ECONOMICS OF POLLUTION CONTROL

Transcription

1 The Economics of the Environment and Natural Resources R. Quentin Grafton, Wiktor Adamowicz, et al. Copyright 2004 by R. Quentin Grafton, Wiktor Adamowicz, et al. CHAPTER THREE ECONOMICS OF POLLUTION CONTROL Why does an individual pollute? Why does the Los Angeles motorist add his bit to the already smog-laden atmosphere? Why does the family on a picnic dump its litter in the park?... The individual pollutes, he creates public bad, because it is in his private, personal interest to do so. (James M. Buchanan, The Limits of Liberty: Between Anarchy and Leviathan, pp ) 3.1 INTRODUCTION Pollution comes in all shapes and sizes. For some pollutants the effects are only felt at the time of discharge and can be readily assimilated by the environment, so they are called flow pollutants. For others, their effects accumulate over time and dissipate slowly so they are termed stock pollutants. Pollution may also be described in terms of its source. Pollutants that come from an identifiable source that is mobile (such as an aircraft) or stationary (such as a smokestack) are called point sources. They are often easier to identify and control than non-point sources (such as fertilizer run-off from farms). The effects, dispersal, and location of pollutants are important in determining the appropriate method of pollution control. In some cases, the possible effects of pollutants are well understood (such as untreated sewage), while in others considerable uncertainty exists about the impacts (such as persistent organic pollutants). Some emissions quickly become uniformly dispersed while others remain highly concentrated for long periods of time (such as solid waste). Uncertainty may also exist in terms of the costs of abating or mitigating the pollution, and the benefits of reducing emissions. Whether pollution is local, regional, or crosses national boundaries, and the institutional jurisdiction where it occurs also help to determine the preferred method for its control. Given the huge variation in how, when, and where pollution occurs, different methods of pollution control have been developed for different circumstances. In

2 62 ECONOMICS OF THE ENVIRONMENT this chapter, we first explain the notion of an efficient level of pollution then describe the criteria that economists use for comparing methods of pollution control, and investigate the properties of different methods of pollution control. 3.2 AN EFFICIENT LEVEL OF POLLUTION An efficient level of pollution is defined using the concept of Pareto efficiency (see chapter 2). An outcome is efficient if it is not possible to change the allocation of assets and resources to make someone better off without making someone else worse off. An efficient level of pollution does not imply pollution is desirable. In an ideal world, we would like to produce what we need at zero cost with no pollution. Unfortunately, we live in a world where reducing or abating pollution imposes costs on polluters that use up real resources. Just as there can be too much pollution, there can also be too much pollution abatement if the benefits of reducing pollution are outweighed by its costs. Thus, for many pollutants an efficient level of pollution is positive. An efficient level of a flow pollutant exists when the marginal benefits of pollution control exactly equal the marginal costs of reducing or abating pollution, and is defined as some fixed level of emissions per unit of time. By contrast, the efficient level of pollution for a stock pollutant is not, in general, fixed but is rather a function whose values will change over time. The efficient level of pollution for a flow pollutant, illustrated in figure 3.1, is the point where the marginal cost associated with pollution reduction or abatement exactly equals the marginal benefit of abatement. The marginal benefit represents the reduction in the marginal external costs associated with pollution. For example, a factory may pollute a river, imposing costs on users of the water downstream. The increased costs imposed on downstream users is a negative externality (see chapter 2), and represents expenses external to the factory that negatively affect the utility or production functions of others. Reductions in the discharges by the factory into the river that reduce these downstream costs represent the benefit of abatement. The cost of abatement represents the expenditures incurred by the polluter in reducing its discharges. The possibility also exists that the marginal external cost is greater than the marginal cost of abatement, whatever the level of pollution. In such a situation, the marginal external cost curve would be greater than the marginal cost of abatement for all levels of pollution, so that a zero level of pollution is efficient. The curvatures of the marginal cost of abatement and marginal external cost curves can vary enormously depending on the pollutant and industry. In general, marginal costs of abatement are not smooth or differentiable and may be relatively flat over a range of pollution. However, increasing abatement will often increase costs of pollution reduction. For the first units of pollution reduction a firm may simply employ a relatively cheap end-of-pipe treatment, but as more and

3 ECONOMICS OF POLLUTION CONTROL 63 $ Marginal cost of abatement Marginal benefit of abatement = marginal external cost p* Efficient level of pollution Abatement q* Quantity of pollution Figure 3.1 An efficient level of pollution more units of pollution are reduced a completely new production system may be required at very high cost. For some pollutants low levels of discharge may be tolerated quite easily (such as noise pollution), but at higher and higher levels the cost they impose may increase at an increasing rate. Indeed, beyond a threshold, prolonged exposure to noise pollution at very high decibel levels may even cause death. 3.3 COMPARING METHODS OF POLLUTION CONTROL The objective of an efficient level of pollution is almost never attainable, because we do not have the information to know the marginal cost of abatement or the marginal external cost of all pollution sources. An achievable goal is to ensure that the method of pollution control is cost-effective. In other words, a given amount of pollution reduction or abatement occurs at least cost. Using only this criterion, methods of pollution control that give polluters the flexibility to adjust their production and level of emissions in response to a pollution price (such as a market price of permits (see chapter 2) or charge per unit of emissions) will, in general, be preferred over regulatory methods that impose a maximum and uniform level of emissions. In the former case, polluters will equate their marginal cost of abatement with the price of pollution. If marginal costs of abatement are increasing and polluters cannot influence the price of emissions, a polluter has an incentive to increase its emissions (reduce its abatement) if its marginal cost of abatement is greater than the pollution price.

4 64 ECONOMICS OF THE ENVIRONMENT $ $ Marginal cost of abatement (MCA 1 ) Price of emissions to polluters Marginal cost of abatement (MCA 2 ) B A e * 1 Emissions e * 2 (polluter 1) e 1 ~ e 2 ~ Emissions (polluter 2) Figure 3.2 Cost-effective pollution control with heterogeneous polluters The concept of efficiency can be seen in figure 3.2. For polluter 2, the marginal cost of abatement exceeds the pollution price when it discharges e 2 ~ units of emissions. Thus if polluter 2 were to increase its emissions from, say, e 2 ~ to e * 2, the extra cost from increasing emissions would be the area beneath the price line and the horizontal axis between e 2 ~ to e * 2. This can be compared to the reduced abatement cost represented by the area beneath the MCA 2 curve and the horizontal axis between e 2 ~ and e * 2. The net gain or net cost reduction to polluter 2 is given by the triangular area A. Conversely, if the marginal cost of abatement of a firm is less than the pollution price, the firm has an incentive to reduce its emissions (increase its abatement). For example, for polluter 1 in figure 3.2, the net gain or net reduction in costs in reducing emissions from, say, e 1 ~ to e * 1 is the triangular area B. Thus provided that all polluters face the same price and their abatement cost curves are smooth, the marginal costs of abatement are equalized and emissions are controlled in a cost-effective way. Polluters will minimize costs of pollution control by equating their marginal cost of abatement to the price of emissions. For polluters one and two, respectively, this point in figure 3.2 is shown by e * 1 and e * 2, where e * 1 e * 2. Thus if polluters marginal abatement costs differ, the cost-effective level of emissions will, in general, vary across polluters. By contrast, a uniform maximum level of emissions will not, in general, ensure least cost pollution abatement with heterogeneous polluters. This is because with heterogeneous polluters identical emissions results in different marginal costs of abatement. This is also shown in figure 3.2 for the level of emissions e 1 ~ and e 2 ~ where e 1 ~ e 2 ~, but MCA 1 MCA 2. Identical emissions with heterogeneous polluters implies that the combined cost of abatement would be less if the polluter with the lower marginal cost of abatement reduced its emissions by a marginal amount and the polluter with the higher marginal cost of abatement increased its emissions by the corresponding amount. Other definitions of efficiency also exist and have also been used to compare methods of pollution control. For example, dynamic efficiency, in this context, refers

5 ECONOMICS OF POLLUTION CONTROL 65 to the ability of a method of pollution control to provide on-going incentives over time to polluters to further reduce their emissions or discharges. A related notion in terms of the dynamic effects of the method of pollution is how flexible is the method of pollution control to changes in circumstances. For example, a method of pollution control that automatically adjusts the price of pollution based on market forces is flexible. By contrast, a method of pollution control that requires a regulatory review (with appeals) to be changed is not. The term economic efficiency refers to a situation where a firm is both producing maximum output for given level of inputs (technical efficiency) and is using its inputs in a way that minimizes costs for a given level of output (allocative efficiency). Thus economic efficiency commonly refers to how efficient firms are in terms of their overall production and output decisions. Thus it is possible for a firm to be efficient in its pollution abatement, such that the marginal cost of abatement equals the marginal external cost, and still be economically inefficient in the sense that it may not be using the least-cost mix of inputs in its production process. Although economists place a great deal of attention on efficiency, other criteria are also important in choosing between different methods of pollution control. The notion of equity refers to who bears the costs and who enjoys the benefits of pollution control. For instance, some people have argued that it is inequitable for those causing the pollution not to pay at least some of the cost of reducing emissions. This notion of equity is encompassed in the polluter pays concept that states that those who pollute should be the ones to bear the costs of abatement and remedial actions (Pezzey, 1988). Another criterion to evaluate different methods of pollution control is institution costs. Some methods are expensive to set up and ensure adequate monitoring and enforcement. Depending on the institutional setting, these costs may be unaffordable in some jurisdictions and in others the capabilities of the institutions to adequately monitor and enforce emissions may be lacking. Thus, a method of pollution control that may be preferred in, say, the United States, may be inappropriate in a poor country with poorly functioning public institutions. 3.4 COMMAND-AND-CONTROL METHODS Command-and-control methods of pollution control refer to a wide range of approaches that impose regulatory standards: standards for maximum permissible emissions, standards for the technology that can be used in a production process, or other controls that might specify the use of inputs and outputs and location of pollution generating activities. As with any method of pollution control, command-and-control approaches require monitoring of polluter behavior, and the use of fines or other sanctions for polluters not in compliance. Command-and-control methods are particularly useful for location and planning decisions. For example, regulations that separate activities that generate pollution from other activities hindered by emissions are highly desirable. In

6 66 ECONOMICS OF THE ENVIRONMENT many situations zoning decisions satisfy the maxim an ounce of prevention is better than a pound of cure. For instance, a zoning regulation that prevents industrial activity in residential suburbs is a low-cost way of avoiding potentially large negative externalities. Similarly, for some pollutants with threshold effects and very high external costs (highly radioactive wastes), stringent regulations as to where they may be stored or processed can help prevent major environmental costs. In this sense, a rigid control or standard with monitoring and penalties for non-compliance may be preferred to alternative approaches. Command-and-control approaches also offer a means to address non-point sources of pollution where alternative approaches developed for point sources may be difficult to apply. For example, detecting the source of some pesticides and insecticides can be problematic. Thus, regulations that prohibit or restrict how and when they are used may be the preferred method for their control. Another advantage with command-and-control approaches is that by fixing a maximum permissible level of emissions, they are often the first tier of regulation for transboundary or global pollutants. For example, under the 1997 Kyoto Protocol, most rich countries (a notable exception is the United States) have agreed to reduce their emissions of greenhouse gases (GHGs). Thus a national commitment to not emit beyond a fixed quantity of GHGs is a type of command and control, although it does not prevent a country from using other approaches, such as a carbon tax, as a second-tier instrument within its borders to reduce the cost of meeting the abatement target. Such a combination of instruments can help ensure standards are achieved in a cost-effective way (Baumol and Oates, 1971). In a world of perfect information and zero transactions costs, standards could be set differentially to ensure Pareto efficiency, by making the marginal external costs of each emission source equal its marginal abatement cost. Unfortunately, such information is almost never available. Thus uniform regulations are often imposed for a whole industry or vintage of equipment. Where there exist differences in the marginal costs of abatement among pollution sources, uniformity of emissions ensures the costs of pollution abatement are not minimized and the approach is not costeffective. This can be shown for n pollution sources where each source has a maximum and identical permissible level of emissions of e ~, and the total cost of pollution abatement for a firm i is c i (e i ) and this is decreasing in the level of emissions, i.e., c i (e i ) 0. In this case, a uniform standard is a least-cost method of pollution control if and only if all pollution sources have the identical marginal costs of abatement for the same level of emissions, i.e., c 1 (e ~ ) c 2 (e ~ )... c n (e ~ ). The greater the heterogeneity in the marginal costs of abatement of pollution sources for a given level of pollution, the larger is the difference between the least-cost abatement and the cost of pollution control with a uniform standard. In a summary table of 20 different studies that compares the least-cost with the command-and-control costs of abatement for air pollution, the US Environmental Protection Agency (2001) finds that the ratio of command-and-control costs to a least-cost method of control ranges from 1.07 (sulfates emissions in Los Angeles) to 22 (particulate matter in the lower Delaware valley). In the same summary

7 ECONOMICS OF POLLUTION CONTROL 67 table, a total of eight studies had estimated ratios of command-and-control costs to the least-cost alternatives of between 1.1 and 2.0. Some of the most important emission standards, in terms of air pollution, have been those imposed on US automobile manufacturers (see box 3.1). For a variety BOX 3.1 US AUTOMOBILE EMISSION STANDARDS Starting in 1965 with the first amendments to the US Clean Air Act, uniform national emission standards were introduced (starting with model year 1968) for new cars to control carbon monoxide and hydrocarbon emissions. In 1970 much more stringent emissions standards (90 percent reduction in carbon monoxide from 1970 levels) were enacted for new cars beginning in To help automobile manufacturers, extensions to the deadlines were subsequently permitted until the early 1980s. The standards were designed to achieve ambient standards in the worst urban air quality areas (Los Angeles) based on air quality measures in Standards were also imposed on all new vehicles in 1984 for high altitude driving to help address air pollution in low air quality areas such as Denver. In 1990, further more stringent standards were imposed on all new vehicles. Regulations were also introduced on fuel including the banning of lead additives after 1995 and the use of reformulated (cleaner burning) fuels in areas where air quality standards had not been met. In addition, in areas where air quality standards have not been achieved, all operators with ten or more vehicles will eventually be obliged to use clean fuel vehicles with very low emissions for a range of pollutants. Notwithstanding these national standards, California has implemented even more stringent standards for vehicles sold in the state. Emission standards have been highly successful at reducing the total national emissions of various pollutants from gas or petrol vehicles. For example, in 1970 total lead tail-pipe emissions from vehicles was almost 172,000 tons, but by 1996 the amounts were negligible. Total gasoline-powered vehicle emissions of particulate matter, carbon monoxide, and volatile organic compounds declined to 34 percent, 65 percent, and 45 percent of their levels in 1970 by 1995, despite a large increase in the total number of vehicles on the road over the period. The emissions standards have raised the cost of new vehicles and led to a rebound effect whereby households now own their cars for longer than they used to, which has reduced the expected reductions in emissions. The costs, and especially the benefits, associated with the vehicle emission standards are very difficult to determine. Nevertheless, several cost benefit studies have been undertaken that indicate that the costs of achieving automobile emissions standards may have exceeded the benefits. In part, this is because national standards that are used to ensure a minimum level of air quality in polluted locations, such as Los Angeles or Denver, impose significant costs on the purchasers of new vehicles who live in areas that enjoy good air quality and where such high emission standards are unnecessary. Sources: Callan and Thomas (2000); Crandall et al. (1982); Tietenberg (1996)

8 68 ECONOMICS OF THE ENVIRONMENT of reasons, and in particular where high costs are associated with achieving emission standards, regulators have opted for technology-based standards. Such standards often impose a level of technology on new or modified pollution sources that leads to lower level of emissions than the average across all emitting sources. If only imposed on new pollution sources they often provide a competitive advantage to older or existing (and often higher polluting) sources. A possible justification for technology standards is that if the costs of installing the required technology are relatively low at the time of construction, the associated costs of pollution abatement will also be relatively small. The problem with technology standards is that they often only indirectly control the pollutant, and do not allow polluters to determine themselves the least-cost way to achieve a given level of emissions. This lack of flexibility can impose significant costs on polluters and society. For example, a 1979 revision in the US standards governing sulfur dioxide emissions from coal and oil electric utilities eventually forced all sources to install scrubbers to help remove sulfur dioxide, irrespective of the sulfur content of the fuel used by the utilities. Perl and Dunbar (1982) estimate that the net benefit of this particular technology standard, in 1980 dollars, was negative $2.94 billion. In addition, imposing a particular technology on pollution sources, rather than a technology with a particular level of performance, may be distortionary and bias the use of certain factors of production (such as capital) over others (such as labor). Finally, both emission and technology-based standards are dynamically inefficient in the sense that unless standards become progressively more stringent over time, they provide no on-going incentive for further pollution control. 3.5 POLLUTION CHARGES AND SUBSIDIES One way to control pollution is to levy a charge per unit of emissions or pay a subsidy per unit of emissions abated, either of which creates an incentive for polluters to consider the costs that their emissions impose on others. Before we evaluate the economics of emissions charges and subsidies we first note two reasons why these instruments may not be ideal. First, while they offer theoretical advantages, high monitoring and enforcement costs may make an alternative instrument preferred. For example, if the level of emissions is closely related to the use of inputs (such as the carbon or sulfur content of coal, oil, or gas) or the output (solid waste), it may sometimes be easier to impose the charge on something other than the emissions themselves. This is particularly true in the case of mobile pollution sources (such as cars) where the costs of monitoring and enforcing a tax on the fuel used in vehicles is likely to be several orders of magnitude cheaper, on a national basis, than those of charging for the exhaust pipe emissions for each vehicle. For this reason, fuel taxes have been adopted by several nations to help address the externalities associated with vehicle use.

9 ECONOMICS OF POLLUTION CONTROL 69 Another potential problem with emissions charges arises when the timing and the location of the emissions affects the external costs of the pollution. For instance, GHGs rapidly and uniformly disperse such that where and when the emissions occur have no impact on their effect on the environment. By contrast, for some pollutants (such as smoke and whether it occurs upwind or downwind of a community), the timing and location of the pollution affects the external costs it imposes on others. In such situations, a uniform charge on the smoke emitted by polluters will not result in an efficient outcome. This is because each pollution source imposes a different external cost that cannot be resolved by a uniform price on all pollution sources. Implementing a charge that differs according to the marginal external costs of emissions by source requires a degree of information that almost never exists. The next best alternative is to impose a charge based on ambient measures of the emissions at defined receptor points. In other words, measure the effect of the pollution source by measuring its impact on air or water quality and defined locations. Unfortunately, the information required to implement ambient-based charges renders them difficult to implement in many cases. Thus, often for practical reasons, charges are frequently based on the level of emissions or related outputs and inputs rather than directly on the effects of emissions. Many examples of such charges exist. For instance, in Germany and the Netherlands charges especially for discharges into water bodies are an important method of controlling water pollution. Provided that charges are set at the appropriate level, they can be highly effective at addressing the externalities associated with pollution in a cost-effective way. Emissions charges on flow pollutants Pollution charges and subsidies that are imposed directly on the level of emissions are often called Pigouvian taxes and subsidies, after the economist A. C. Pigou, who argued in the 1920s for their use as a means to rectify pollution that arises from market failures. The simplest way to represent an emissions charge or subsidy (Mumy, 1980) is as follows: (e i ē i ) (1) where is the charge per unit of emissions by polluter i, e i is the emissions of polluter i over the specified time period and ē i is the baseline level of emissions assigned to firm i that allows us to model both charges and subsidies. If e i ē i then the polluter pays a charge per unit of emissions in excess of the baseline level of emissions, and if ē i 0 the amount of tax paid equals e i. By contrast, if e i ē i, the polluter receives a per-emission unit subsidy for abatement below the emissions baseline.

10 70 ECONOMICS OF THE ENVIRONMENT If we examine the case with no emissions baseline where ē i 0, a cost-minimizing polluter will choose its level of emissions to solve the following problem, Min c i (e i ) e i (2) where c i (e i ) is the total cost of abating or reducing emissions and, as before, is decreasing in the level of emissions, i.e., c i (e i ) 0. Thus a necessary condition for a cost minimization by the polluter is c i (e i ). (3) Provided that all pollution sources face the same charge per unit of emissions ( ), all polluters will have the identical marginal cost of abatement despite the fact that, in general, their emissions will differ. Such a result ensures that the emission charge is cost effective. In other words, no pollution source has a lower marginal cost of abatement than any other, and for a given total level of pollution and technology, abatement occurs at least cost. The least-cost outcome, however, will be efficient if and only if the emissions charge per unit of emissions ( ) equals the marginal external cost of emissions at the efficient level of emissions for all sources. To illustrate, the efficient level of emissions is found by solving the following minimization problem. Min n i 1 c i (e i ) D( n where D n i 1 e i is the external cost associated with the flow of uniformly mixed emissions from all sources and is increasing in emissions, i.e., D ( n e i 1 i) 0. Thus a necessary condition for the efficient outcome is, i 1 e i ) (4) c i (e i ) D ( n i 1 e i ) i (5) It follows, therefore, that for an emission charge tax to yield the efficient outcome, the marginal external cost of emissions must be identical for all sources and be equal to the marginal abatement cost of each source. For a uniform emissions charge this outcome will only arise under special conditions such as when the per unit emissions charge equals the marginal external cost of emissions which is a constant and the same for all sources. Thus the greater the heterogeneity in the marginal external cost of emissions imposed by polluters, the further away will the emissions charge be from the efficient outcome if all polluters face the same tax per unit of emissions. Emissions charges on stock pollutants The appropriate emissions charge is more difficult to derive for a stock pollutant because emissions today impose an external cost in the future. The easiest way to

11 ECONOMICS OF POLLUTION CONTROL 71 show how to calculate the efficient emissions charge for a stock pollutant is to set up a two-period problem where there is no abatement and the pollutant stock is directly related to the firm s output. The efficient level of pollution is the solution to the following problem: Subject to: Max (px 1 c(x 1 ) g(a 1 )) (px 2 c(x 2 ) g(a 2 ) ) (6) a 2 a 1 x 1 (7) a 3 a 2 x 2 (8) a 1 ā 1, a 3 ā 3 (9) where p is the price per unit of output for the polluter in both periods, x t is polluter output in period t, c(x t ) is the firm s private costs in period t, g(a t ) is the external cost from the stock pollutant in period t, a t is the quantity of the stock pollutant in period t and is measured in the same units as x t, (0, 1) is the factor by which the pollutant stock decays from one period to the next, and there is no time discounting. The corresponding Lagrangian function is, Max L (px 1 c(x 1 ) g(ā 1 )) (px 2 c(x 2 ) g( ā 1 x 1 )) (ā 3 ( ā 1 x 1 ) x 2 ) and the necessary conditions for a maximum are, L/ x 1 0 p c (x 1 ) g ( ā 1 x 1 ) (10) L/ x 2 0 p c (x 2 ) (11) L/ 0 ā 3 ( ā 1 x 1 ) x 2 0 (12) Conditions (10) and (11) require that the marginal net return from production (including the costs imposed on others) equal the shadow price of the stock pollution. To simplify the necessary conditions and to derive a numerical result we assume that p 5, c(x t ) x t 2, g(a t ) a t, 0.5, ā 1 0 and ā Thus, (10), (11) and (12) become 5 2 x (10) 5 2 x 2 (11) x 1 x 2 0 (12) Using (10) and (11) to obtain an expression for x 1 in terms of x 2 and substituting this expression into (12) we obtain the efficient level of output in periods one and two, the value of the Lagrangian multiplier and the terminal value of the stock pollutant, i.e., (x 1 *, x 2 *, *, a 2 * ) (1, 0.5, 4, 1).

12 72 ECONOMICS OF THE ENVIRONMENT This problem could also be solved using dynamic programming that uses an algorithm to solve problems in discrete time (see chapter 1, section 1.5). In this method, the output of the pollution source is the decision or control variable and the value of the stock pollutant is the state variable. The approach is to write a functional recurrence equation that enables us to work backwards in time and solve for outputs and values of the stock pollutant, i.e., Subject to: V t (a t ) max x(t) [5x t x t 2 a t V t 1 (a t 1 )] (13) a t a t x t (14) where V t (a t ) is the return function and is the maximum value for (6) at time t, given the value of the stock pollutant a t and (14) is the transition equation that determines the value of the next period s state variable. The functional recurrence equation when t 2 is Subject to: V 2 (a 2 ) max [5x 2 x 2 2 a 2 V 3 (a 3 )] (15) a 3 0.5a 2 x 2 (16) a 3 1 (17) where V 3 (a 3 ) has the value of zero as it is the value of the return function after the end of the program or optimization period. Combining the constraints (16) and (17) we can obtain an expression for x 2 in terms of a 2 that we can use to rewrite the functional recurrence equation solely in terms of a 2, i.e., V 2 (a 2 ) 5(1 0.5 a 2 ) (1 0.5 a 2 ) 2 a 2 (18) The next step is to write the functional recurrence equation for the previous period, t 1, i.e., Subject to: V 1 (a 1 ) max [5x 1 x 1 2 a 1 V 2 (a 2 )] (19) a 2 0.5a 1 x 1 (20) a 1 0 (21) We can substitute in the previously found return function V 2 (a 2 ) and then use (20) to obtain an expression for (21) solely in terms of a 1 and x 1, i.e., V 1 (a 1 ) max [5x 1 x 1 2 a (0.5a 1 x 1 ) (1 0.5(0.5a 1 x 1 )) 2 0.5a 1 x 1 ]

13 ECONOMICS OF POLLUTION CONTROL 73 The necessary condition for a maximum requires that, V 1 (a 1 )/ x 1 5 2x (1 0.5(0.5a 1 x 1 )) 1 0 This implies that a necessary condition for the return function at t 1 to be at a maximum is, x 1 * a 1 (22) Given that a 1 0, then from (22), (20), and (16) we can obtain (x 1 *, x 2 *, a 2 *) (1, 0.5, 1) which is identical to the result found by using the method of Lagrange. By contrast to the efficient level of output in periods t 1 and 2, the pollution source would maximize its profits by ignoring the stock externality and setting its profit maximizing output to (x 1 ~, x 2 ~ ) (2.5, 2.5). In this particular case, there is a one-to-one correspondence between the firm s output and its contribution to the stock pollutant. Thus a tax on the output is identical to a tax on the source s emissions. The tax on the firms output in period 1 ( 1 ) and in period 2 ( 2 ) to achieve the efficient output level can be calculated by solving the polluter s first-order condition, but including the tax on the output for each period, i.e., 5 2x t * t 0 where if (x 1 *, x 2 *) (1, 0.5) then ( 1, 2 ) (3, 4). As we might expect, the tax rate that is applied to the firm s output is different for the two periods. The efficient tax in the second period obliges the polluter to pay $4 per unit of output produced in the second period. This cost per unit is the negative of the value of the Lagrangian multiplier or co-state variable found previously when we solved for the efficient level of pollution. This is no coincidence. In general, the tax rate to arrive at an efficient level of emissions per time period should equal the negative (a tax is a cost) of the shadow price or shadow cost of the dynamic constraint that transforms the current period s stock pollutant and the current period s decision into the next period s stock pollutant. In the case where emissions generate both stock and flow externalities, the optimal tax will exceed the shadow cost of pollution. Moreover, setting the tax at too low a level in the presence of a stock externality or ignoring the flow externality can have effects on both transitory and steady-state output, emissions and tax payments (Sandal et al., 2003). Other features of emissions charges In addition to being cost-effective, emissions charges can be described as dynamically efficient in the sense that they provide an on-going incentive to polluters to reduce their pollution. Of course, if the per-unit charge is set at too high a level, the incentive may be such that the level of abatement will exceed the efficient

14 74 ECONOMICS OF THE ENVIRONMENT level. In general, however, the opposite is true and emission charges are at set at too low a level and thus do not provide an effective incentive to polluters. Indeed, considerable evidence exists that in some jurisdictions, such as China, the pollution charges imposed are many times below what the efficient level should be. Despite the relatively low level of charges in China, they have been responsible for ensuring that China s industrial pollution is far less serious than it would have been without the levies (World Bank, 1999, p. 46). Another advantage of charges is, to the extent that innovation in reducing emissions is induced by economic incentives, emission charges can spur technological developments in reducing the emissions per unit of output. This notion, in its most optimistic form, is known as the Porter hypothesis (Porter and van der Linde, 1995), and suggests that pollution control may even lead to unanticipated technological innovations that may reduce overall production costs, thereby reducing both pollution and total costs. Although serendipitous and unanticipated cost-saving innovations due to pollution controls are possible at a firm level, it seems unlikely that a free lunch of such a magnitude is available on an economy-wide basis (see chapter 10). Pollution charges that tax bads also generate revenue that can be used to reduce taxes (such as payroll taxes or income taxes) which can have a negative impact on economic activity. The distortions from traditional taxes that arise from a reallocation of resources can be large, and in the US range from $ per dollar for payroll tax raised and between $ per dollar of income tax raised (Morgenstern, 1995). Thus emission charges, and environmental taxes in general, offer the possibility of a double dividend whereby environmental quality can improve while at the same time increasing incentives to work (by reducing marginal income tax rates or payroll taxes) and raising productivity. To what extent a double-dividend exists, and at what level should the environmental tax be set at relative to the social marginal damages of pollution, has provoked a heated debate among economists (Goulder, 1997; Jaeger, 2001). Although most agree that simultaneously reducing tax distortions and correcting environmental externalities can be welfare enhancing, there has been a lively discussion as to the appropriate level to set pollution charges in a second-best world and whether they should be higher or lower than the marginal external cost of pollution. The answer depends, in part, on the potential distortions from environmental taxes, especially if they are levied indirectly on outputs or inputs rather than directly on emissions, and the distortions imposed by the taxes they replace. As with any switch from one form of taxation to another, some people will pay more and some will pay less and thus the distributional outcomes with such changes are an important policy consideration. Emission charges also suffer from some limitations. First, introducing or increasing existing taxes can be politically difficult. Second, in a dynamic world where technologies change rapidly or the overall price level increases at a fast rate, a fixed per unit Pigouvian tax may soon become ineffective. Third, a uniform Pigouvian tax applied to all polluters where there exist large differences in the marginal

15 ECONOMICS OF POLLUTION CONTROL 75 $ Marginal external cost t* t' Marginal abatement cost e* Emissions e' Figure 3.3 Potential error from an emissions charge under uncertainty external costs per unit of emissions is likely to underprice pollution for some sources and overprice pollution for other sources. In turn, this could result in pollution hotspots in some locations, and more abatement than is desirable in others. Fourth, taxes are a price instrument and only indirectly control the level of pollution. In a world where a regulator has a good knowledge of the costs of pollution abatement this may pose only a small problem, but where such information is lacking the possibility exists that the tax will be set at too high or too low a level resulting in an undesirable level of pollution. Depending on the shape and level of uncertainty of the marginal cost of abatement and marginal external cost curves, it may be preferable to use a quantity instrument that controls the level of emissions directly. This potential problem of an emissions charge, in a world of uncertainty, is illustrated in figure 3.3. The efficient tax should be set at t* yielding an efficient level of emissions of e*. However, in an uncertain world a relatively small error in setting the tax at t leads to a much larger level of emissions than is desired, represented by the distance e* to e. Weitzman (1974) was the first to show that when setting a tax in a world of uncertainty, the magnitude of the difference between the actual and desired emissions level will be greater the steeper is the marginal external cost curve and the more gently sloped is the marginal cost of abatement curve. In such situations and where uncertainty exists over the slopes of the marginal cost of abatement and marginal external cost curves, it may be better to use a quantity instrument that directly controls the level of emissions than a price instrument (such as a tax) that only does so indirectly. In reference to the type of cases illustrated by figure 3.3, and under uncertainty, Weitzman observes, it is hard to avoid the impression that there will be many circumstances where the more conservative

16 76 ECONOMICS OF THE ENVIRONMENT quantity mode will be preferred by planners because it is better for avoiding very bad planning mistakes (Weitzman, 1974, p. 486). More recently, Stavins (1996) has shown that if the marginal external cost and marginal abatement costs are positively correlated, in a world of uncertainty, this will also tend to favor quantity instruments over price instruments. An alternative to a pollution charge is to combine a charge with a standard. In this sense, the charge helps to reduce the costs of abatement while the standard ensures that pollution does not exceed critical levels. Roberts and Weitzman (1993) have proposed such an approach whereby a charge per unit of emissions is imposed in excess of a standard. For polluters with a high marginal cost of abatement the mixed instrument will operate more like a charge, but for most polluters the approach will function more like a standard. Similarly, Roberts and Spence (1976) propose combining marketable emission permits (see chapter 2) with a fee and subsidy. Polluters are allowed to emit above the number of emission permits they own, but must pay a fee per unit of emissions beyond their allowances. Polluters that emit less than the emission permits they own, receive a per unit emissions subsidy, but which is less than the charge. At the same time, polluters are free to trade permits among themselves where the subsidy is set to be equal to or less than the market price of emission permits and the charge is set equal to or greater than the permit price. For both mixed approaches, the charge acts as a pressure valve which gives polluters flexibility in deciding on their level of emissions, but only if their marginal costs of abatement are much higher than expected. Pollution subsidies Subsidies exist in many forms, and often contribute to pollution as they encourage production or the use of inputs that can lead to pollution. Pollution subsidies, however, represent direct payments to polluters for reducing their level of emissions. These subsidies can come in one of two main forms. The subsidy could represent a payment or co-payment for the purchase of capital equipment that reduces emissions by polluter. Alternatively, the subsidy, as shown in equation (1), could represent a payment per unit of emission for reductions in the level of emissions below a defined benchmark (ē i ). Both emissions and capital or investment subsidies have potential problems. The most practical difficulty in subsidizing polluters with emissions subsidies is that it is politically unpopular to do although capital or investment subsidies for pollution abatement are widely employed. If the government or regulator does not wish to create or enlarge a fiscal deficit, a subsidy also requires that other sectors of the economy be taxed to pay for subsidy payments to polluters. Beyond these practical difficulties, capital or investment subsidies for emissions reduction equipment will be cost-effective if and only if the subsidized equipment reduces emissions at least cost for all polluters and the marginal costs of abatement are

17 ECONOMICS OF POLLUTION CONTROL 77 identical for all polluters. Given heterogeneous polluters, investment subsidies for abatement will not, in general, be cost effective. The potential problem with an emissions subsidy, or subsidy per unit of emissions abated, is that if the subsidy is paid to any polluter operating in an industry, it might encourage entry of additional firms and may possibly increase total emissions, even if emissions per polluter declines. In other words, provided that a polluter s benchmark emissions exceed its current emissions (ē i e i ), additional entrants may be attracted by the subsidy, thus increasing total emissions over what is desired. A way to overcome this entry incentive problem is to create a property right over the payment of the subsidy to the polluter. In this situation, only existing polluters at the introduction of the emissions subsidy receive the emissions benchmark or allowance of ē i, and any new entrant i receives a zero allowance and faces an emissions charge of e i (Pezzey, 1992). Provided that polluters receive the subsidy ē i when it exits or shuts down, the economic profit per time period of an existing polluter i that chooses not to exit is, i pq i c(q i, e i ) (e i ē i ) ē i where the last term, ē i, is the opportunity cost incurred by the polluter when it chooses to not exit, and equals the payment it would receive if it were to shut down. In this case, the emissions subsidy is identical to an emissions charge in both its short and long-run effects. Moreover, with perfect information it is theoretically possible to set the baseline emissions (ē i ) for the polluters so that some pay an emissions charge while other are subsidized to reduce emissions and, overall, the scheme is revenue-neutral. 3.6 MARKETABLE EMISSION PERMITS A marketable or tradable emission permit is a license to emit a certain quantity of a pollutant, where the licence can be bought or sold among polluters and third parties. They were proposed as a method of pollution control in the 1960s (Dales, 1968), but it was not until the 1970s that marketable emission permits were first used. Marketable permits can also be denominated in terms of ambient measures of environmental quality for defined sites or receptors. Thus, instead of regulating the emissions of polluters, ambient permits regulate the effects of emissions. Whenever the external effects per unit of emissions differs across sources, ambient permits offer an advantage over emissions permits by providing a better price signal to polluters in terms of the costs they impose on others. The major problem with implementing ambient permits, and why they are not used in practice, is the difficulty in tracing the ambient effects to particular sources, and the transactions costs of trading where there are many sources and multiple receptors. We will focus our attention on marketable emissions permits. They have been employed or are currently used in a number of different countries including the

18 78 ECONOMICS OF THE ENVIRONMENT European Union (ozone depleting substances), Chile (particulate matter), Canada (pilot programs for volatile organic compounds and nitrogen oxides), and the USA, especially for air pollutants (Stavins, 2001a). Such programs are a subset of what may be described as market-based rights that involve the use of tradable quantity instruments to regulate a variety of environmental problems (see chapter 2). By far the most important marketable emission permit schemes, in terms of their effect and scope, have been in the USA and most have been developed to improve air quality. The broad types are credit programs whereby polluters receive tradable emission credits for any reductions in their emissions below an admissible standard and so-called cap-and-trade programs where an overall cap or total level of emissions is set by a regulator and sources trade among themselves. The US emission credit programs grew out of offsets instituted by the US Environmental Protection Agency (EPA) designed to ensure new sources of air pollution in areas with less than acceptable air quality both installed technology that had the lowest achievable emission rate, and offset their emissions by reducing emissions from existing sources by a greater amount. The scheme has led to more than 10,000 trades in offsets worth about $2 billion (USEPA, 2001). Most of these trades have involved firms shutting down their own existing sources to build new plants. The offset program contributed to the emergence of emissions reductions credits (ERCs) following 1977 amendments to the US Clean Air Act. The ERCs are administered by states. They are created when a source reduces its emissions below its permitted level, and the state certifies the reduction is permanent and is not required by the state under any other existing regulations. ERCs can be banked for a limited period of time and can be traded among sources. Despite the existence of ERCs, the number of trades has been much less than expected in many states. This is explained by limitations and restrictions imposed by some states on trading of ERCs across geographical areas, an administrative reduction in some states of the ERCs available for sale after a source banks its credits so as to reduce overall emissions, and relatively high offset ratios. Combined, these restrictions have raised the transactions or institution costs (see chapter 2) of trading ERCs and reduced the amount traded. The development of ERCs on a state level has spurred further use of marketable emission permits. One of the most developed state programs is the Regional Clean Air Incentives Market (RECLAIM) in the Los Angeles area. The program began in 1994 with the creation of RECLAIM Trading Credits (RTCs) for nitrogen oxides and sulfur oxides for most stationary sources in the designated area. For each source, the allocated RTCs are scheduled to decline each year until 2003 to improve overall environmental quality. Trades worth over $2 million took place in 1994, and were worth $21 million in 1997 with prices for nitrogen oxides and sulfur oxides averaging $227 and $64 per ton (USEPA, 2001). Other air emissions trading programs also exist on a state basis and have been developed for effluent discharged into water bodies. Unlike their counterparts in terms of air emissions, effluent programs have generated far fewer trades especially in one of the earliest

19 ECONOMICS OF POLLUTION CONTROL 79 schemes on the Fox River in Wisconsin due to high transactions costs from trading (Devlin and Grafton, 1999). On a federal level in the US, trading schemes were established in the phase-out of CFCs and lead in gasoline. In the case of CFCs, a marketable emission permit scheme was implemented for producers and importers. Lead tradable credits were allocated to refiners, importers, and blenders of ethanol. The savings associated with these permit schemes, relative to command-and-control approaches, amounted to over $300 million for the CFCs program and over $200 million for the lead program (USEPA, 2001). By far the most important marketable emissions trading scheme anywhere in the world is for sulfur dioxide for US fossil-fueled electric utilities (see box 3.2). The principle behind marketable emission permits is that each and every pollution source faces the same price for their emissions and that the permits represent a durable and exclusive property right (see chapter 2). If markets are competitive and transactions costs are low, a market price per unit of emissions provides an economic signal to polluters similar to an emissions charge. Namely, if a polluter s marginal cost of abatement is less than the market price of emissions it pays the polluter to abate and sell the excess permits it no longer needs. Conversely, if a polluter s marginal abatement cost exceeds the market price of emissions it pays to buy permits and reduce the level of abatement. Thus the marginal cost of abatement is equalized across all sources, ensuring a cost-effective method of pollution control. To illustrate, in the absence of uncertainty, but with competitive markets and zero transactions costs, each polluter will minimize the following, Subject to: Min c i (e i ) (m i t i ) (23) e i m i t i (24) where e i is the polluter s emissions, c i (e i ) is the cost of abating or reducing emissions where c i (e i ) 0, is the market price of emissions, m i is the initial allocation of emission permits to polluter i and t i is the amount of permits bought ( 0) or sold ( 0) by polluter i. Substituting the compliance constraint (24) into (23) and differentiating with respect to e i, the necessary condition for cost minimization for firm i is c i (e i ). (25) Provided that a market equilibrium exists for emission permits at the price (see chapter 2), all polluters will face the same price and the marginal cost of abatement is equalized across all sources. This is the same result we found for an emissions charge and arises whenever polluters face the same per unit price of emissions,