tax revenue could be used to reduce taxes like the income tax, one might expect that it would have the additional benefit of reducing some the inefficiency associated with those taxes. As it turns out, it is true that the presence of other taxes does affect the amount of additional tax one would place on pollution to achieve efficiency. However, the issue is complicated. For example, suppose there are two private goods produced, one is polluting, and there is a uniform rate of tax on both goods that raises revenue for a public good. If we now consider raising the tax on the polluting good and lowering it on the non-polluting good in order to raise the same revenue, it is not always the case that the rate of tax on the polluting good will be higher than that on the non-polluting good by an amount equal to or greater than the marginal pollution damage caused by the good. The reason is that pre-existing taxes distort the labor-leisure choice and this distortion may be worsened by an adjustment in the 21 tax scheme.

SUBSIDY APPROACHES At one time, some economists suggested that a subsidy per unit of pollution eliminated would provide an equivalent incentive to a pollution tax. Such a subsidy would be set at level s* such that s*=t*. from the viewpoint of the firm, it would pay to reduce pollution to z* for a given output level, since they would receive more in subsidy than it would cost them in control cost for each unit removed down to that level of pollution. Below z*, the subsidy would be less than the marginal cost of control (mcz), and therefore those units would not be removed. Subsidies sound nicer than taxes, so such an approach might have some appeal. However, this subsidy approach would be generally poor way to reduce pollution. In the first instance, any subsidy implies the existence of taxes on something else in order to fund the subsidy, so one does not really escape the need to impose a tax. Furthermore, while the subsidy per unit of pollution reduction does provide a positive incentive to reduce the level of pollution for a given level of output, it provides the wrong incentives when it comes to the output dimension of the pollution problem. A subsidy per unit of pollution reduction would more than remove any burden of pollution control cost from the firm and not add any burden for the remaining pollution still emitted. In fact, the firm would presumably make a "profit" on removing the early, less costly, units of pollution. This means that the firms' net cost of production would be lower than it was without any pollution regulation at all. Therefore, since price will reflect average and marginal cost in the long run, output will be priced below marginal social cost and will tend to be larger than it was without regulation. In an extreme case, where pollution relative to output 22 is lowered very little and output expands a great deal, total pollution might actually increase from such a policy. In fact, a subsidy per unit of pollution eliminated has not been tried. However, subsidization of some portion of the costs of pollution control has been tried. Tax laws have allowed accelerated depreciation of some pollution control equipment. At one time the Federal government subsidized the construction of waste water treatment plants. By themselves, these cost subsidies fall short of providing a positive incentive to reduce pollution unless some of the benefits of treatment are internalized by those receiving the cost subsidy. Some internalization of the benefits may have existed with the local governmental entities that received the construction grants for waste water treatment since the local population would presumably have gained something from improvement in the water quality of nearby rivers and lakes. We will analyze this issue further when we discuss actual policies used in the area of water pollution. For an ordinary firm, it my be assumed that no internalization of the benefits of reducing pollution would occur. However, if enforcement of pollution standards is a problem because of limitations on the ability of the regulator to impose fines, then a subsidy of costs may aid in ensuring the compliance of the firm with the standard. A firm weighing the cost of controlling pollution against the fines and other penalties that might be applied if the firm is discovered violating the standard, may be swayed in the direction of compliance if some of the control costs are paid for by cost subsidies. Note that with this type of subsidy, the firms' costs of production will always be more than it would be with no regulation since the only way to receive a subsidy is to incur some privately borne control costs. Thus, the cost subsidy approach does not have the potential for adverse output effects that the subsidy per unit of pollution reduction has. 23

POLLUTION TAXES WITH NON-UNIFORMLY MIXED POLLUTANTS (See also Tietenberg, 7th edition, pages 353-360) The previous discussion of pollution taxes and other approaches to controlling pollution has assumed that the pollutant is uniformly mixed into the medium into which it is released. For example, with air pollution it is being assumed that emissions from any polluting source have the same effect on the concentration of pollution at every location at which a person might experience it. This assumption is certainly factually incorrect, although for some purposes it may be not too far wrong. However, if the pollution levels around a source of pollution are much higher than they are further away from the source and if all sources are not located in a similar manner in their geographical relationship to the victims of pollution, then the level of marginal damage per unit of emissions is likely to vary across sources of pollution. In this case, the natural extension of the previous reasoning is to have each source face an emission tax equal to the marginal damage that its emissions cause at the efficient level of control. To see how the emission tax would relate to the source’s impacts on the victims, one has to consider both the number and location of the victims as well as the way in which emissions translate into pollution concentration levels at the sites of the victims. Suppose there are two sources of pollution, where the source is designated generically by i=1,2. Suppose for the moment that there is only one location for the victims. One may think of the appropriate Pigovian tax per unit of emissions on source i as being determined by ti=(mdc)ai, where mdc stands for marginal damage per unit of concentration and ai is the rate of change of air pollution concentration with respect to a unit of emissions from source i. The ai is sometimes referred to as the “transfer coefficient.” In this formulation it is still true that the marginal damage 24 per unit of concentration is the same for both sources 1 and 2 since they are both affecting the same population in the same location. Clearly, if source 1 is much closer to the receptor victims of pollution, then its transfer coefficient will be higher than for source 2 and the rate of tax per unit of emissions should be correspondingly higher. In a competitive market, a firm would presumably only locate at a site with a higher rate of pollution tax if there were some offsetting reduction in cost in another aspect of its operations. Now suppose that there are two locations, A and B, for the victims of pollution. These locations will vary in their distance from each of the pollution sources. In addition, the number of individuals at locations A and B may not be the same. Therefore, to calculate the marginal damage of pollution emissions from a source i one must consider its distinct transfer coefficients for locations A and B, where these can be denoted as aiA and aiB. Furthermore, one must consider the population levels at A and B, denoted as NA and NB. In this case the Pigovian pollution tax on source i will be calculated as ti=(NAaiA+NbaiB)(mdcp), where (mdcp) is defined to be the marginal damage per unit of concentration per person, where this is assumed to be the same for all persons. Thus, the Pigovian tax is calculated to account for the number of people affected times the rate at which the concentration of pollution increases with an increase in emissions at the location of the particular groups. Now if the transfer coefficients are such that a1A=a2A and a1B=a2B, then the taxes on the two sources will be the same. However, in general one would expect that sources located in different places will yield different marginal damage per unit of pollution emissions. Furthermore, if the pollution damage per unit of emissions is not the same, efficiency is no longer served by equality of marginal cost of emission control across sources of pollution. Of course, firms will not be induced 25 to have equal marginal cost of emission control if the Pigovian taxes vary from source to source depending upon location. Administrative costs of having taxes or standards that vary according to location may make the net benefits of such an approach less than the costs. In this case one gets into the area of “second best” regulatory policy. Second best resource allocation is what occurs when efficiency is pursued with some limitation or constraint on what one can achieve due to problems of insufficient regulatory knowledge, ability, or other limitation. In a case like the one being discussed a uniform Pigovian tax that produced the most efficient outcome given the fact that different sources of pollution create different marginal damage per unit of emissions would be called a second best Pigovian tax. Roughly speaking, a second best uniform tax would be a weighted average of the first best set of locationally differentiated taxes. The problem of pursuing second best policies comes up repeatedly in discussing environmental policies. A second best problem that is quite different from the one just discussed is addressed in the section on the monopoly polluter. The inability of regulators to vary the pollution tax from times when pollution is higher to when pollution is lower creates a problem of a similar second best nature to the one just discussed. Unfortunately, it is hard to make general statements about the nature of second best policies since there are a huge variety of possible limitations on the ability of regulators to attain the first best allocation. In all cases, one has to carefully assess the benefits and costs of each available policy compared with the alternatives.

ZONING AS A COMPLEMENTARY APPROACH TO CONTROLLING EXTERNALITIES (There is virtually no reference to zoning in Tietenberg.) Zoning rules determine what kinds of activities can be placed in what locations. Some areas are zoned for single family homes 26 only. Other areas are zoned for commercial and industrial use. Minimum lot sizes may be set for houses. Minimum amounts of open space between a commercial building and the street may be set. The unique aspect of zoning in comparison with the previous discussion of pollution taxes and standards is its emphasis on the spatial arrangement of actions that may cause externalities. While, as just discussed, pollution taxes in particular, and externality taxes in general, can account for differences across locations in the marginal damage caused by pollution, there is a coordination issue that may be more easily addressed by zoning regulations than by Pigovian taxes. For example, it may be clear that houses and steel mills should be located in separate places. However, exactly which place each activity should be located may not be clear. It may be useful to have a zoning plan that states that houses will be in the east part of the jurisdiction, and steel mills will be in the western part, so that a potential homeowner does not guess incorrectly where the steel mill is going to be built. Thus, zoning is most uniquely aimed at arranging activities so that the total external cost or damage from a given amount of different activities is at its lowest level. To be more concrete, a zoning regulation is trying to locate the polluting activities in places where the exposure resulting from the pollution emissions will be as low as possible, other things being the same. Of course, other things are seldom the same. Restricting the location of particular types of firms may increase the overall cost of those firms producing a given amount of output and pollution. Thus, there will be trade-offs. One simple trade-off may be between locating the polluting firm farther away from a population center while at the same time increasing its costs of delivering its product to that population center. Of course, if the amount of land area allowed for a certain activity also raises the cost of particular types of firms 27 operating and will tend to limit both output and pollution. However, when one restricts land area for an activity, one is restricting the use of only a single input into production. Restricting a single input, particularly when that input is not one closely associated with the negative externality, is unlikely to be the most efficient way to limit the total amount of an externality creating activity.

THE MONOPOLY POLLUTER AS A SECOND BEST PROBLEM (Tietenberg, 7th edition, discusses monopoly on pages 76-78, but does not include an externality problem.) We have heretofore assumed that all the markets are perfectly competitive, and that the pollution problem in the market we analyze is the only imperfection in the economy. Of course, the real world is far more complicated than this. A general rule of thumb in trying to attain the first best level of efficiency, is that the government needs as many instruments of control over the economy as there are sources of deviations from efficiency. When the regulator has fewer instruments of control than necessary to produce a first best efficient solution, we are said to be a situation of seeking a second best optimum. Among the countless reasons why one might be in a situation of seeking the best "second best" solution to externality problem is that it may be prohibitively expensive to observe, and therefore directly regulate, some sources of pollution. The regulator might then seek indirect ways of controlling the pollution through the regulation of the uses of certain types of inputs which may be strongly related to the pollution releases. Or the regulator may specify that certain technologies must be used, or in other cases, certain technologies may be prohibited. These types of regulations do occur and we may suppose that they do so in response to certain problems of measurement and observability of pollution. We will 28 explore these types of issues in more detail when we discuss actual regulatory policies in use. For the present, it is worthwhile to explore a relatively simple problem in seeking second best efficiency which illustrates the potential for surprising outcomes. Consider an unregulated monopoly which produces an output by a process which simultaneously creates a pollutant in fixed proportion to the output. The unregulated monopolist will maximize profits by setting marginal revenue (MR) equal to marginal private cost (MPC), of which the latter is assumed to be constant. Because the marginal revenue curve is below the demand (D) curve, the monopolist will charge a price above its marginal private cost. The marginal social cost (MSC) curve is drawn so that it hits 29 30 the demand curve at exactly the monopoly price. This is merely fortuitous, and not in any way a necessary feature of the example. However, the implication of this particular situation is that the monopolist is setting output exactly at the efficient level. A pollution tax would, in fact, cause the monopolist to reduce output below the efficient level. In other words, the monopolist's tendency to charge a price above marginal (private) cost works in this case to reduce output by the amount desired. In a sense, the monopolist is (accidently) charging (and collecting) the right level of pollution tax. Thus, in this case the effects of the two problems of monopoly and pollution simply cancel each other out as regards efficiency. Of course, the curves may be drawn so that the monopolist's price is higher than marginal social cost, in which case some regulation designed to lower price would be necessary to produce efficiency. If the monopolist's price were to be below marginal social cost then a policy would be called for which raised the price charged to the consumer. However, the nature of the tax that would create this result would have to be calculated in manner differently from simply setting it equal to marginal external cost at the efficient output level. Exactly how one would compute such a tax would require a discussion more complex than the importance of the example would warrant. But the reader should be convinced the most efficient policy toward a negative externality in a second best world may depart substantially from a simple application of a pollution tax. 31

APPENDIX THE INTERACTION OF POLLUTION AND OUTPUT WITH A POLLUTION TAX (Tietenberg, 7th edition, does not address in any significant way the interaction of the pollution and output dimensions in discussing the effects of pollution taxes, standards and other approaches to controlling pollution externalities.) The effects of imposing a pollution tax extend to the output dimension. The pollution tax adds to the costs of the firm by causing the firm to incur pollution control costs and by imposing the pollution tax itself. This will add to the marginal and average cost of producing output by each firm and therefore affect the supply curve and equilibrium price and output. Figure is meant to illustrate how the concepts of control costs (E), remaining pollution damages (R), and the net benefits of pollution control (G) can be translated from Figure 5 to the output dimension.

Holding output constant at Q0, the same level as in the Figure

5, we have designated two marginal social cost curves, MSC0 and

MSC*. The higher curve (MSC0) represents the marginal social cost of output when pollution is uncontrolled; that is, when each firm incurs no control cost in order to reduce pollution. In this case, amount of pollution per unit of output is presumably quite high. Marginal external cost is therefore at a level corresponding to

ME0=(MD)w0, where w0 represents the ratio of pollution to output with uncontrolled pollution. The lower curve (MSC*) represents marginal social costs with a level of pollution control which equates the marginal costs of control with the marginal damage of pollution. Thus, ME*=(MD)w*, where w* is the ratio of pollution to output when pollution is controlled at an optimal level for any given output. The difference in heights between these two marginal social cost curves represents the difference in marginal social cost of 32 output under no control and optimal control of pollution. Incrementing these differences over all the units of output up to

Q0 gives a net reduction in social cost at that amount of output that exactly corresponds to the net benefit of pollution reduction 33 34 in Figure 5, which is designated in Figure 7, as well as in Figure 5, by the letter G. The two (lower) curves in Figure 7 are identifiable as marginal private cost curves (MPC0 and MPC*). The lower curve

(MPC0) is the supply curve under the assumption that no control cost is incurred. The higher curve (MPC*) is the supply curve under the assumption that the firm incurs the pollution control costs necessary to equate marginal damage to the marginal control cost, but does not pay any pollution tax. In other words, MPC* is the supply curve under the imposition of an ideal standard at each level of output on firms. Accordingly the difference in the heights of the two curves represents the difference between the cost of adding another unit of output when the firms do not have to control pollution and when they have to control additional pollution to the efficient degree. The area between the two MPC curves up to the output level Q0 thus represents the pollution control costs designated in this Figure 5 and Figure 7 as area E. By construction, it follows that the difference in the heights of MPC* and MSC* represents the marginal external cost when pollution is controlled to level at which marginal damage equals the marginal cost of control at every level of output. In other words, MSC*=MPC*+ME*, where ME*=(MD)w*. Accordingly, the area between MPC* and MSC* up to the output Q0 therefore represents total external cost, which is the same as total damages, remaining after efficient pollution control has taken place. In Figure 5 and in Figure 7, this area is represented by R. In Figure 8, these curves have been reproduced with the purpose being to indicate graphically the nature of the area representing the net gain from using the pollution tax in comparison with doing nothing. This is not simply the area G as previously represented, because the reasoning leading to the area

G ignored the effect of the pollution tax on output. Taking Q0 as 35 36 the market output when there is no regulation, the output that will result when there is a pollution tax will be determined by the intersection of the MSC* and demand curves. This will yield the output level labeled Q*. The overall increase in net benefits from the pollution tax will be the result of lowering the marginal social cost of producing the output Q0 and the reduction in excessive output created by the effective upward shift in the supply curve to reflect the true marginal social cost of output. This mixture of areas like G in Figure 5, and A in Figure 3, leads to the area M+J in Figure 8, where M+J includes all of the areas indicated by M or J. The net gain indicated by area M+J is larger than G because of the favorable reduction in output created by the pollution tax. Given the definitions of the curves, the net benefits of using a pollution standard approach can be calculated by recognizing that the equilibrium quantity in the market will be determined by the intersection of the MPC* and demand curves. This output is labeled

Qs and is somewhat larger than optimal because MSC* is higher than the demand price at that output. However, the relative loss from using a standard rather than a tax is not particularly large in this diagram. It amounts to the area J defined by the gap between the demand (marginal benefit) curve and the (lower) marginal social cost curve (MSC*) between the outputs Q* and Qs. All the area M (not including J) would be the net benefit of using a standard approach relative to no regulation.