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European Economic Review 47 (2003) 125146

www.elsevier.com/locate/econbase

Environmental policy incentives to adoptadvanced abatement technology:

Will the true ranking please stand up?

Till Requatea ;

, Wolfram Unoldb

a Department of Economics, Kiel University, Olshausenstr. 40, 24098 Kiel, GermanybSiemens Financial Services, Hofmannstrasse 51, 81359 Munich, Germany

Received 1 December 1999; accepted 1 September 2001

Abstract

We investigate incentives through environmental policy instruments to adopt advanced abate-

ment technology. First, we study the case where the regulator makes long-term commitments

to policy levels and does not anticipate arrival of new technology. We show that taxes pro-vide stronger incentives than permits, auctioned and free permits oer identical incentives, and

standards may give stronger incentives than permits. Second, we investigate scenarios where the

regulator anticipates new technologies. We show that with taxes and permits the regulator can

induce rst-best outcomes if he moves after rms have invested, whereas this does not always

hold if he moves rst. c 2002 Elsevier Science B.V. All rights reserved.

JEL classication: L5; Q2; Q28

Keywords:Emission taxes; Auctioned permits; Grandfathering; Emission standards; Technology adoption

1. Introduction

Among the wide array of pollution control instruments, economists prefer those

which provide incentives through prices rather than through command and control.

The main advantage of market-based instruments such as emission taxes, subsidies on

abatement, and dierent regimes of tradeable permits is their (static) cost eciency.

A further criterion at least as important for judging (environmental) policy instru-

ments is the extent to which they provide dynamic incentives to develop and adopt

Corresponding author. Tel.: +49 431 880-2199; Fax: +49 431 880-1618.

E-mail addresses: [email protected] (T. Requate), [email protected] (W. Unold).

0014-2921/03/$ - see front matter c 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 0 1 4 - 2 9 2 1 ( 0 2 ) 0 0 1 8 8 - 5


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126 T. Requate, W. Unold / European Economic Review 47 (2003) 125 146

new technology. 1 In a series of papers, Downing and White (1986), Malueg (1989),

Milliman and Prince (1989) and, more recently, Jung et al. (1996) have attempted

to rank environmental policy instruments with respect to their incentives to spur the

adoption of advanced, low-polluting technologies. Notably, Milliman and Prince (1989)compare pollution control instruments such as taxes, auctioned permits, free (or grand-

fathered) permits, subsidies, and emission standards at rm level. More recently, Jung

et al. (1996) extended this analysis to a heterogeneous industry by investigating the

incentive to adopt a new technology on an aggregate level. Both papers come to the

conclusion that the dierent control regimes can be ranked in the order (i) auctioned

permits, and (ii) taxes and subsidies, (iii) free permits, and (iv) emission standards.

In this paper we challenge these rankings. In particular, we raise doubts about the

methods used to establish these rankings. We argue that the ranking derived in this

sector of the literature relies basically on calculating the aggregate cost savings achieved

by an industry-wide adoption of new technology. On the assumption that all rms adopt

the new technology, the authors of these papers calculate the total costs for industry

before and after adoption of the new technology and then compare the dierences.

These aggregate cost savings, however, do not reveal a single rms incentive to adopt

a new technology in equilibrium. This approach ignores the fact that a single rm

can free ride on a decreasing permit price caused by other rms investment. To put

it dierently, equilibrium aspects with respect to the rms investment decisions have

been neglected completely, in particular for the permit regimes. Our analysis reveals

that equilibrium aspects are crucial for the ranking of the policy instruments.

Our contribution is twofold. First, we reexamine the situation considered by Millimanand Prince (1989) and Jung et al. (1996), where the regulator has committed to both

his policy instrument and the level of his instrument before knowing about the new

technology and without anticipating that a new technology may become available in

the foreseeable future. For the sake of fair comparison, we set up our model as close

as possible to both models by Milliman and Prince, and by Jung et al. In contrast to

those authors, however, we do not a priori assume that all the rms will adopt the

new technology. Instead, we inquire how many rms will invest and adopt the new

technology in equilibrium under dierent policy instruments and dierent policy levels

(e.g. emission tax rates). Secondly, we study two scenarios where the regulator does

anticipate adoption of the new technology. The two scenarios dier with respect to theorder of who moves rst: the regulator, by setting the level of his policy instrument

(e.g. his tax rate), or the rms by investing.

Examination of the rst situation (no anticipation of the new technology) is important

mainly from a positive point of view, since constant policy levels for long periods of

time are typical in real politics. The U.S. Environmental Protection Agency (EPA),

for instance, has committed to a constant total supply of permits for more than 15

years. Several European countries have committed to constant, or even increasing, tax

rates regardless of both new technological developments and increasing oil prices. For

1 This was stressed earlier by Kneese and Schulze (1975, p. 38) Over the long haul, perhaps the most

important single criterion on which to judge environmental policies is the extent to which they spur new

technology toward the ecient conservation of the environment.


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T. Requate, W. Unold / European Economic Review 47 (2003) 125 146 127

this regime of commitment and non-anticipation of new technology, we nd that taxes

usually provide higher incentives to invest than permits and standards. More precisely,

for any given emission target there are as least as many rms investing under taxes as

under permits or standards. The reason is that, apart from the case of one particulartax rate where rms are indierent between investing and not investing, either all

the rms invest or none of the rms invest. Under permits, by contrast, we observe

the equilibrium price to fall if more rms invest. This provides incentives for some

rms to free ride on the other rms investments by taking advantage of decreasing

permit prices. Hence, in equilibrium we may observe both types of rms, with old and

new technology, being simultaneously active in the market. Thus if the regulator has

implemented a particular emission target before the new technology was known and

available, there may be complete adoption of the new technology under taxes, but only

partial adoption under permits. Furthermore, we nd that in contrast to the claims in

the literature there is no dierence between grandfathering and auctioning o permits.

The reason is that, in comparison to auctioning, grandfathering amounts to a lump-sum

transfer to the rms, which does not aect the rms decisions. Furthermore, we nd

that while taxes provide higher incentives than emission standards, the comparison

between standards and permits is ambiguous. Depending on the aggregate emission

target, in equilibrium more rms may invest under standards than under permits.

Within this regime of commitment and non-anticipation of new technology, we also

follow Milliman and Prince in studying the special case where the regulator has set

the level of his policy instrument to be optimal, given the old technology. Although

not entirely realistic, this assumption serves as a useful benchmark in asking whichpolicies may induce over- or under-investment. We nd that over-investment will typi-

cally emerge under taxes, whereas under-investment will be the typical outcome under

permits. Under standards, we may observe both over- and under-investment, depending

on the parameters of the social damage function.

In the second situation studied in this paper, the regulator anticipates the new tech-

nology and chooses the level of his policy instruments accordingly. This perspective

is important from a normative point of view, since the regulator should choose his

policy optimally with respect to the available technologies. We study two scenarios

which dier in terms of timing. In the rst scenario, the regulator moves rst by com-

mitting to both the policy instrument and the level of his instrument (e.g. the tax rateor the aggregate number of permits to be issued). In the second scenario, the timing

is reversed. Before the (proper) game starts, the regulator makes a commitment to the

choice of his policy instrument only. The rms invest in the rst stage of the game.

Thereafter, the regulator observes how many rms have invested, and then chooses the

level of his instrument in the second stage.

We obtain the following results: if the rms move rst and the regulator second, then

under both market-based policies (taxes and permits), there exists a unique subgame

perfect equilibrium where the optimal number of rms invests and the regulator charges

the socially optimal tax rate or issues the optimal number of permits, respectively

(leading to socially optimal emission levels). If the timing is reversed, i.e. the regulatormoves rst by committing to both the type and the level of his policy instrument,

rst-best outcomes are only unique equilibrium outcomes in the permit case. Under


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taxes, by contrast, inecient equilibria are possible if it is socially optimal for some

but not all of the rms to adopt the new technology. Under uniform emission standards,

rst-best allocations are of course not possible as a result of decentralized investment

decisions. This, in fact, holds true for both types of timing.Like Milliman and Prince (1989) and Jung et al. (1996), Downing and White

(1986) and Malueg (1989) also ignore equilibrium aspects of investment and thus

are methodologically not very dierent from Milliman and Prince. Besides this branch

of literature, other authors have examined the issue of environmental technology adop-

tion under dierent institutional frameworks. Biglaiser and Horowitz (1995) consider

adoption of the new technology under taxes if rms can also engage in R&D and

sell their new technology to unsuccessful research rms or non-research rms. The

focus of their paper is mainly on R&D incentives rather than on the comparison

of dierent pollution control instruments. In contrast to those authors, Fisher et al.

(1999) focus on the incentives for a single rm to engage in (deterministic) R&D

in cases where the rm can sell its new technology to other rms. Like Milliman

and Prince (1989) and Jung et al. (1996) and unlike our paper, they assume com-

plete adoption of the new technology in all cases. They compare taxes and

permits mainly by numerical simulations, but do not arrive at unique results.

Gersbach and Glazer (1999) and Gersbach (1997) compare taxes and permits with

respect to the incentives to adopt new technology in the context of a governments

hold-up problem when large rms have an impact on future environmental regulation

by their investment decisions. Assuming that no pollution control policy exists prior

to investment into abatement technology, they argue in favor of permits, since per-mits can mitigate the governments hold-up problem in a better way than taxes. By

contrast, Laont and Tirole (1996) argue that permits may induce over-investment if

the marginal cost of public funds is taken into account. The reason is that, if the

regulator has revenue objectives by auctioning o permits, he is not interested in too

much abatement. Thus, there is a trade-o between improving environmental technol-

ogy and mitigating distortions of the tax system by collecting revenues from selling

permits. To overcome the problem of over-investment, the authors propose accompa-

nying the permit regime by a system of future markets. Carraro and Siniscalco (1994)

reject both taxes and permits as an incentive device for technology adoption. With-

out presenting a formal model, they claim both instruments to have similar eects.Instead, they favor direct subsidies in order to avoid an increase in the rms oper-

ating costs. Very recently Feess and Gleaves (2001) independently come to similar

results to those presented in Section 6. The reader interested in further literature is

referred to the excellent survey by Jae et al. (2000), which also covers the empirical

literature.

This paper is organized as follows: In the next section, we discuss the ranking of

policy instruments as presented in the literature so far. In Section 3, we set up the

model and show that taxes always induce the same incentives as subsidies and that

auctioned permits always induce the same incentives as grandfathering. In Section 4,

we derive the socially optimal allocation. Section 5 investigates the rms incentive toinvest under taxes, subsidies, auctioned permits, grandfathering, and standards if the

original policy levels have been set optimally before the new technology was available.


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Fig. 1. Single rms investment incentive under taxes.

At the end of that section, we use our results to compare the policy instruments forany

aggregate emission target. In Section 6, we study two scenarios where the regulator

anticipates adoption of the new technology. The nal section presents our conclusions.

Technical proofs are found in Appendix A.

2. A critical discussion of previous literature

As mentioned earlier, several articles have compared environmental policy instru-

ments with respect to their incentives to adopt new abatement technology (see in par-

ticular Milliman and Prince (1989) and Jung et al. (1996)). The argument is outlined

in Fig. 1. MAC0 denotes the marginal abatement cost curve of a representative rm

running a conventional abatement technology, whereasMACIis the marginal abatement

cost curve after adoption of some advanced abatement technology. Let emaxi (i= 0; I)denote the largest possible emission level a rm would choose under a laisser-faire

policy. It is natural to assume that emaxI emax0 .

Let us rst consider pollution control by an emission tax. If a particular rm switches

from conventional to advanced technology, its savings in variable abatement cost plus

tax payments is given by the area A+ B. If, as is usually the case, installing a new

technology causes a xed set-up cost F 0, it will be protable for the rm to invest

in the new technology if and only if F A+B. 2

Now consider pollution control by auctioning o permits in each period, say, a year.

Let 0 denote the original price for permits (see Fig. 2) before the advanced technology

2 In a dynamic framework, Fmust be interpreted as the annuity of the xed cost per period. In this case,

the criterion F A+B is conditional on the tax remaining constant for a suciently long time.


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Fig. 2. Single rms total cost reduction if all rms invest under permits.

is available. Assume rst that only one small rm has access to that new technology.

Then the incentive for this single rm to install the new technology is the same as

under taxes, provided that the price for permits is not aected by the rms decision

to switch technology. (This was correctly observed by Milliman and Prince.) Assumenow that all the rms have access to the new technology. Then the price for permits

will fall if a considerable number of rms adopts the new technology. Jung et al.

assume such a price, say I, to be exogenously given (see Fig. 2). Then indeed, each

rm that has adopted the new technology has lower variable costs than in a situation

where no other rm has adopted the new technology. The cost dierence is equal to

the area A+B + C depicted in Fig. 2. This cost dierence, however, has nothing to

do with a single rms incentive to adopt the new technology. In other words, the

criterion for whether or not to adopt the new technology is not determined by the

inequality F A +B + C. To see this, let us assume that there are a large number of

rms n of similar size. Each rm is small compared to the entire industry. As before,let 0 denote the price before any rm has adopted the new technology, and let Idenote the price afterall the rms have adopted the new technology. Assume now that

(n 1) rms have adopted the new technology and the last rm has not yet done so.Since the last rms impact on the price can be neglected, the price for permits is now

approximately I. When will the last rm adopt the new technology? The answer is

given by Fig. 3. It will do so if F A1, which is smaller than A1+ A2+ B=A+B.

Now if A1 F A+ B holds, the last rm would adopt the new technology under

taxes but would not do so under permits. Hence the incentive to invest under permits

must be lower than under taxes.

Assume further that A1FA +B holds, i.e. F is considerably greater than A1 butconsiderably smaller than A +B. Then even the (n1)th rm will probably not investin the new technology. On the other hand, the rst rm has an obvious incentive to


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Fig. 3. Single rms investment incentive under permits.

adopt the new technology if no other, or a very small number of other rms will adopt

the new technology. Given these considerations, it should have become clear by now

that it is necessary to determine endogenously the number of rms adopting the new

technology.Assuming that all the rms will adopt the new technology as both Milliman and

Prince (1989) and Jung et al. (1996) do is tantamount to assuming the xed set-up

cost to be suciently low, i.e. FA1. But if we assume that ex ante all the rms will

adopt the new technology, it is no longer of interest to ask which policy instrument

will provide a higher incentive to adopt the new technology. The aim of this paper is to

determine how many rms will adopt the new technology in equilibrium. By doing so,

we will be able to establish that the criterion deciding whether one policy instrument

will provide higher incentives to invest than another is its success in inducing more

rms to invest.

3. The model and some basic results

Consider a competitive industry consisting of n small rms where industry size is

assumed to be exogenous. All the rms emit a homogeneous pollutant which can be

abated. The rms abatement cost functions Ci satisfy the usual properties: Ci(ei) 0

for ei emaxi , and Ci(ei) = 0 for ei e

maxi , where e

maxi denotes the maximal emission

level under laisser-faire. Moreover, marginal abatement costs are positive in the rel-

evant range, i.e. Ci (ei) 0 for ei emaxi , and decreasing with more emissions, i.e.

Ci (ei) 0 for ei emaxi . Since the product market is assumed to be competitive, de-cisions about output need not be modelled explicitly. Those decisions are implicitly

accounted for in the abatement cost functions.


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In the following we assume that initially all the rms are alike, thus having the same

abatement cost curve C0. However, the rms can invest in an advanced abatement

technology leading to a lower marginal abatement cost curve CI (see again Fig. 1)

with

CI(e) C

0(e) for all e emax0 :

Buying and installing the new technology involves a xed cost F 0.

In the next section, we will inquire when and to what extent rms will adopt

advanced abatement technology under taxes and auctioned permits. Then we briey

address grandfathering, subsidies, and nally uniform emission standards.

3.1. Taxes and auctioned permits

Assume initially that the regulator can choose between setting a tax or issuing anumber of tradeable permits L where denotes the market price for permits. In the

following, let p denote a tax rate or a permit price. Then, cost minimization on the

rm side requires

C0(e0) =p; (1)

CI(eI) =p (2)

for rms with conventional and new technology, respectively.

First consider regulation by emission taxes. For most of the paper, we assume that

the regulator cannot commit to a policy which makes the tax on emissions vary withthe number of adopters. Put dierently, we assume that the regulator moves rst, setting

a tax rate and committing to the level of that tax rate for a time period long enough

to enable the rms to amortize their investment. (We will relax this assumption in

Section 6.) Then a typical rm decides to adopt the new technology if

C0(e0()) +e0() CI(eI()) eI() F 0:

Firms are indierent about adopting the new technology if

C0(e0()) +e0() CI(eI()) eI() F= 0: (3)

Next consider the case where the rms are regulated by permits. Here, the equi-librium price of permits depends on the number of rms that have adopted the new

technology. The rms, however, do not view their investment decisions as aecting

the market price of permits. Since more rms with new technology will lead to a

lower aggregate marginal abatement cost curve, it is obvious that the greater nI n,

the smaller the equilibrium permit price denoted by (nI).

Now we call nI an investment equilibrium number of rms if

C0(e0) +(nI)e0 CI(eI) (nI+ 1)eIF6 0; (4)

i.e. no conventional rm wants to invest in the new technology, and

C0(e0) +(nI 1)e0 CI(eI) (nI)eIF 0; (5)i.e. no rm that has invested in the new technology would be better o by not having

invested.


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Suppose now that the rms are numbered according to the order in which they can

decide whether or not to adopt, and assume that (4) and (5) are satised for some

0 nI n. Then market forces clearly lead to equilibrium.3

If the rms are numerous enough for an additional rm switching technology tohave (almost) no impact on the equilibrium price, we can replace the two equations

(4) and (5) by a single one:

C0(e0) +e0 CI(eI) eIF= 0: (6)

Apart from the substitution of for , this equation is the same as (3), and we can

apply the following lemma to both the tax and the permit case:

Lemma 1. There exists at most one tax rate or permit price ; respectively; with

= =: p such that rms are indierent between adopting and not adopting the new

technology. For this price p; there exist unique emission levels eI ande 0 chosen by

the rms with and without advanced technology; respectively. If or (

or ) all rms (no rm) want(s) to adopt the new technology. Moreover; p is

increasing in F.

The proof is given in Appendix A. If, in case of taxation, , no rm will adopt

the new technology, and we will obtain the highest possible emission level E= ne 0,

while if , all rms will adopt the new technology and we obtain the lowest

possible emission levelE=neI. If= , the number of rms that adopt is undeterminedand the total emission level is in [E; E]. But this also implies that if rms with dierent

kinds of technology are in the market at the same time, the tax (or the permit price)

must be equal to .

Now assume the industry is regulated by auctioning o permits (we treat free permits

in Section 3.2). Then, in contrast to taxes, we always obtain a unique equilibrium

number of investing rms, as the following lemma shows:

Lemma 2. Let L be any number of permits being issued; and let be the market

clearing price for permits. Then the following holds:

(i) IfL E; then (as dened in Lemma 1) ; and no rm will adopt the newtechnology.

(ii) If L E; then ; and all the rms will adopt the new technology.

3 If rms act simultaneously and play pure strategies, the equilibrium is only unique up to the equilibrium

price for permits and the number of rms which adopt the new technology in equilibrium. The equilibrium is

not unique, however, in terms of which rms adopt the new technology. In this case we have a coordination

game. We can always obtain uniqueness by assuming that nature draws a random order in which the rms

may decide. In this case, the equilibrium given by (4) and (5) can be shown to be a subgame perfect

equilibrium of this sequential move game.If rms play mixed strategies in the decision stage about whether or not to invest, there exists a unique

mixed strategy equilibrium. In that case, the number of rms adopting the new technology may vary with

the realization of the random outcome.


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Fig. 4. Quantity=price schedule for permits (few rms).

(iii) If E6L6E; then = ; and precisely

nI=ne 0 L

e 0 eI(7)

rms will adopt the new technology.

The proof is given in Appendix A. Note that the equilibrium is unique up to any

permutation ofnI among n rms adopting the new technology (see footnote 3). It may

appear surprising that we obtain the same equilibrium price = for a whole range of

dierent quantities of permits. If rms with dierent technologies are in the market at

the same time, then, the rms must be indierent between the two technologies. This

can only be the case for one particular price. What would happen if we reduce the

number of permits slowly from L to L? The price would increase a little until it pays

for one more rm to adopt the new technology. If this happens, the price falls again to= . So strictly speaking, forL [L; L] the permit-supply=equilibrium-price schedule isas indicated in Fig. 4. If the market is suciently large, the equilibrium-price schedule

is almost a at line on the interval L [L; L], see Fig. 5.

3.2. Grandfathering

According to Malueg, Milliman and Prince, and Jung et al., free permits provide

lower incentives to adopt new technology than auctioned permits. The argument they

propose is that innovating makes rms permits depreciate. However, innovating depre-

ciates the rms permits anyway, irrespective of whether these permits are auctionedo or distributed for free. In contrast to what Jung et al. claim, the original permit

price is completely irrelevant with regard to the incentive to adopt a new technology


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Fig. 5. Quantity=price schedule for many rms.

in equilibrium. To see this more clearly, let e i = e be the rms (identical) initial

endowment of permits. As the rms are alike before innovation, there will be no trade

before the new technology is available. Since the advanced technology leads to lowermarginal abatement costs for each emission level, the investors must be sellers and the

non-investors must be buyers of permits. In an equilibrium with partial adoption, rms

must be indierent about adopting the new technology or not, i.e.

C0(e0) +[e0 e] =CI(eI) [e eI] +F: (8)

We see that e cancels out. Thus, (8) is equivalent to (6) and we obtain the following

result:

Proposition 1. Suppose that the distribution of permits is not too dierent (in order

to exclude market power). Then the incentive to adopt a new technology is the same

for free (grandfathered) as for auctioned permits.

By a similar argument, it is easy to show that taxes and subsidies on the reduction

of emissions are equivalent. This is in line with the results of Milliman and Prince,

and Jung et al.

3.3. Uniform emission standards

Finally, consider a uniform emission standard e, sometimes referred to as commandand control policy. Under such a standard, which means that a rm is not allowed

to emit more than e units of the pollutant, the rm will be indierent between staying


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with the conventional technology and adopting the advanced technology if

C0( e) CI( e) F= 0: (9)

Since C0( e) C

I( e), the LHS of (9) decreases in e. This means that the cost

advantage of the new technology decreases as the emission standard is relaxed. This

leads us immediately to the following result:

Lemma 3. Let F be given and let e (depending on F) be the standard which exactly

satises (9). Then

(i) no rm will adopt the new technology if e e;

(ii) all rms will adopt the new technology if e e.

Before we investigate the incentives of the three policy instruments under discussion,we consider socially optimal adoption of new technology.

4. The social optimum

To investigate the social optimum, we assume that a social damage function D(E)

evaluates aggregate emissions in monetary terms. This implies that only aggregate

emissions matter, not the location of rms. Assume further that the damage function

is increasing and convex in E, i.e. D(E) 0 and D(E) 0. If the new technology

is available, the social planner seeks to minimize total social costs:

mine0 ;eI; nI

{nI[CI(eI) +F] + [n nI]C0(e0) +D(nIeI+ [n nI]e0)}: (10)

The socially optimal allocation can be characterized as follows:

Proposition 2. There is an interval of xed costs [F; F] such that

(i) no rm should adopt the new technology for F F;

(ii) all the rms should adopt the new technology for F F;

(iii) for F (F; F) partial adoption is optimal. The optimal number of rms nI

adopting the new technology is decreasing in F. The optimal marginal dam-age MD(F) is increasing in F (F; F).

The proof is given in Appendix A. The intuition is straightforward. If the xed cost

of installing the advanced technology is extremely high, advanced abatement technology

should not be installed at all. In this case, the optimal emission level, E

, and the op-

timal marginal damage MD

are independent of F. If the xed cost is suciently low,

all the rms should adopt the new technology. In this case too, the optimal emission

level E and the optimal marginal damage MD are independent of F. For intermedi-

ate xed costs, partial adoption is optimal. The lower the xed costs, the more rms

should adopt the new technology, and the lower the corresponding marginal damagewould be. We are now ready to evaluate the performance of our policy instruments in

comparison with the socially optimal allocation.


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5. The incentives to adopt if the original policies have been set optimally

In order to make a judgement about whether some policy instruments provide too

little or possibly too strong incentives to adopt a cleaner technology, we haveto be more specic about the behavior of the regulator. In this section we assume

that the regulator does not anticipate the new technology and has made a commitment

to the level of his policy instrument for a suciently long period of time. Such a

commitment was made by the Clean Air Act Amendments 1990 with respect to the

total supply of permits. In some European countries, commitments to certain tax rates

were made independent of technological development. We further assume that the

regulator has set his policy to the optimal level with respect to the old technology.

Although not entirely realistic, this assumption serves as a useful benchmark (see the

criticism of Marin (1989)). For this purpose let 0 denote the optimal tax rate before

the new technology was available, L0 the corresponding optimal amount of permits, and

e 0=L0=n the corresponding uniform emission standard. Then we obtain the following

three results. All proofs are given in Appendix A.

Proposition 3 (Taxes): If the tax rate has been set to the optimal level; given the old

technology; there will be

(i) no adoption for F F (where F is dened in Proposition 2);

(ii) complete adoption for F F; and

(iii) for F=F ; the number of rms which adopt the new technology is ambiguous.

However; there is no positive incentive for any rm to adopt the new technology ;i.e. non-adoption is an equilibrium.

This result rests mainly on our assumption that the regulator has committed him-

self to maintaining the tax rate at the level 0 for a time horizon suciently long to

guarantee amortization of the investment. The intuition behind Proposition 3 can easily

be understood with reference to Lemma 1: according to Lemma 1, adoption is either

complete or totally absent for almost all tax rates. Only for one particular tax rate are

rms indierent about adopting and not adopting. This switching tax rate, however,

depends on the xed cost.

An important consequence of our result is that for F (F; F) too many rmswill adopt the new technology under taxes. In other words, for F (F; F) taxes in-duce over-investment. For permits, on the other hand, we obtain the following

result:

Proposition 4 (Permits): If the amount of permits has been set to the optimal level;

given the old technology; there is a xed cost F F such that

(i) there will be no adoption for F F;

(ii) there will be complete adoption for F F;

(iii) the number of adopting rms is less than optimal for F (F; F).

The intuition is that the more rms adopt the new technology, the lower the price

for permits. This induces some rms to free ride on decreasing permit prices and thus


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Fig. 6. Comparison in incentives by permits and standards, the case F=F.

reduces the incentive to adopt the new technology. Since the aggregate supply for

permits is not adjusted by assumption, the incentive to adopt is suboptimal.

Finally we consider uniform emission standards:

Proposition 5 (Standards): If the uniform emission standard has been set optimally;

given the old technology; there is a xed cost F with F F F such that

(i) no rm adopts for F F;

(ii) all the rms adopt for F F; and

(iii) for F = F; the number of rms adopting the new technology is not uniquely

determined. However; there is no positive incentive for any rm to adopt the

new technology.

Whether F is smaller or greater than F is ambiguous.

Fig. 6 illustrates the intuition underlying the result. If the xed cost of investment

is equal to F; and the original standard was equal to e= E

=n, then under permits

the incentive to invest for the rst rm is represented by the area A +B + C whereas

under a standard the cost saving corresponds to the smaller area A +B. By continuity,

some rms will invest in equilibrium for F slightly smaller than F under a permit

regime, whereas no rm will do so under a standard. A converse argument works

for F slightly greater than F. In that case, some rms will invest under permits in

equilibrium, whereas all rms want to invest under a standard.

The results of Propositions 35 are summarized in Fig. 7 and Table 1. In Fig. 7,

curve B denotes the socially optimal number of rms, curve C denotes the numberof rms that invest under permits, under curve A under taxes, and D under standards.

The results stand in sharp contrast to both the claims of Milliman and Prince and


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Fig. 7. Number of rms investing in the advanced abatement technology.

Table 1

Degree of adoption under dierent policies

Degree of adoption under

Range of F Taxes or Auctioned permits Command and control(Case F F) subsidies or grandfathering

F6 F Complete (optimal) Complete (optimal) Complete (optimal)

F (F; F] Complete (optimal) Under-investment Complete (optimal)

F (F;

F] Over-investment Under-investment Over-investmentF (F; F) Over-investment Under-investment Under-investment

FF No adoption No adoption No adoption

(optimal) (optimal) (optimal)

those of Jung et al. Surprisingly, for a considerable range of parameters, both taxes

and standards induce more rms to adopt a new technology than permits do. Although

environmentalists may prefer taxes and standards for this reason, from an economic

and thus from a broader social point of view we cannot rank taxes and standards

above permits in general. It will depend on parameters which of those instruments will

lead to the lowest welfare loss compared to the rst-best allocation.

6. Optimal policy in anticipation of the new technology

In the previous section, we assumed that the regulator does not know or anticipate the

new technology and thus adheres to the originally optimal policy level for a long period

of time. In this section we assume that the regulator either knows the new technology

before it is adopted, or learns about it after it has been adopted. We investigate two

dierent scenarios:

Timing A (Ex ante optimal policy): In the rst stage, the regulator makes a com-mitment to both the choice and the level of his policy instrument. In the second stage

the rms invest.


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Timing B (Ex post optimal policy): The regulator announces his policy instrument.

Then the rms invest. Thereafter, the regulator observes both the number of rms

adopting the new technology and the cost of the new technology, and then decides

about the level of his policy instrument. (Milliman and Prince refer to the latter asratcheting.)

6.1. Ex ante optimal policy

Consider rst the case where the regulator is the rst to move. Then the rms

observe the new tax rate or the total supply of permits, and then decide whether or

not to adopt the new technology. Denote by LI the optimal number of permits if the

new technology is available. Then we obtain the following result:

Proposition 6 (Ex ante optimal policy): If the welfare-maximizing regulator moves

rst; then:

(i) Under permits there is a unique subgame perfect equilibrium where the regulator

issues the socially optimal number of permits LI in the rst stage. In the second

stage; the socially optimal number of rms adopt the new technology.

(ii) Under taxes for both cases; F6F and FF; there exists a unique subgame

perfect equilibrium leading to a rst-best outcome. If F6F; the regulator sets

= MD in the rst stage; and all the rms adopt the new technology in the

second stage. If FF; the regulator sets =0= MD

in the rst stage; and

no rms adopt.For F (F; F) there are multiple equilibria. One of these equilibria is ecientbut there are also many inecient equilibria with too little and too much in-

vestment.

Proof. See Appendix A.

In the case of permits, the result is driven by the fact that the permit price decreases if

more rms adopt the new technology, whereas the tax is unaected by the rms be-

havior through the very timing of the game. Under taxes, rst-best outcomes can easily

be achieved if either no adoption or complete adoption is socially optimal. A problemarises for the regulator if partial adoption is socially optimal, i.e. for F (F; F). Foreach F a particular number of rms should invest for an optimal outcome. This would

require a lot of coordination between rms. Since rms, however, are indierent be-

tween investing and not investing if the tax rate equals the socially optimal marginal

damage which is a necessary condition for optimality inecient outcomes are likely

to occur in this case. Thus permits are better than taxes because with permits there is

a unique equilibrium that implements the ecient allocation.

6.2. Ex post optimal policy

We now consider the case where the regulator moves immediately after rms have

adopted the new technology. Here things look very simple:


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Proposition 7 (Ex post optimal policy): If the regulator sets his optimal policy after

observing the number of investing rms; then under both taxes and permits there is

a unique subgame perfect equilibrium where the optimal number of rms invests ; and

the regulator sets the rst-best tax rate; or issues the optimal number of permits;respectively. Standards; by contrast; induce only second-best allocations if partial

adoption of the new technology is optimal.

The intuition behind the result is that under the tax regime the regulator can now mimic

the permit market. Moving second, he can set the optimal price for pollution relative to

the number of rms which have adopted the new technology. Since the rms anticipate

this, the optimal number of rms will invest in the rst stage. If fewer than the optimal

number of rms invested in the rst stage, the marginal damage would be higher than

optimal. Hence the regulators response would result in setting a tax rate higher than

socially optimal (or in issuing a corresponding number of permits). But then it would

not have been optimal for the non-investing rms to refrain from investing, and an

allocation with less than the optimal number of rms investing would not have been

an equilibrium in the rst stage of the game. If, by contrast, more than the optimal

number of rms invested in the rst stage, the regulators response would result in

a tax rate (or the corresponding number of permits) lower than socially optimal. But

then some rms will be better o by not having invested. Thus, if the regulator can

react immediately after investment and the rms anticipate this, the rst-best outcome

is a subgame perfect equilibrium under the two market-based instruments.

Under standards, rst-best outcomes cannot be achieved through decentralized invest-ment decisions. This even holds true for both types of timings studied in this section.

The reason is that if partial investment were optimal, dierent emission levels are opti-

mal for rms with old and new technology, respectively. By its very nature, however,

a uniform pollution standard requires uniform emission levels for both types of rms.

7. Conclusions

The aim of this paper was to investigate the incentives provided by environmental

policy instruments to adopt advanced abatement technology. Our point of departure wasthe ranking of environmental policy instruments in the traditional literature, a ranking

derived by comparing aggregate cost savings rather than by investigating the rms

incentives to invest in equilibrium. We have called into question this methodology and

have demonstrated that the comparison of environmental policy instruments leads to

quite dierent results if the number of rms which adopt new technology is determined

endogenously through equilibrium considerations. In the framework of Milliman and

Prince (1989) and Jung et al. (1996), where the regulator is assumed to have set the

level of his policy instrument without anticipating a new technology, all that can be said

in terms of general policy rankings is that taxes (and subsidies on abatement) provide

higher incentives to invest than all other policy instruments under consideration. Underwelfare aspects, however, even this ranking breaks down. It depends on the parameters

which policy instrument will lead to lower welfare losses compared to the rst best.


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If the regulator, however, anticipates the new technology, we nd that price-based

instruments in particular taxes and all the permit regimes are equivalent and superior

to standards provided that the regulator implements the level of his policy instrument

immediately after rms have adopted the new technology. If, by contrast, the regulatormoves prior to the rms investment decisions, only permits will succeed in inducing

rst best allocation in all cases. Taxes may fail to do so if partial adoption of the new

technology is socially optimal. These results show that unlike other policy scenarios,

for instance monetary policy we do not run into a problem of commitment and time

consistency here. There is no need for the regulator to commit ex ante to a certain

level for his policy instrument. It suces to commit to the type of policy instrument

and to an immediate adjustment of this instrument as soon as rms have invested. The

level of the instrument, however, can be chosen after observing the rms investment

decisions.

One aspect not addressed in this paper is the explicit time dimension. The regulator

may learn about the new technology by observing its adoption and then respond with

policy adjustment after a certain, exogenously given, lapse of time. In a case like this, a

comparison between price and quantity policies is more dicult. As shown in Section

5, rms may over-invest under taxes and under-invest under permits if the regulator

sticks to the levels of his originally optimal policy for a suciently long period of time.

If the regulator has no choice but to delay his reaction to technology adoption, he may

prefer permits since he will be able to induce additional rms to invest by reducing

the supply of permits. By contrast, it is not feasible and does not make sense

to reduce the number of investing rms to the ex ante optimal level by adjusting thetax rate, since the investment is mostly irreversible. A detailed welfare analysis of a

situation like this, however, goes beyond the scope of this paper and has to be left to

further research.

Acknowledgements

We are grateful to Eberhard Feess, Hans Gersbach, Andrew Jenkins, Paul Mensink,

Armin Schmutzler, two anonymous referees, and especially the editor, Klaus Schmidt,

for their very helpful comments.

Appendix A

Proof of Lemma 1. We give the proof for taxes. The proof for the case of permits

is similar. From our assumptions on the abatement cost functions; (1) and (2) imply

e0 eI for any . Dierentiating the total cost dierence; i.e. the LHS of (3); w.r.t.

we obtain e0 eI by the envelope theorem. Thus; as increases; the total cost

dierential between the two types of rms also increases. Hence; Eqs. (1)(3) canhave at most one solution in . Since for = 0 the LHS of (3) is equal to F;and since for suciently large ; the LHS of (3) becomes positive; there exists at


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least one triple (; e 0; eI) which solves (1) (3). Dierentiating (3) w.r.t. F yields

d=dF= 1=(e0 eI) 0 by the envelope theorem.

Proof of Lemma 2. We proceed indirectly. One can easily show that the rms factordemand for permits decreases if the price for permits rises and only one technology is

available.

Consider rst the case L E and suppose . Then the LHS of (6) is positive.

Hence all the rms would adopt the new technology. Since by denition for =

aggregate pollution equals E if all the rms have adopted the new technology, at prices

the factor demand for permits cannot exceed E E. Thus the permit market

would not be in equilibrium ifL E. If= , the rms are indierent between staying

with the old technology or switching to the new one. Since the rms choose their

emission levels according to (1) or (2), respectively, the highest possible aggregate

factor demand for permits is E. Here again, the market for permits would not be in

equilibrium. Hence, must hold. Consider now the case L E. Following the

same arguments as in the rst case, one can show . Finally, assume E6L6E.

The arguments from the previous cases imply = . Since rms are indierent between

the two technologies, the factor demand for permits is nIeI+ n0e 0 and depends on the

number of rms nI which have purchased the new technology. Since the supply of

permits is unique, there must be a unique equilibrium (except for renumbering of

rms) such that L=nIeI+n0e 0. Solving for nI establishes (7).

Proof of Proposition 2. The Lagrangian of the maximization problem is given by

L= nI[CI(eI) +F] +n0C0(e0) +D(nIeI+n0e0) 0n0

InI (n0+nI n);

where i are the KuhnTucker multipliers of the non-negative constraints for nI and

n0=n nI. The rst-order conditions yield:

Ci (ei) +D(E) = 0; i= 0; I; (A.1)

Ci(ei) +eiD(E) +F i = 0; i= 0; I; (A.2)

eliminating yields:

CI(eI) C0(e0) + (eI e0)D(E) +F I+0= 0: (A.3)

First; suppose that there exists an interior solution; i.e. 0 =I=0. Dierentiating system

(A.1) and (A.3) w.r.t. F and using the envelope theorem in (A.3) yields:

Ci (ei)ei (F) +D(E)E(F) = 0; i= 0; I;

D(E)E(F)(e0 eI) 1 = 0; (A.4)


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where ei (F) = dei=dF and so on. This yields

E(F) = 1

D

(E)(e0 eI)

0; (A.5)

i.e. optimal aggregate emissions are increasing in F. Substituting (A.5) into (A.4)

yields ei (F) 0. Hence; optimal emissions of each rm are decreasing in F if it is

optimal for both types of rms to produce.

Now total emissions can be written as E(F) = nI(F)eI(F) + n0(F)e0(F). Dierenti-

ating this equation w.r.t. F and solving for nI(F) yields

nI(F) =E(F) nI(F)e

I(F) (n nI(F))e

0(F)

(eI e0) 0:

Now suppose thatFis large. Since CI(eI)C0(e0)+(eIe0)D

(E) must be bounded, Imust be positive for suciently large F, hence nI=0. Optimal aggregate emissions E

are given byAMAC0(E

)=D(E

). On the other hand, ifF0, 0 is clearly positive ifCI(eI)6C0(e0). IfCI(eI) C0(e0), the term CI(eI)C0(e0) must be smaller than (eIe0)D

(E) due to (2). Hence also 0 0 and thus n0=0. Optimal aggregate emissions E

are given by AMACI(E) =D(E), where AMACI(E) denotes the aggregate marginal

abatement cost ifall rms have adopted the new technology. As the social cost function

SC is strictly convex and all equations are continuous in F, the solution is unique and

continuous in F. Therefore the values F and F exist.

Proof of Proposition 3. Observe that the optimal tax rate before adoption is alwaysgiven by the intersection of the AMAC0 curve and the marginal damage curve. Hence

by construction we always have 0 =MD

. By Proposition 2 the optimal emission

level for FF is given by E

. Hence by construction of F the emission level before

adoption is always equal to E

. Now dene (F) as the tax rate which satises (3)

for given F; and observe that 0 = (F). Then for F F the LHS of (3) is clearly

negative and no rm will adopt the new technology. For F F the LHS of (3) is

positive and all the rms will invest. For F=F rms are indierent and there is no

positive incentive to adopt new technology.

Proof of Proposition 4. First observe that if the new technology is available; the so-cially optimal allocation could be implemented by issuing a quantity of permits equal

to the socially optimal emission level E. Hence the socially optimal marginal damage

after adoption is equal to the corresponding optimal permit price . Now if FF;

then it is socially optimal for no rm to adopt; and E =E

=L0. Since the new

socially optimal emission level is an equilibrium on the permit market; no rm will

adopt the new technology for FF. Next let F (F; F). Then partial adoption issocially optimal and E E E

. Note that Eq. (7) implies that nI is decreasing in

L. Hence; since E L0; fewer rms than socially optimal will adopt the new technol-

ogy for L=L0. Finally; let F6F. In this case; it is socially optimal for all rms to

adopt; and E =E. From the previous case; we know that a number of rms nI nwill adopt for F=F and L=L0. Dierentiating Eq. (7) w.r.t. F in the neighborhood

of F= F now yields nI(F) = n[e

0()eI+ e

I()e 0](F)=[e 0 eI]

2 0. Now observe


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that for F= 0 clearly all rms will adopt the new technology. Hence; there must exist

an F with 06 F F such that nI n for F F and nI=n for F6 F.

Proof of Proposition 5. By assumption; the initially optimal emission level is E

.Hence the originally optimal number of permits is L= E

and the optimal standard

is e = E

=n. Denote by (F) the permit price of the market; when the xed cost is F.

Now let F=F. Then (F) =MD

and the optimal marginal damage for F=F. In

this case no rm adopts; rms are indierent between adopting and non-adopting; i.e.

C0(e0((F))) CI(eI((F))) =F=A+B+C where the latter refers to Fig. 6. Ob-serve that e0((F))= e. Hence; C0( e)CI( e) =A +B F. By continuity we also haveC0( e)CI( e) C0(e0((F)))CI(eI((F))) forF slightly smaller than F. Hence somerms adopt under permits but no rm adopts under standards. ForF=F; the opposite is

true. We have complete adoption under permits and C0(e0((F)))CI

(eI

((F)))=A=F

(see Fig. 6) but C0( e)CI( e) =A +B F. Hence by continuity forFslightly greaterthan F; all rms will adopt under standards but only some rms will do so under

permits.

Proof of Proposition 6. (i) For permits the regulator sets L(F) =E(F); i.e. the per-

mit supply is equal to the socially optimal emission level contingent on F. If partial

adoption is optimal; then L(F) =n0 (F)e

0 (F) + (n n

0 (F))e

I(F); where n

0 (F) is the

optimal number of conventional rms and ej(F) the optimal emission level of the type

j rm contingent on F. Clearly; n0= n

0 is an equilibrium with =MD(F). This is

so because; given that (2) holds; Eq. (6) is satised for those values. Now we showthat n0 = n

0 cannot be an equilibrium: for n0 ()n

0 ; clearly ()MD(F); and

hence n0e0() + (n n0)eI() ()L(F):(ii) For F F and F F the result is obvious. Now let F F F. Recall that

MD(F) denotes the socially optimal marginal damage if the xed investment cost is

F. If the regulator sets a tax such that =MD(F), then by (2) rms are indierent

between adopting and not adopting. Hence for M D(F) all the rms adopt the

new technology, whereas for MD(F) no rm will. If in the case of indierence

we make the additional behavioral assumption that no rm will adopt, rst-best cannot

be implemented and either all rms or no rm will adopt. The regulator then has to

decide between =MD

or=MD

depending how close F is to F orF, respectively.For standards the socially optimal allocation can obviously not be achieved if partial

adoption is socially optimal.

Proof of Proposition 7. In stage 1 the rms decide whether or not to invest. In stage

2 the regulator sets the optimal tax level; permit supply; or environmental standard;

contingent on the number of rms having invested. Assume that under taxes fewer than

the socially optimal number of rms adopt the new technology. Then the regulator sets

the tax higher than MD(F). But then it would have been better for those rms that

have not invested in stage 1 to have done so. Thus this is not an equilibrium. Under

permits; the regulator issues a higher number of permits than L(F) if fewer than theoptimal number of rms have invested. In this case; however; the permit price is also

higher than socially optimal. Then again it would have been better for those rms that


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have not invested in stage 1 to have done so. A similar argument holds if more than

the optimal number of rms have invested in stage 1.

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