An emission fee levied against polluters will tend to

E M I S S I O N P R I C E S A N D F E E S

IN CHAPTERS 4 AND 5, WE SAW THAT MARKETS CANNOT BE RELIED ON TO PROVIDE THE

right amount of pollution—markets fail when it comes to public bads. Normally, consumer preferences are communicated to producers through the price system. The basic problem in the case of pollution is that without a price system, polluters do not "see" the damage caused by the pollution they emit. The simplest way to correct this lack of a signal to polluters is to establish a price for pollution. Just as the price of labor signals to a firm to conserve labor inputs, a price on pollution will signal to the firm to cut back on pollution as much as is eco- nomically feasible. The theoretical idea of placing a price on pollution is from the English economist Arthur C. Pigou and dates to the early twentieth century.1 The more practical idea of regulating pollution by charging polluters an emission fee per unit of pollution has its modern origins in the pathbreaking environmental economist, Alan Kneese, who spent virtually his entire professional career at Resources for the Future in Washington, DC.2

I. H O W D O P O L L U T E R S R E S P O N D T O E M I S S I O N F E E S ?

Before turning to how one determines how large or small an emission fee should be, it is important to understand how polluters will respond when charged a specific fee for their emissions. We first define an emission fee:

DEFINITION An emission fee is a price or fee paid by a polluter to a regulatory entity for every unit of emissions the polluter emits.

Consider a firm producing some good (for example, electricity) along with pollution, x. If the emission fee is p and the polluter emits x units of pollution, the payment from the polluter to the regulator is px. To determine how much the polluter will emit, let C(x) be the production costs associated with emitting x units of pollution, holding goods output fixed. One would expect C to decline as x increases—the polluter saves money by emitting pollution. Total costs for the firm (abatement costs and costs of the fee) are given by

TC(x) = C(x) + px (12.1)

241

242 CHAPTER 12 EMISSION PRICES AND FEES

We know something is minimized when its marginal is zero; furthermore, the marginal of a sum is the sum of the marginals (the derivative of a sum is the sum of the derivatives). Therefore, total cost in Eq. (12.1) is minimized when x is chosen so that

p = -MC(x) = MS(x) (12.2)

The interpretation of Eq. (12.2) is that the firm chooses to operate where the marginal savings from emitting one more unit of pollution (which happens to be equal to the mar- ginal cost of reducing pollution by one unit) is equal to the price of pollution. Emitting a smaller amount of pollution would involve abatement costs that are higher than the pol- lution price—lowering emissions raises total costs. Emitting a larger amount of pollution than called for in Eq. (12.2) would mean that abatement costs are lower than the emission fee; thus increasing emissions increases fee payments more rapidly than abatement costs are lowered and is also a bad idea.

Equation (12.2) indicates that when faced with an emissions fee, firms will abate pol- lution up to the point where the marginal cost of abatement (or equivalently, the marginal savings from emitting) is equal to the emissions fee. This point is where the firm's total costs are lowest.

With multiple firms, each firm will abate to the point where the marginal cost of abatement is equal to the emissions fee. Thus the equimarginal principal will automati- cally hold—each firm sets the marginal cost of abatement equal to the same number (the fee), and thus the marginal cost is the same for all firms.

This is illustrated in Figure 12.1 for two firms—Riley Wreckers and Tucker Tools. In the left-hand panel of the figure, marginal savings to the firm are shown as a function of emissions: by emitting one more unit, there is a cost savings to each of the firms. The right panel shows exactly the same thing, except from the point of view of abatement and the marginal cost of abatement. With no pollution regulations, there will be no abatement and emissions will be at the point where marginal savings is zero: £T for Tucker Tools and ER for Riley Wreckers.

to ra Dl ro z

p

— Tucker Tools

\ V<— MST

\ \ MSR

V

\ \ \ \ \ : V : \ • \

+-• o

c

A3 Z

/ /

/-<- /

/ /

/ /

S .'

-MCT

/**—MCR

ET ET ER ER Emissions AT AR

(a)

Abatement

(b)

FIGURE 12.1 Firm choice of emissions/abatement when faced with emission fee, p.

—*

Pigovian Fees 243

With an emission fee equal top, the two firms cut back on emissions (increase abate- ment) to the points £.,. and ER (respectively, A,, and AR) for the two firms. Firms operate where the marginal cost of abatement/marginal savings from pollution is exactly equal to the emissions fee.

One of the bonuses of an emissions fee is that the equimarginal principle automati- cally holds. Because the two firms face the same emission fee, they will both set their mar- ginal cost of abatement to the same number and thus marginal costs will be equalized between the two firms (or among any number of firms facing the same emissions fee).

The London Congestion Charge

One of the most successful applications of an environmental charge is the charge on automobiles in the centers of congested cities. And one of the most prominent of these is the charge in London, England. Although not a charge on emissions, the congestion charge is still a good example of the use of a tax or fee to correct an externality.

By the 1990s the speed of travel in central London was slower than it was in 1900, before the advent of the automobile. In 2002 the average daytime speed was less than 15 km/hr, compared to more than twice that speed in the less congested night time. In order to address this problem, in 2003 a charge of £5/day (raised to £8/day in 2005) was levied on all vehicles traveling or parking in central London during the day, excluding weekends and holidays. The charge is collected by voluntary payment of the charge by motorists, accompanied by enforcement using cameras and computers that read license plates. Enforcement is only 85% or so effective, yet the £100 penalty for scofflaws is sufficient for the system to work.

Although paying the charge is not popular (a similar system has been proposed for New York but has faced political opposition), a significant reduction in congestion has been achieved. Private car travel in central London is down by a third and daytime travel speeds have increased 20%.

(Source: Leape, 2006.)

P I G O V I A N F E E S

As was mentioned at the beginning of the chapter, approximately a century ago the English economist Arthur C. Pigou argued for the imposition of taxes on generators of pollution. The Pigovian fee, as it has come to be called, is a special kind of emissions fee—an emission fee that is set at the marginal damage of pollution in an attempt to restore Pareto optimality to a situation of market failure:

DEFINITION A Pigovian fee is an emission fee exactly equal to the aggregate marginal damage caused by the emissions when evaluated at the efficient level of pollution.

We examine this definition in more detail, first for the case of a single polluter and then for the case of multiple polluters. In both cases, there are multiple victims of the pollution.

244 CHAPTER 12 EMISSION PRICES AND FEES

A . A S i n g l e P o l l u t e r

Suppose we have a factory generating pollution in the amount x at a cost C(x), with marginal costs, MC(x). Since costs decline as x is increased, marginal costs are actually negative. Another way of thinking about this is in terms of marginal savings—the savings from emitting one more unit of pollution. Of course the marginal savings is the negative of the marginal costs: MS(x) = -MC(x). As in the case of an emission fee, this is exactly the same as the marginal cost of abatement.

Further assume there are N people surrounding the factory and that pollution causes damage. For the time being, assume that people cannot use locational choice to change the amount of pollution they face. Thus there is nothing a person can do to reduce his or her exposure, short of getting the factory to cut back. For person i, the damage from pollution is D.(x), which is positive and increases in x. There are several other ways of interpreting this damage. We could also say that person i benefits from the pollution in the amount B.(x) with benefits negative and decreasing in x. Or, we could say that D.(x) is the willingness to pay to eliminate the pollution. Total damages are given by

D(x)=Z.Di(x) (12.3)

The efficient amount of pollution is the amount that minimizes total costs and damages:

x* minimizes {C(x) + D(x)} (12.4a)

We know that something is minimized when its marginal is zero. Further, the marginal of a sum is equal to the sum of the marginals. Thus we can set the marginal of the quantity in braces in Eq. (12.4a) to zero:

MC(x*) + MD(x*) = 0 (12.4b)

Substituting the marginal version of Eq. (12.3) into Eq. (12.4b) and recognizing that mar- ginal savings is the negative of marginal cost, we obtain

MS(x*) = E. MD.(x*) (12.4c)

In other words, we seek a level of pollution such that the marginal savings to the firm from pollution (-MC) is equal to the marginal damage from pollution over the entire population. Since pollution is a public bad, the aggregate marginal damage (MD) is the vertical sum of the individual marginal damages (MD.).

This situation is illustrated in Figure 12.2 for the case of one polluter and two victims of the pollution. Shown in the lower half of the figure is the marginal cost of pollution. Note that this is negative since every extra unit of pollution the factory is allowed to emit lowers total costs for the factory (up to a limit of course). The marginal savings to the factory is the negative of this and is shown in the first (upper) quadrant. As the factory increases pollution from no emissions at all, savings are initially quite high. When emis- sions are relatively large, the savings from emitting a little more are much smaller. Thus MS(x) is downward sloping.

•^

MD(x)

MDy(X~) MD2(,x)

x (emissions)

Pigovian Fees 245

FIGURE 12.2 Pigovian fee on pollutant emissions with two victims of pollution. MD^x), marginal damage to victim 1; MD2(x), marginal damage to victim 2; MD(x), aggregate marginal damage; MC(x), marginal cost of emitting for the polluter; MS(x), marginal savings from emitting for the polluter; X, pollution levels with no regulation; x*, efficient amount of emissions; p*, Pigovian fee.

Also shown in Figure 12.2 are the marginal damage functions for the two victims of the pollution: MDt(x). Marginal damage is the negative of the demand function for pollution for each of the individuals. Each of the marginal damage schedules is upward sloping. When pollution levels are small, one more unit of pollution causes little damage. When pollution levels are higher, that extra unit causes more damage. Since the pollution is a public bad, aggregate marginal damage, like aggregate demand, is the vertical sum of individual marginal damages. This is also shown in the figure [MD(x)]. The optimal amount of pollution is the x for which MD(x) = MS(x), shown as x* in Figure 12.2. Also shown in Figure 12.2 is the Pigovian fee, p*. If the polluter is charged p* per unit of pollu- tion, the polluter basically sees pollution as priced at p* and thus the polluter will pollute so that price equals marginal cost:

MC(x*) =-p* or MS(x*) = p' (12.5)

The total amount of money the firm pays for the pollution is p*x*. Note that the Pigovian fee is defined as the marginal savings from pollution genera-

tion at the optimal level of pollution. If we are not at the optimum, the Pigovian fee will be neither the current marginal cost of pollution control nor the marginal damage from pollution. Thus the Pigovian fee is not any emission fee; it is the marginal savings from pollution at the optimal pollution level.

B. M u l t i p l e Pol lu ters

We have seen how a Pigovian fee can generate the efficient amount of a public bad. The case we have looked at involves a single polluter. Suppose we have more than one polluter. For the time being, assume we have two polluters. Figure 12.3 illustrates the case for two polluters in which the marginal damage function (MD) is the aggregate damage to all consumers. Shown is the marginal savings to each of two firms from generating pollution. How much pollution should each firm generate and how should the Pigovian fee be set to support that level of pollution?

An aggregate marginal savings function for a group of polluters indicates what the marginal savings will be if the total amount of pollution increases by one unit. This

246 CHAPTER 12 EMISSION PRICES AND FEES

MD(x)

FIGURE 12.3 The case of two polluters. MSX (x), marginal savings from emitting firm 1; MS2(x), marginal savings from emitting firm 2; MS(x), aggregate marginal savings from emitting; MD(x), marginal damage from emitting; p*, Pigovian fee; x*, total amount of emissions with Pigovian fee; x*, emissions from firm 1 with Pigovian fee; x*. emissions from firm 2 with Pigovian fee.

Emissions(x)

depends, of course, on what assumptions are being made about how the total amot of pollution is distributed among the individual polluters. If one polluter is doing all i the pollution control and all other polluters are doing none, the marginal savings will I higher than if the pollution control were more "evenly" distributed among the polluters. One way of avoiding this ambiguity is to assume the polluters are sharing the obligation of pollution abatement in an efficient or least-cost manner. The logical (and cost-minimizing) way of apportioning the abatement responsibility is to equate marginal cost of abatement (marginal savings of emitting) among the firms. As we saw in Chapter 4, the equimar- ginal principle calls for the equalizing of marginal costs.

Numerical Example: Suppose the two marginal savings functions in Figure 12.3 are given by:

MS{xJ = 10 - 2 x, MS2(x2) = 5-3x2

(12.6a) (12.6b)

To construct an aggregate marginal savings function, first solve each of these for emissions:

x, = (10 - MS,)/2 x2 = (5 - MS2)/3

(12.7a) (12.7b)

We now ask what is the total emissions (X = x, + x2) for any given MS? By inserting MS into Eqs (12.7) and then summing the two equations one obtains:

X = (10 - MS)/2 + (5 - MS)/3

Which, with a little manipulation, becomes

MS = 8-1.2 X

(12.8a)

(12.8b)

The exact same approach would be taken in constructing an aggregate marginal abatement cost curve.

Returning to Figure 12.3, how do we aggregate the two marginal savings functions to obtain an aggregate? The aggregate marginal savings function is found by horizontally

Fees Versus Subsidies 247

summing the marginal savings for the two firms.3 The aggregate marginal savings curve is the curve that indicates for a particular pollution price, how much pollution each firm would generate. This is the standard way of generating an industry marginal cost func- tion from firm-level marginal cost functions. Thus for any level of the fee, MS(x) tells us how much x in total will be emitted and each MS.(x) tells us how much each firm will contribute to that total. We have constructed MS(x) in such a way that the amount of pol- lution from each firm will sum to the total.

In Figure 12.3, to determine the efficient amount of pollution, we note where the marginal savings curve (MS) intersects the marginal damage curve (MD). That deter- mines the optimal amount of pollution (x*) and the marginal savings to polluters at x*: p*. Thusp* is the correct Pigovian fee. This is shown in Figure 12.3. At that fee level, firm 1 will generate x* and firm 2 will generate x*. Note that each firm operates so that mar- ginal savings from polluting is set equal to the Pigovian fee:

MSi(x*)=p*

Furthermore, by the way in which MS(x) was constructed,

(12.9)

MS(x*)=p' (12.10)

Equation (12.9) illustrates one of the primary virtues of the Pigovian fee: all firms will control pollution at the same level of marginal costs. Marginal costs of pollution control will be equated across all polluters. Firms with different pollution control costs receive the correct signals regarding how much pollution to generate. Those with high control costs will control relatively less than firms with lower control costs.

F E E S V E R S U S S U B S I D I E S

The notion that the source or cause of a pollution problem should pay for cleaning up the problem rings true to most people. In many parts of the world, it is institutionalized in the polluter pays principle. But a logical question arises: is it possible to obtain the same outcome by subsidizing firms to reduce pollution? In the "real" world, is there any danger in providing tax breaks and other subsidies for pollution control, rather than making polluters pay for the pollution they generate? Is it possible to obtain efficiency using a subsidy instead of a fee? This is an important question since subsidies are usually much more politically popular than taxes or fees.

The answer to this is that these two approaches yield different outcomes.4 The tax is efficient, whereas the subsidy can result in too many firms in the industry and thus an inefficient amount of both pollution and the good associated with the pollu- tion. We will consider two cases. The first is for the short run—there is no time for new firms to enter the industry. The second is for the long run—there is time for entry and exit (although exit in the sense of shut-down is always possible, even in the short run).

248 CHAPTER 12 EMISSION PRICES AND FEES

A . T h e S h o r t R u n

Let us consider a competitive industry, producing some good in conjunction with pollti tion. Initially, assume all of the firms in the industry are identical. Under a pollution tax (t), the production costs of a typical firm would be

CT(y,e) = V(y,e) + t e + FC (12.11)

where y is the amount of the good being produced, e is emissions, V(y,e) represents vari- able production costs for producing e and y, and FC is the fixed cost of production. To simplify things, suppose there is a fixed relation between output and emissions—the more you produce, the more you pollute. In particular, suppose emissions are related to output by e = ay where a is a constant. We can rewrite Eq. (12.11) as

C (y,ay) = V(y,ay) + tay + FC (12.12a)

Recognizing that V and CT are now functions of y only, we let TC(y) = Cfy,ay) and VC(y) = V(y,ay) and rewrite Eq. (12.12a) as

TC(y) = VC(y) + tay + FC

This means that marginal production costs are

MC(y) = MVC(y) + at

(12.12b)

(12.13)

So basically, marginal costs are increased by at. Now consider what happens with a subsidy, s. With no attention to pollution control,

a firm might pollute at the level e. With a subsidy, the firm will be paid to reduce emis- sions. If the firm reduces emissions to e, the subsidy payment will be s(e- e). This means that costs will be

TC(y) = VC(y) + FC - s(e - e)

= VC(y) + say + {FC - se)

(12.14)

Note that the term in braces is a fixed cost, consisting of the standard fixed cost plus a lump-sum transfer of se that is independent of the firm's choice of y or e. Thus the variable costs in both cases [Eqs. (12.12b) and (12.12)] are exactly the same. Only the fixed costs are different. Consequently the short-run marginal costs of production will be identical in the two cases and the firm will produce exactly the same amount of pollution and the good. In fact, the marginal costs from Eq. (12.14) are

MC(y) = MVC(y) + as (12.15)

which is exactly the same as Eq. (12.13) except we have an s here instead of a t. Consequently, our first result is that in the case of identical firms in the short run,

Pigovian fees and subsidies yield exactly the same outcome. We should note that this result applies even if there is a more complex relationship between output and emissions

Fees Versus Subsidies 249

than the fixed ratio assumed here. Showing that is more cumbersome mathematically so we omit it here.

We now turn to an industry with heterogeneous firms. This may be because of differ- ent technologies used by different firms due, for instance, to their different ages. This case is best understood graphically. Suppose we have an industry composed of two classes of firms, old firms and new firms. Newer firms may have higher fixed costs but lower vari- able costs. We are concerned with industry behavior in the short run under Pigovian fees and subsidies. Since this is the short run, no new firms may enter. Any firm may, however, choose to produce nothing, shutting down. If a firm produces nothing, the subsidy disap- pears. In other words, we only pay firms to produce less pollution. We do not continue to pay firms if they decide to go out of business.

Figure 12.4 shows the marginal cost curves and average variable costs for these two types of firms. Since this is a short-run analysis, we are not concerned with total costs. The issue is whether prices cover average variable costs and, if they do, production will be at marginal cost equals price. As we saw above, the effect of a tax on marginal cost is identical to the effect of a subsidy on marginal cost—both raise marginal costs relative to the unregulated case. The U subscripts in the figure correspond to average variable cost (AVC) and marginal cost (MC) in the unregulated, pretax, or presubsidy case. The T and S subscripts refer to the case of a Pigovian tax or subsidy, respectively.

i

Pj

Ps Pu

I MCj, MCS ,

* /A / / / / / / / /

" r " " I i I i I i /

i / i 1

/ v / ^ A V C u / f

/ / / / t / / / AVCS / / K * +* M / / • / • / X x t,s

>~ Goods output

?s Pu

MCj, MCS i lMQ

AVCS /

At/Cy

Goods output (a) (b)

FIGURE 12.4 Variable costs for heterogeneous industry, short run. (a) Old firms; (b) newer firms, MCU marginal cost unregulated case; MCS marginal cost, with emission control subsidy; MCV marginal cost, with emission fee; AVCU, average variable cost, unregulated case; AVCS, average variable cost, with emission control subsidy; AVCV average variable cost, with emission fee; pu, goods price, unregulated case; ps goods price, with emission control subsidy: pv goods price, with emission fee.

250 CHAPTER 12 EMISSION PRICES AND FEES

1

Pj

\ SupplyT ..,, /'. /bupplyu

/ „ Demand __/ .-4 Supplys

w Goods output

FIGURE 12.5 Short-run supply and demand, heterogeneous industry, with and without taxes and subsidies. Supply^ goods supply, unregulated case; Supplys, goods supply, with emission control subsidy; SupplyT, goods supply, with emission fee; demand, goods demand; pu, goods price, unregulated case; ps, goods price, with emission control subsidy; p , goods price, with emission fee.

Note in Figure 12.4 that although the tax and the subsidy raise the marginal costs by I same amount, the subsidy lowers average variable cost whereas the tax raises average vari; cost. The reason is that we have assumed the subsidy applies only if the firm is operating.' lump sum se in Eq. (12.14) goes away if the firm shuts down. Thus it counts as a variable cc Fixed costs (FC) are incurred whether or not the firm shuts down (in the short run).

Now we turn to determining what the market price of the good might be under the three regimes. Figure 12.5 traces out the short-run supply functions for this industr for the three cases, unregulated, Pigovian taxes, and subsidies. Also shown is a typic demand function for the good. Recall that firms will operate on the portion of their marginal cost curve that lies above the average variable cost. We can see that with bot the unregulated and subsidy cases, both types of firms are operating, yielding prodii prices of pu and ps, respectively. In the case of the Pigovian tax, only the newer firms operate, yielding product price px. These prices are shown on Figure 12.4. Note that all prices are above average variable costs for the newer firms, which is why they operate in all three cases. However, for the old firms, pT is below AVCT, the average variable cost for the Pigovian tax case. This is why the old firms shut down in this case.

Our conclusions are that taxes and subsidies have different effects in the short run. A subsidy may allow firms to continue operating that would not continue in the case of a tax. Which is efficient? The subsidy requires a lump-sum transfer, which has to be obtained from somewhere. Even more important, the subsidy involves the operation of firms that are really losing money (negative profits). This is not efficient.

B. T h e L o n g R u n

We now turn to the case of the long-run effects of Pigovian taxes and subsidies. We saw in Eq. (12.12)-(12.15) that the effect of a tax or subsidy was to raise marginal costs, but that a subsidy lowered average costs while a tax raised average costs. This applies in the short run as well as in the long run. If we assume a constant-cost industry, all firms will operate at the bottom of their average total cost curve, in long-run equilibrium. Thus the supply sched- ules for the industry will be horizontal and as shown in Figure 12.6b. The result of this is that goods prices will be higher with a Pigovian tax than with a subsidy. Furthermore, there will be more firms in the industry with a subsidy than with a Pigovian tax.

Other than the fact that a subsidy has to come from somewhere, a subsidy is undesir- able because it does not allow the market to communicate the true costs of the product

Imperfect Competition 251

MCTc /

i

X i T

1 i \ 5u

1 1 i \ Ss

D

1 1 1 w

(a) Goods output (b)

QT 9U 9S

Goods output

FIGURE 12.6 Long-run supply and demand, constant cost industry, with and without taxes and subsidies. MCU, marginal cost, unregulated case; MCV marginal cost, with emission control subsidy or emission fee; ATCU, average total cost, unregulated case; ATCS, average total cost, with emission control subsidy; ATCV average total cost, with emisison fee; D, goods demand; Su, long-run supply of good, unregulated case; Ss, long-run supply of goods, with emission control subsidy; ST, long-run supply of goods, with emission fee; qu equilibrium goods output, unregulated case; qs, equilibrium goods output, with emission control subsidy; (c/T, equilibrium goods output, with emission fee.

being consumed to the consumer. To be quite concrete, suppose we are dealing with paper mills producing paper from trees and polluting rivers at the same time (virgin mills). Other mills produce paper from recycled products and we will assume they are pollution free (which is not actually the case). A pollution subsidy to clean up the virgin mills will make virgin paper more attractive (compared to recycled paper) than if the virgin paper manufacturer had to pay a pollution tax. The result is that a subsidy results in the overuse of trees and underuse of recycled paper, compared to the case of a Pigovian tax. If a prod- uct generates pollution, we want consumers to see the full costs associated with producing that product when the consumers decide what to buy and how much to buy.

IV. I M P E R F E C T C O M P E T I T I O N

When markets are not competitive, a host of efficiency problems generally arise, and controlling pollution is no exception. There are two cases we will consider. One concerns

252 CHAPTER 12 EMISSION PRICES AND FEES

a monopolist in some goods market who is also a polluter. For instance, the monopolist may dominate the steel market while also generating smoke. The second case is more likely: a firm that is the only producer of smoke in some appropriate region. In this case we have a monopoly, but a monopoly in the provision of the bad.

The general conclusion that results from the analysis is that when there is market power, an emmisions fee can make matters worse. This is a result in what economists call the theory of "second best." When there is a distortion in an economy, such as monopoly, levels of output and prices will be distorted—not at their efficient levels. In such a case, the best way to correct inefficiencies such as pollution will not be to blindly use prescriptions from theory developed for efficiency. Other, "second best" methods must be used to cor- rect the problems. This is a large area of study in economics. We will consider only the example of monopolists and monopsonists generating pollution.

A . M o n o p o l i s t in t h e G o o d s M a r k e t

Assume the steel industry is a monopoly and it produces smoke.5 There are many smoke producers but only one producer of steel. For simplicity we will assume, as in the previ- ous section, that smoke and steel output are proportional. We know from intermediate microeconomics what the steel mill should do. This is illustrated in Figure 12.7. Shown in Figure 12.7 is a typical demand curve for steel and the associated marginal revenue func- tion. Also shown is the marginal cost of producing steel, ignoring pollution, MCV, and the marginal social cost of producing steel, including pollution, MCr The producer will produce where marginal costs equal marginal revenue, at S , and price on the demand curve. Conventional analysis would call for computing the inefficiency (the deadweight loss) as the sum of the hatched and solid portions of Figure 12.7. But pollution is being generated. Taking into account the social costs of steel production, the optimal amount of steel production would be S*. So, in actual fact, the deadweight loss (inefficiency) associ- ated with the unregulated output of steel is just the solid area in Figure 12.7. This is the area between the true marginal cost function (MCT) and the demand curve, bounded by S,, and S*. This is smaller than when we used MC,, instead of MCn.. The reason is that when

U U 1 an unregulated monopolist reduces output to increase profits, it also reduces pollution.

Extra DWL from Pigovian fee

DWL from unregulated monopolist Additional DWL from conventional analysis (ignoring pollution)

MCj

MCy

ST SU S«

FIGURE 12.7 Imposing a Pigovian fee on a goods monopolist. MCU, marginal private cost of producing steel; MCV marginal social cost of producing steel; D, demand for steel; MR, marginal revenue for steel; S0, steel output level, unregulated; ST, steel output level with Pigovian tax; S*. socially optimal output of steel.

Steel Production (S)

Imperfect Competition 253

Suppose we impose an emissions fee on the smoke generation, raising the private marginal cost of producing steel to MCr The monopolist will not keep producing at Su, but will produce where the new marginal cost function equals marginal revenue, at S.,.. Now the inefficiency is the sum of the shaded and solid areas in Figure 12.7. The imposi- tion of the emissions fee has made matters worse!

The intuition behind this is quite simple. Efficiency is not served if there is too much or too little pollution. Monopoly tends to reduce output and emissions, assuming there is no intervention. If an emissions fee is also imposed, output is restricted even further. Now we have much too little goods output and somewhat smaller smoke output than desirable. The emissions fee has overdone it.

B. M o n o p o l i s t in B a d s P r o d u c t i o n

The second case we consider is that of a firm that is competitive in its goods output mar- ket but is the sole supplier of pollution. This is a remarkably common situation. Consider the company town with one large producer of pollution. Since the pollution has relatively local effects, not spilling over to the next town, this firm is the monopolistic provider of pollution.

This situation is illustrated in Figure 12.8. We focus on the output of smoke since the goods market is competitive. Shown in Figure 12.8 is the marginal savings (MS) to the firm from producing smoke levels s. Also shown is the marginal damage to the populace (MD) from smoke. The enlightened population of the town where the polluter is decides to impose a pollution tax equal to marginal damage from the smoke. But rather than set the tax equal to marginal damage at s*, they set the tax to MD(s), at whatever level of s prevails. Because the polluter sees a slope to the marginal damage function, it knows it can lower its emission tax by reducing its emissions. True, this will cost the firm some- thing in terms of increased abatement costs, but this is a trade-off the firm may be willing to take. This is very similar to a monopsonist consciously using less of an input (such as labor) in order to drive down the price of the input, even though production costs in other respects will be higher.

MD(s)

SM S* Smoke (s)

FIGURE 12.8 Monopolist in provision of pollution. MS, marginal savings from polluting; MD, marginal damage from polluting; MT, marginal emission fee payments; t*, Pigovian fee; tm, monopoly emission fee level; §* efficient amount of smoke; sm, monopoly emissions of smoke.

254 CHAPTER 12 EMISSION PRICES AND FEES

To see how this works, note that the tax payment by the firm is

T(s) = s MD(s) (12.16)

As is always the case, the firm wants to produce where marginal cost (i.e., marginal tax payments) equals marginal revenue (i.e., marginal savings from polluting). To compute marginal tax payments for some level of smoke, s, we start with total tax payments and purturb s a bit, by As. Total tax payments will also change:

T(s + As) = (s + As) MD(s + As) (12.17)

The marginal tax payments will be the ratio of the change in taxes to the change in smoke levels:

MT(s) = T(s + As) - T(s) (s + As) MD (s + As)-s MD (s)

As As

= s {[MD(s + As) - MD(s)]/As} + MD(s + As)

= s MMD(s) + MD(s + As)

* s MMD(s) + MD(s)

which can be more simply written using calculus:

MT(s) = dT(s)/ds = d[s MD(s)]/ds = s dMD(s)/ds + MD(s)

(12.18a)

(12.18b)

The MMD(s) in Eq. (12.8a) is the marginal marginal damage of smoke, i.e., how much marginal damage changes for a small change in smoke levels. Since MD(s) is getting larger as s gets larger in Figure 12.8, MMD(s) is positive. Also, the last approximate equality (=) in Eq. (12.18) applies if As is very small so that s and s + As are virtually the same.

Note from Eq. (12.18) that the marginal tax payment is in excess of the marginal damage. If the firm generates one more unit of smoke, tax payments go up because the firm has to pay MD(s) for that extra unit of smoke. But also, the tax rate goes up by a little, which means payments for all smoke, not just the last unit, go up a bit. Consequently the total tax bill goes up by more that just MD(s). The discussion is exactly equivalent to why marginal revenue for a monopolist in a goods market is lower than price. As monopolists expand output by one unit, they gain the revenue for that unit (which is the price) but the price goes up a bit for all the units they are still selling. This is why marginal revenue is less than price.

Now the rational smoke monopolist will produce where the marginal tax payments equal the marginal savings from polluting, namely sM in Figure 12.8. Efficiency would call for smoke levels of s*. The firm is underpolluting. At s* the emission fee would be f*. However, the smoke monopolist has managed to drive the emission fee down to rv(. The deadweight loss associated with this is the shaded area in Figure 12.8.

To summarize, the monopolist provider of pollution can manipulate the emission tax by reducing pollution below the efficient level. It is tempting to say that this outcome is fine. We have less pollution than otherwise, which cannot be too bad. However, it is important to realize that too little pollution may mean too many resources are devoted to pollution control. Those resources are being diverted from other socially desirable purposes.

The Double Dividend 255

V . T H E D O U B L E D I V I D E N D

Governments must raise revenue. Unfortunately, most taxes tend to introduce ineffi- ciencies and distortions into the economy. A labor tax (wage income tax) makes labor more expensive and thus discourages work. A capital tax makes capital more expensive and thus discourages investment. A number of authors have tried to measure the inef- ficiencies associated with taxation. Edgar Browning (1987) estimates that the last dollar collected through wage taxation in the United States has an additional welfare loss of approximately 40

In recent years, there have been a number of proposals to substitute pollution taxes for more traditional revenue raising taxes, such as income taxes. The general idea is that these "green taxes" would be revenue-neutral. Any income generated by the taxes would be offset by lost income from reductions in labor (income) taxes or other taxes. The idea is that such taxes would not only reduce pollution but would also reduce the distortions associated with existing taxes—a "double dividend." This policy suggestion has prompted an examination of the efficiencies of pollution taxes when there are preexisting distortions.7 Consider the case of a competitive economy where distortionary taxes exist (such an income tax). Now suppose there is a polluting industry and the government levies an emission fee on that industry. What happens? Pollution goes down (this is a benefit); revenue comes in, which we use to offset distortionary labor income (this is a benefit); deadweight loss from the income tax increases from interactions between the emission fee and the income tax (this is a loss). This third interaction effect is not at all obvious, and we explore it further in the following paragraphs. So the double dividend has morphed a bit.

There are a number of implications of this result. One is that the net benefit of the emission tax (the sum of the three effects) may be smaller than just the gain from the reduction in environmental damage (i.e., the sum of terms two and three may be a cost, not a benefit). Another implication is that if an environmental regulation is used that does not generate any revenue (such as prescriptive regulations or freely distributed tradable permits), then only the first and third terms count—the net benefits will be lower than with a pollution tax.

These are classic results in what is known as the theory of second best. What is advisable in an economy without distortions is not necessarily a good idea when there are distortions, even in apparently unrelated parts of the economy.

To see this result, we start with a representative consumer who chooses how much labor, L, to provide (in exchange for a wage, w) and how much of a polluting good to con- sume, X. A polluting good means that pollution is generated when the good is produced. Suppose there is a tax on wages, tx (which, for simplicity, assume the firm pays). With this tax on labor, a certain amount of labor is provided, L*. With a lower tax, employers could pay more and thus more labor would be supplied; with a higher tax, less labor would be supplied. Figure 12.9a shows a supply curve for labor and a horizontal demand curve set at the value marginal product of labor (assumed constant). We see that the labor tax lowers the amount of labor supplied to L*. We can also look at this in terms of demand for leisure, since workers divide their total time into labor and leisure. A tax on labor is the same as a subsidy to leisure. The higher the wage tax, the greater the subsidy to leisure and the more leisure will be provided (less labor). This is shown in Figure 12.9b,

256 CHAPTER 12 EMISSION PRICES AND FEES

VMPL =

i

k

i Demand for labor, no tax

y

Demand for labor, tax -

/

' ' yr t t L

Supply of labor

•K

—•

A Supply of leisure, no tax

w

Demand, postenvironmental tax

Supply of leusure, tax = fL

Demand for leisure

(a) (b) H' H* H

FIGURE 12.9 (a,b) Effect on leisure from environmental tax. VMPL, value of marginal product of labor; tL, tax on labor; w, wage rate; H*,L*, supply of leisure and labor with tx ~ 0; t^ tax on X; H*. quantity of leisure with tx > 0; BCDE, wage tax revenue loss from tx > 0.

where H* is the amount of leisure that will be consumed when the labor tax is tL (ignc the broken line and the shaded area for the time being). Without the tax on labor, the would be more labor and less leisure. The deadweight loss from the labor tax is shown it Figure 12.9b as the triangle ABC. Thus to raise revenue th L*, a deadweight loss of ABC i incurred.8 Define V as the marginal deadweight loss, i.e., the deadweight loss that wot be incurred to raise one more dollar of revenue when the tax rate is set at t.

Now consider demand for a polluting good, i.e., a good whose manufacture general pollution. Figure 12.10 shows a typical demand curve for the good, as well as a marginal private cost curve and a marginal social cost curve that includes the damage from pol- lution. Without any intervention, the amount of the good produced is X*. Now suppose we wish to reduce the amount of this good produced. This may be accomplished by tax- ing the production of the good (or the production of pollution) or simply by command and control, directing the firm to reduce pollution and thus incur additional production costs. In either case, assume marginal costs are increased by an amount tx and the output is reduced from X* to X*. This is shown in Figure 12.10. If tax revenues result, then labor taxes will be reduced to keep the total government revenues constant.

The increased price of X has an effect on the demand for leisure. In general, we would expect X and leisure to be substitutes.9 Thus an increase in the price of X will shift the demand for leisure outward, as shown by the broken line in Figure 12.9b. This results in an increase in the quantity of leisure to H+. The amount of this shift can be computed from the cross-price elasticity of demand for leisure with respect to the price of good X:

nHX = (AH/H)/(APx/px) = [(H + - H*)l Apx) (px IH*) (12.19)

In Eq. (12.19), r\hx indicates how much the demand for leisure changes when the price of X changes. This is the cross-price elasticity of demand for leisure with respect to the price of X. For a substitute, this will be positive.

The Double Dividend 257

private

FIGURE 12.10 Supply and demand of polluting good. MCsocial, marginal costs of producing X, including pollution damage; A7Cprivate, marginal costs of producing X, excluding pollution damage; X*, production without internalizing externality; t^ product tax necessary to internalize externality; X\ production with tax tv.

We see from Figure 12.9b that the reduction in X has increased the quantity of leisure and thus decreased tax revenues by the shaded area in Figure 12.9b. The area of this shaded area is (H* - H*) tv This loss must be made up and every dollar that is raised through labor taxation actually costs society 1 + V. Thus [using Eq. 12.19] the indirect loss from the environmental controls on X is

IE=(\ + V) (H+- H*) tL = (1 + V) tL Apx nHX H*/px (12.20)

This is termed the "tax interaction" effect (IE). Though IE in Eq. (12.20) is positive, remember that it is a loss. The tax interaction effect is the extra inefficiency from a pol- lution regulation due to the fact that labor is already taxed. Note that if the labor tax rate is zero (rL = 0), the tax interaction effect is zero. Furthermore, the greater the value of nHX, the larger the effect. Basically, what is happening is that the pollution tax is generating a deadweight loss by marginally changing the very significant preexisting deadweight loss associated with labor taxation.

Although IE is unequivocally a welfare loss (provided the good is a substitute for lei- sure), there are two welfare gains that are possible from pollution regulation. The most obvious one is the reduction in damage associated with the pollution. Less pollution means less damage. Term this the Pigoevian effect (PE). In the context of the double dividend debate, suppose any tax revenue raised by the pollution tax is offset by a reduction in labor tax. Call this the revenue recycling effect (RE). In the context of Figure 12.10, clearly

RE=VtvX + (12.21)

The revenue raised is txX+, which is used to offset labor taxes that have a marginal dead- weight loss to revenue ratio of V. It is clearly positive—a gain. Note, however, that if no revenues are raised through the environmental regulation, RE is zero. If the regulation is prescriptive, no revenue is raised. If the regulation is marketable permits for pollution, then revenue is raised if the permits are initially auctioned. If the permits are given away initially (as is often the case), then RE = 0.

To summarize, we conventionally think of the Pigoevian effect (PE) as the primary gain from a pollution control regulation. We have just seen that if pollution tax revenues can be used to reduce distortionary taxes, we have a bonus of the revenue recycling

258 CHAPTER 12 EMISSION PRICES AND FEES

effect (RE). But we have also seen that reducing pollution will generate a loss throuj the indirect effect on preexisting distortionary taxes (IE). The big question is, how big a problem is this tax-interaction effect? That question is empirical. Using a very simple model and typical parameter values for the United States, Parry (1995) calculates that the optimal pollution tax should be 63% of marginal damage (not equal to marginal damage as suggested by conventional wisdom).

The lesson to be learned is that pollution regulation can result in significant indirect costs due to preexisting tax distortions in the economy. Much of this distortion can be eliminated if pollution taxation raises revenue, which is used to offset the preexisting distortion. Without revenue recycling, only much weaker environmental regulations are justified on efficiency grounds.

It might seem that it is "unfair" to have the environment bear the cost of the inef- ficiency introduced by the wage tax. But this is not really the correct interpretation of the result. In fact, in this sort of second-best environment, it is difficult to interpret what is happening with the emission tax without looking at the distortions throughout the economy introduced by the income tax. For instance, if the polluting good and leisure are substitutes as assumed, the subsidy to leisure may already have reduced consumption of the polluting good in the economy. Thus we do not need to reduce it as much with the emission tax. In fact, it has been shown that when there are no commodity taxes and an optimal income tax, it can be welfare improving to subsidize the consumption of goods that are substitutes for leisure.10 Although we have made no assumption that the income tax is optimal, if it were and there were no tax or subsidy on the polluting good, the opti- mal action would be to simultaneously tax the polluting good at the full marginal damage but then add a subsidy to account for the distortions of the income tax. The net effect is that the tax on the polluting good is less than marginal damage.

SUMMARY

1.

2.

3.

4.

5.

6.

An emission fee or tax is a charge per unit of emissions levied by a regulator on a polluter.

A Pigovian fee is an emission fee set equal to the marginal damage of pollution, at the efficient level of pollution generation.

An emissions fee is levied by the government, which collects the fee revenue. The fee generally induces provision of an efficient amount of pollution.

With multiple polluters, efficiency in pollution control requires that the marginal cost of control be the same for all polluters, provided the emissions from each pol- luter contribute to damage in the same way. This is the equimarginal principle.

In comparing a subsidy for pollution control with a tax on pollutant emissions, both result in the same marginal conditions for pollution emissions. However, the subsidy results in excess production in the polluting industry, in both the short and long run.

If a monopolist is the sole producer of a good in a market and also pollutes as a by- product of goods production, an emission fee can make matters worse. An emission fee will raise costs of production and thus reduce output of the monopolized good even more, which increases the inefficiency associated with monopoly.

Problems 259

10.

11.

7. With a monopolist in pollution production, if an emission fee is set equal to marginal damage, the monopolist will drive the fee down below the level of a Pigovian fee and reduce emissions below the efficient level.

8. The "double dividend" refers to the possibility that imposing a revenue-neutral tax on pollution will have have two effects: (a) reduce pollution and thus pollution dam- age (the Pigouvian effect) and (b) reduce distortionary taxes on labor and thus the deadweight loss associated with those taxes (the revenue recycling effect). There is a third effect that acts in the opposite direction, the tax interaction effect.

9. When pollution is reduced, the demand curve for leisure is shifted outward (if the polluting good and leisure are substitutes). If labor is taxed, this shift will generate an additional deadweight loss that must be attributed to the reduction in pollution. This is the tax interaction effect.

A tax on pollution increases welfare through the Pigouvian effect and the revenue recycling effect but reduces welfare through the tax interaction effect.

The size of the tax interaction effect is an empirical question and will vary from one polluting industry to another. Ian Parry calculates that a pollution tax should be set at 63% of marginal damage to account for the tax interaction effect.

PROBLEMS

1. Assume an economy of two firms and two consumers. The two firms pollute. Firm one has a marginal savings function of MSfe) = 5 - e where e is the quantity of emis- sions from the firm. Firm two has a marginal savings function of MS2(e) = 8 - 2e. Each of the two consumers has marginal damage MD(e) = e, where e is this case is the total amount of emissions the consumer is exposed to.

a. Graph the firm-level and aggregate marginal savings functions.

b. Graph the aggregate marginal damage function.

c. What is the optimal level of pollution, the appropriate Pigovian fee, and emis- sions from each firm?

2. In Section IV,B does the problem of monopoly provision of a bad arise with a true Pigovian fee? Why?

3. Consider the case of a rival bad. Would efficiency require that a Pigovian fee be levied on the producer of the bad and the receipts given to the consumers as compensation? Does it matter if the bad is excludable or nonexcludable?

4. The Fireyear and Goodstone Rubber Companies are two firms located in the rubber capital of the world. These factories produce finished rubber and sell that rubber into a highly competitive world market at the fixed price of £60 per ton. The process of producing a ton of rubber also results in a ton of air pollution that affects the rubber capital of the world. This 1:1 relationship between rubber output and pollution is fixed and immutable at both factories. Consider the following information regarding the costs (in £) of producing rubber at the two factories (Qf and QQ):

Fireyear Goodstone

Costs: 300 + 2QT Costs: 500 + QQ

2 Marginal costs: 4Qf Marginal costs: 2Q

260 CHAPTER 12 EMISSION PRICES AND FEES

NOTES

Total pollution emissions generated are Ef + Ec = QF + QG. Marginal damage from pollution is equal to £12 per ton of pollution.

a. In the absence of regulation, how much rubber would be produced by each firm? What is the profit for each firm?

b. The local government decides to impose a Pigovian tax on pollution in the com- munity. What is the proper amount of such a tax per unit of emissions? What are the postregulation levels of rubber output and profits for each firm?