On reducing the windfall profits
in environmental subsidy programs∗
Carmen Arguedas+ and Daan P. van Soest++
+
Departamento de Teoría e Historia Económica, Universidad Autónoma de Madrid
++
Department of Economics and CentER, Tilburg University
October 30, 2008
Abstract
Investment subsidies are widely used to induce adoption of new technologies that
are able to reduce emissions at lower (marginal) cost. To economize on the amount
of subsidies provided, governments would like to distinguish between firms that need
to receive a subsidy to adopt a new technology, and firms that would adopt that
technology even without subsidies. We show that policies consisting of a menu of
emission taxes and investment subsidies can induce firms to self-select. But we also
find that such separating policies do not necessarily result in lower social costs.
JEL Codes: D82, H23, Q52.
Key words: Investment subsidies, environmental policy, abatement technology
adoption, asymmetric information.
∗
Please send all correspondence to: Daan van Soest, Tilburg University, Department of Economics,
P.O. Box 90153, 5000 LE Tilburg, The Netherlands; email: [email protected], tel: +31—13—466 2072;
fax: +31 13 466 3042. Carmen Arguedas gratefully acknowledges the hospitality of CentER, Tilburg
University, where part of this paper was written, and financial support from the Spanish Ministry of
Education under research project SEJ2005-05206/ECON. Daan van Soest is grateful to the Netherlands
Organization for Scientific Research (NWO) for financial support as part of the NWO/Novem research
program. The authors thank Jan Boone, Bouwe Dijkstra, Larry Kranich, Till Requate, Marta Risueño,
Herman Vollebergh, Cees Withagen and two anonymous referees for valuable comments on an earlier
version of this paper.
1
1
Introduction
Subsidies rank high among the instruments most frequently used in environmental policy
making (Parry [37]). In some instances, they are simply the most efficient instrument
to achieve certain environmental objectives. Examples include the use of subsidies to
stimulate investment in abatement technologies if there are positive adoption spillovers
(Schneider and Goulder [45]), to foster the use of clean inputs if pollution itself is unobservable (Stranlund [49], Fullerton and Mohr [14], Fullerton and Wolverton [15]), and to
complement pollution taxes in case of imperfect competition (Loeb and Magat [28], Kim
and Chang [24]). But subsidies may also be the preferred instrument because of ‘political
economy’ considerations such as concerns about the potential negative impact of other
environmental policy instruments on an industry’s international competitiveness (Baumol and Oates [4]), distributional fairness considerations (Johnson et al. [19]), political
self—interest (Fredriksson [12], but also Aidt [1]), etc.1
Independent of the reason why subsidies are being used, society always has a stake in
reducing the amount spent, especially if subsidies generate windfall profits for the agents
receiving them. If subsidies were straightforward transfers between the government and
the recipients, there would be no welfare loss associated with giving agents more money
than strictly necessary to compensate them for the costs incurred when undertaking the
desired action. However, in most instances raising funds for subsidies requires exacerbating tax distortions elsewhere in the economy, imposing a loss on society in the range of
$0.20—$0.30 for every $1 raised (Ruggeri [44]; see also Laffont and Tirole [25] and [26]).
1
For a detailed overview of (the political economy) arguments regarding instrument choice, see Dietz
and Vollebergh [11].
Of course it would be easy for the regulator to eliminate all windfall profits if she knew
the ‘reservation subsidy level’ for each individual agent, but obtaining such agent—specific
information is in many instances prohibitively expensive (cf. Kim and Chang [24] and
OECD [35]). Therefore, the question is whether a mechanism can be designed that induces agents to self—select into different groups, ranked according to the minimum amount
of money needed to compensate them for providing the desired action.
In this paper we take the first step in answering this question by solving the problem
for straightforward (lump sum) investment subsidies.2 These subsidies are used very
frequently in practice (Jenkins and Lamech [18], OECD [34]) and can be highly effective
in stimulating diffusion of new technologies. The regulator can induce any number of firms
to adopt by offering a sufficiently large subsidy such that the private adoption benefits3 of
all targeted firms are (weakly) higher than their investment cost net of this subsidy. But
unless all targeted firms face identical adoption benefits, this policy gives rise to windfall
profits in the industry. Whereas the subsidy may only be just sufficient to induce adoption
by some firms, others actually obtain a net gain —some may even collect the subsidy while
they would have adopted the new technology anyway. Indeed, empirical studies suggest
2
Despite its societal importance, mechanisms to reduce windfall profits have received surprisingly
little attention in the environmental economics literature. Indeed, as is evidenced by recent surveys of
the literature on technology adoption (see for example Jaffe et al. [16], Nelissen and Requate [33], Requate
[42], and Stavins [50]), most attention has been paid to the effectiveness of taxes, quotas, performance
standards, and permits (e.g., Jung et al. [21], Milliman and Prince [32], Requate [40]—[41], and Requate
and Unold [43]). Also, and probably as a consequence of the difference in focus on policy instruments, the
issue of the social costs of raising funds has not received much attention. Indeed, the bulk of the literature
either ignores the issue or rather focuses on the (existence of a) ‘double dividend’ of environmental policies
—i.e., pollution taxes fostering abatement while at the same time raising funds to reduce distortive taxes
elsewhere; see De Mooij [10] for an overview. An exception is Parry [37], who analyzes the efficiency cost
of financing subsidies by distortionary taxation, as well as the interaction of these taxes with pre—existing
distortions in the economy.
3
These include, among others, savings on the amount of physical inputs used (e.g., in case of energysaving technologies) and savings on the firm’s environmental tax bill.
3
that the incidence of firms receiving windfall profits in environmental investment subsidy
programs may be as high as 50—60% (e.g., Joskow and Maron [20], Malm [30], and Wirl
and Orasch [54]). Therefore, studying whether and how the windfall profits in technology
adoption subsidy programs can be mitigated is relevant in itself. But the analysis may
provide useful insights into the feasibility of reducing transfers in other environmental
subsidy programs as well.
In this paper, we consider an industry composed of two types of firms that differ
with respect to their abatement costs associated with the use of both the current (or
old) abatement technology, and a new one that is on the market. As a result, the two
firm types also differ with respect to their net benefits associated with adopting the new
technology. Each firm knows its type, but the regulator only knows the number of firms
of each type in the industry. The use of subsidies is motivated in our model by assuming
that there are political economy costs that are an increasing function of the environmental
tax level. Whereas such political economy costs are likely to be a convex function of the
pollution tax rate, we take the simplified approach of assuming a step function: costs are
zero below a certain tax level, and infinitely high above that level. We assume that the
regulator wants all firms to adopt, but that the maximum tax level is too low to induce
industry—wide adoption. Hence, subsidies are needed to complement the tax instrument.4
Given the two instruments available (the constrained pollution tax, and lump—sum
4
We assume that there are just two types of firms in the industry, and that both should be induced
to adopt. However, our model can be generalized to the case of an industry consisting of M > 2 firm
types, where the regulator wishes to induce K types to adopt (M ≥ K ≥ 2). K ≥ 2 implies that there
are potential gains from separating the K types. The same analytical tools developed for analyzing the
case M = K = 2 can be used for M > 2, independent of whether full adoption (M = K > 2) or partial
adoption (M > K > 2) is socially optimal. We focus on M = K = 2 for expositional clarity but we check
the robustness of our results in Section 5.
4
subsidies), the regulator may try to construct a menu of tax/subsidy combinations to
induce firms to self—select (a separating policy), or just impose a uniform policy on all firms
within the industry (i.e., where a specific pollution tax level and a specific subsidy level
apply to all regulated firms).5 Intuitively, one may think that constructing such a self—
selecting policy scheme is a formidable task, but also that if successful, such a separating
policy must be unambiguously preferred to even the best uniform policy. Interestingly, we
find the exact opposite. It is always feasible to construct a set of tax/subsidy combinations
such that firms do self—select, but we also find that separating policies do not necessarily
result in lower social costs than the best uniform policy.
The intuition behind these results is as follows. Separating requires offering two
tax/subsidy combinations, with the tax rate and the subsidy level being lower in one
combination than in the other (if not, all firms would strictly prefer the one with the
lower taxes and higher subsidies). Because of cost—effectiveness considerations6 , the government wants the type that needs the weakest incentives to adopt (i.e., the one that
benefits most from adoption) to opt for the policy combination with the low subsidy level
(and also the low tax rate), and the type that gains least to opt for the other combination.
Offering a lower tax rate is socially costly because of the reduced incentives to abate, but
if the associated subsidy level can be decreased sufficiently, net social costs may fall.
But what determines whether a type actually chooses one policy combination or the
other? In other words, under what circumstances is the government’s preferred policy
5
Note that because all firms are free to choose which tax/subsidy policy they wish to be regulated by,
political feasibility may not be an issue here. As long as there is free choice and equal access, there is no
unfair preferential treatment or discrimination involved. For examples of policy menus used in practice,
see the Danish and Spanish cases discussed below.
6
That is, trying to induce all firms to adopt the new technology at minimum social cost.
5
incentive compatible? The key determinants here are the marginal abatement costs of
the two types when using the new technology. The lower the marginal abatement costs,
the more pollution is abated and hence the smaller is the pollution tax base. And the
smaller the tax base, the larger the increase in the pollution tax rate firms are willing to
accept for an extra dollar of subsidies. That means that the more efficient firms tend to
prefer the higher tax/subsidy combination.
So what does this tell us about the feasibility and desirability of separation? Because
the low marginal abatement cost firms are more prone to choosing the high tax/subsidy
combination, it is always possible to separate the two firm types by making the difference
between the two tax/subsidy combinations sufficiently large. But if the low marginal
abatement cost firms happen to be the ones that gain most from adoption (i.e., they are
the ones that need the smallest incentives to adopt), separation implies paying the largest
subsidies to the type that needs them least. Hence, a necessary condition for separation
resulting in lower social costs is that the firm type with the lower marginal abatement
costs is also the type that gains least from adopting.
We focus on combinations of taxes and subsidies because of two reasons. The first is
that the joint use of these two instruments has received a substantial amount of attention
in the economics literature as a means to implement environmental policies in second—
best situations due to the presence of asymmetric information, market power, etc. (see for
example Carraro and Siniscalco [8], Dasgupta et al. [9], Kim and Chang [24], Lewis [27],
Segerson [46], Sheriff [47], and Spulber [48]; see Alberini and Segerson [2] and Khanna
[23] for useful overviews of this literature). The second reason is that many countries use
combinations of taxes and subsidies to implement their environmental policies regarding
6
for example CO2 emissions reductions and habitat conservation, including, among others,
Australia, Denmark, Finland, Italy, Japan, the Netherlands and the United States (see
OECD/IEA 2008). Many of the policies in place are just uniform policies (in the sense
of imposing the same tax rate on and offering the same subsidy level to all firms in
the regulated industry). But given that the two instruments are used jointly already,
these countries are likely to be willing to consider the advantages of offering a menu
of tax/subsidy combinations. And indeed a couple of examples are available of policies
that offer such menus in practice. Since 2000, the Danish Energy Agency offers firms
in energy—intensive sectors (such as paper, food and beverages, and the steel industry)
combinations of differentiated CO2 tax rates and differentiated subsidies (direct transfers,
but also in the form of tax rebates) depending on the energy—saving technologies adopted
(OECD [35]). And the Spanish government offers a menu of subsidies and feed—in tariffs
to firms to stimulate renewable—resource—based electricity generation (UNEP [51]).
Obviously, our proposal to use taxes and subsidies as instruments to reduce windfall
profits in environmental subsidy programs does not mean that this is the only way in
which the problem can be addressed. One alternative approach is to undertake extensive
firm audits, trying to identify all possible investment projects that could be undertaken
by each firm to reduce its emissions and then offering firms to compensate them for
all costs involved. Indeed, in the period 1995—2000 the Danish Energy Agency tried to
reduce Denmark’s emissions of CO2 by undertaking detailed audits of firms in several
energy—intensive industries; see OECD [35]. All audited firms were compensated for their
investments, and the level of detail of the information obtained was such that the windfall
7
profits obtained were very small — but at the cost of very high transaction costs indeed.7
This paper suggests that the Danish Energy Agency could also have decided to send
auditors to a representative sample of the industry, asking them to identify types of firms,
and then use combinations of subsidies and taxes to induce the socially optimal level of
adoption. A second alternative approach is to use investment subsidies in combination
with instruments other than taxes. However, the results we obtain using tax/subsidy
combinations also hold when using quota/subsidy combinations instead.
By focusing on investment subsidies and assuming that the regulator is constrained
in the use of the tax rate, our model’s results are of direct relevance to all the programs
where the purchase of environmentally friendly technologies is subsidized even if there are
neither (sizable) positive spillovers from adoption nor information asymmetries regarding
polluting input use (as is the case for many of the subsidized technologies in the US Energy
Policy Act of 2005 (Public Law 109–58–Aug. 8 2005)). In these instances policy makers
are effectively unwilling to charge the Pigovian tax to induce the socially optimal level of
adoption (cf. Requate and Unold [43]), and this is captured in our model by assuming
a maximum level for the tax rate below the Pigovian level. But our model is also likely
to provide useful insights in other instances in which environmental subsidies are being
used. Indeed, our characterization of the key factors determining desirability of separation
is very general and is likely to be applicable to many other situations too. Two direct
applications are the Utility Conservation programs as analyzed by Wirl [52], [53], and
Wirl and Orasch [54], and the Payment—for—Ecosystem Services programs as analyzed by
7
This is illustrated by the fact that the Danish Energy Agency discontinued undertaking detailed
audits from 2000 onwards (OECD [35]).
8
Wu and Babcock [55]. In both programs there is a conflict between cost effectiveness and
incentive compatibility very similar to the problem we analyze.
The remainder of the paper is organized as follows. In Section 2, we present the model.
In Section 3, we explore the possible conflict between cost effectiveness and incentive
compatibility. We do so by determining how behavior of the two firm types is affected
by different tax/subsidy schemes, and how this difference in behavior can be used to
induce separation. In Section 4, we identify the conditions under which separating can
be welfare enhancing. In Section 5, we analyze the robustness of our results under more
general assumptions, and our conclusions ensue in Section 6. For the reader’s convenience,
a table with all the notation is presented in Appendix 1. The proof of the main result of
the paper (Proposition 1) is in Appendix 2.
2
2.1
The model
Technology description
We consider an industry composed of two firm types (with at least one firm of each
type). Firms of the two types emit a homogeneous pollutant but differ with respect to the
efficiency with which they can abate emissions. The two firm types are indexed i = 1, 2,
and emissions of firms of type i are denoted by ei > 0. Independent of its type, we assume
that each firm produces 1 unit of emissions unless it engages in abatement (i.e, 0 < ei
≤ 1). Using qi to denote the number of firms of type i (qi ≥ 1 for i = 1, 2), the industry’s
total amount of emissions is E = q1 e1 + q2 e2 ≤ q1 + q2 . Environmental damage D is
assumed to be increasing in emissions (D(E)). Using prime notation to denote first and
second derivatives, we assume D > 0 and D ≥ 0.
9
The costs of emission abatement depend on the type of technology used and on the
amount of emissions abated. Both firm types currently use an abatement technology that
results in type—specific abatement costs equal to Ci (ri ), where ri = 1 − ei is the amount
of emissions abated when using this technology. We assume Ci (ri ) > 0, Ci (ri ) > 0 for
ri > 0, and Ci (0) = 0, Ci (0) = 0. Without loss of generality, ‘firms of type 1’ have the
lowest marginal abatement costs for each level of abatement using the current technology:
C2 (r̄) > C1 (r̄) > 0 for all r̄ ∈ (0, 1].
There is also a new abatement technology which enables firms to abate emissions
at lower marginal costs. For simplicity, the costs of adoption are assumed to be the
same for the two firm types, and are equal to I > 0.8 The associated variable costs are
firm—type specific and are denoted by Vi (Ri ), where Ri denotes the amount of emissions
abated by firms of type i when using the new technology. Lower marginal cost implies
0 < Vi (r̄) < Ci (r̄) for all r̄ ∈ (0, 1]. Furthermore, we assume Vi (0) = 0, Vi (0) = 0, and
Vi (Ri ) > 0 for all Ri ∈ (0, 1].
Regarding the higher order derivatives of Ci (ri ) and Vi (Ri ), we are silent for the
moment on the relative values of the second derivatives — they play a key role in the
analysis, and hence receive due attention later on — but assume that all third derivatives
are negligible.
8
As will become clear below, assuming that firms face different investment costs complicates the
analysis without adding new insights. All that matters is that firms (i) have different marginal abatement
costs when using the new technology, and (ii) have different net private benefits of adoption (= gross
benefits of adoption minus the investment costs). We come back to the consequences of relaxing the
assumption of identical investment costs in Section 5.
10
2.2
The agents’ objectives
There are two types of actors in this model: the firms and the regulator. Firms minimize
private costs, choosing the technology type as well as the optimal abatement level. The
regulator minimizes social costs, consisting of the sum of the costs incurred by each firm
type, the environmental damage, and the deadweight losses associated with her policies.
The regulator has two instruments to influence firm behavior: per—unit emission tax rates
(τ ≥ 0) and lump—sum investment subsidies (S ≥ 0). Each firm takes these levels as
given, and the associated compliance costs (Ki (S, τ )) are the result of its decisions with
respect to investment and abatement:
Ki (S, τ ) = min {(1 − φi ) [Ci (ri ) + τ (1 − ri )] + φi [Vi (Ri ) + τ (1 − Ri ) + I − S]} , (1)
ri ,Ri ,φi
where φi is an indicator function which equals 1 if firm type i adopts the new technology,
and zero otherwise.
The firm solves this minimization problem as follows. First, when using the old or
new abatement technology, the optimal abatement levels are determined implicitly by
Ci (ri ) = τ or Vi (Ri ) = τ ,
(2)
respectively. Using ri (τ ) and Ri (τ ) to denote the solutions of (2), the firm then
calculates the net benefits it obtains when using the new technology:
Bi (S, τ ) ≡ Zi (τ ) + S − I,
(3)
where Zi (τ ) ≡ Ci (ri (τ )) − Vi (Ri (τ )) + τ (Ri (τ ) − ri (τ )) are the variable cost savings
(abatement cost savings plus tax savings) associated with adoption (also referred to as
11
the private adoption benefits of firms of type i), and I − S are the net investment costs.
Firms of type i set φi = 1 if Bi (S, τ ) ≥ 0, and zero otherwise.
Regarding the information asymmetries between the regulator and the firms, we assume that each firm knows its type, but the regulator only knows the number of firms of
each type in the industry (q1 and q2 ). The regulator can use taxes and subsidies (potentially differentiated between firm types) to influence the adoption and abatement behavior
of firms, and aims to minimize the following social cost function:
SC (S1 , S2 , τ 1 , τ 2 ) =
2
qi [(1 − φi ) Ci (ri ) + φi Vi (Ri ) + φi I] + D(E) + F (ST ) ,
(4)
i=1
where ST =
2
i=1 qi φi Si
are the total subsidies provided (conditional on adoption; φi = 1),
and F (ST ) denotes the social costs of raising subsidies (with F (0) = 0, F > 0 and
F ≥ 0).9
Given our two firm type setup, the interesting case for our study is the one in which
full adoption of the new technology is socially optimal (see footnote 4). We therefore
implicitly assume that marginal damage is sufficiently high or that investment costs are
sufficiently low such that full adoption is optimal. That means that if the regulator sets
the tax rate equal to the Pigovian level τ E = D (E), where D (E) = Vi (Ri ), all firms
find it in their interest to adopt — even with zero subsidies (cf. Requate and Unold [43]).
As stated in the introduction, we motivate the use of subsidies by assuming that there
are ‘political economy costs’ which are zero for tax levels below a certain threshold τ
9
Note that we treat the tax revenues as a pure transfer between the firms and the government, and
hence interpret the F function as the extra costs associated with raising funds. Alternatively, it can be
argued that it is not the gross subsidies that should be taken into consideration, but the subsidies net
of pollution taxes, F ST − 2i=1 qi τ i ei . We postpone discussing the consequences of this alternative
specification to Section 5.
12
(where τ < τ E ), and infinitely high above it. That means that there is effectively a
constraint on the tax rate: τ ≤ τ . A uniform policy that results in full adoption (with
τ ∗ = τ and S ∗ = S̄ H ≡ I − min{Z1 (τ̄ ) , Z2 (τ̄ )}) gives rise to windfall profits for one
type. But we assume that uniform policies that induce partial adoption or complete
non—adoption are more costly:
SC (0, τ̄ ) ≥ SC (S̄ L , τ̄ ) > SC(S̄ H , τ̄ ),
(5)
where S̄ L ≡ max{0, I − max{Z1 (τ̄ ) , Z2 (τ̄ )}} is the minimum subsidy needed to induce
adoption by the type that gains most from investing.
Since subsidies are socially costly, it may be in the interest of the regulator to give
smaller subsidies to the firms that have the largest gross benefits of adoption. Of course,
such separating policies need to be incentive compatible, that is they have to meet the
following condition:
Ki (Si , τ i ) ≤ Ki (Sj , τ j ) .
(6)
In words, a pair of tax/subsidy combinations is incentive compatible if firms (weakly)
prefer the tax/subsidy scheme designed for its type.10
The timing of the model is as follows. First the regulator announces the terms of the
policy. Second, firms respond by choosing the policy combination and decide whether
or not they adopt. Next, they collect their subsidies (if any, and if they are entitled to
receive them), and then they choose their abatement levels.
10
The regulator needs a mechanism to elicit firms’ private information. By the revelation principle
(Fudenberg and Tirole [13]: 255), we can concentrate on direct mechanisms where
the
regulator
asks
the firms to report their type, i, and then sets a policy contingent on the report, τ i , S i , that
induces each firm to reveal its true type, i. For simplicity, we assume that if a firm isindifferent
between
announcing any of the two types, then it announces the true one. We denote τ i = τ i , Si = S i .
13
3
Cost effectiveness and incentive compatibility
For our purposes, the most important information required is (i) which firm type needs
the largest subsidies to adopt (cost effectiveness) and (ii) which type prefers the policy
combination with the largest subsidies and taxes (incentive compatibility). Interestingly,
both are determined by the locations of the marginal abatement cost functions firms have
when using the old and the new technology.
Regarding cost effectiveness, let us first calculate the benefits of adoption using the
standard graphical representation (cf. Milliman and Prince [32], Palmer et al. [38], and
Requate and Unold [43]); see Figure 1. Suppose the regulator imposes a tax rate τ . When
using the old (new) technology, firm i abates up to the point where the relevant marginal
abatement costs (Ci (ri ) or Vi (Ri )) are equal to this tax rate; see (2). That means that
given tax rate τ and when using the old (new) technology, the abatement costs of firm
i are abc (ab c ) and its tax bill is bdd c (b dd c ). That means that the variable cost
savings associated with adoption, Zi (τ ) , are equal to the area abb . And type i adopts if
Zi (τ ) ≥ I − S.
So which firm type’s private benefits of adopting are largest, those of type 1 or type
2? From Figure 1 we immediately see that the size of Zi (τ ) depends on the horizontal
distance between type i’s marginal abatement cost functions when using the old and the
new abatement technology, as reflected by the difference in abatement levels using the new
and the old technology (Ri (τ ) − ri (τ )). Given that we assume that the third derivatives
of the abatement cost functions are negligible, the horizontal distance at any tax level (or
the difference in abatement activity, Ri (τ ) − ri (τ )) is larger the larger the difference in
14
$
Ci’
Vi’
Zi (τ)
b
τ
a
b’
d
c
c’
ri(τ)
Ri(τ)
d’
1
1-ei
Figure 1: Technological progress and the benefits of adoption.
the slopes of the old and new marginal abatement cost functions. The formal condition
for Z1 (τ ) being larger or smaller than Z2 (τ ) is given in Lemma 1.
Lemma 1 Zi (τ ) > Zj (τ ) for all τ > 0 if and only if (Ci − Vi ) Cj Vj > Cj − Vj Ci Vi .
Proof. Differentiating Zi (τ ) ≡ Ci (ri (τ )) − Vi (Ri (τ )) + τ (Ri (τ ) − ri (τ )) with respect
to τ and using (2), we have Zi (τ ) = Ri (τ ) − ri (τ ) > 0. Then, Zi (τ ) = Ri (τ ) − ri (τ ) =
1
Vi
− C1 =
i
Ci −Vi
,
Ci Vi
which is a constant. Our assumptions Ci (0) = Vi (0) = 0, 0 < Vi (r̄) <
Ci (r̄) for all r̄ ∈ (0, 1] and negligible third order derivatives imply Ci − Vi > 0, and
hence Zi > 0. Since Zi > 0 and Zi (τ ) > 0 for all τ > 0, straightforward integration
yields Zi (τ ) > Zj (τ ) for all τ > 0 if and only if
Ci −Vi
Ci Vi
>
Cj −Vj
.
Cj Vj
Therefore, cost effectiveness dictates that the regulator gives the largest subsidies to
type j if and only if Cj − Vj Ci Vi < (Ci − Vi ) Cj Vj .
15
To be able to determine whether cost effective policies are also incentive compatible,
we describe firm behavior using two (sets of) functions for each firm type: its adoption
barrier and its (set of) isocost curve(s). The adoption barrier is the combination of all
policies (S, τ ) such that a firm of type i is indifferent between adopting and not adopting;
Bi (S, τ ) = 0 (cf. (3)). An isocost curve consists of all (S, τ ) under which the firm
incurs the same costs, dKi (S, τ ) = 0. The set of isocost curves represents the firm’s
costs associated with each policy combination (S, τ ). The relevant characteristics of these
functions are described in the following lemmas.
Lemma 2 Each firm type’s adoption barrier Bi (S, τ ) = 0 is downward sloping in (S, τ )
dτ space ( dS
< 0). Also, for τ > 0, Bi (S, τ ) > Bj (S, τ ) if and only if Zi (τ ) > Zj (τ ).
Bi =0
Proof. Because 0 < Vi (r̄) < Ci (r̄) for all r̄ ∈ (0, 1], equation (2) yields Ri (τ ) > ri (τ )
for all τ > 0. Total differentiation of the adoption barrier Bi (S, τ ) = 0 (cf. (3)) yields:
dτ −1
=
< 0.
dS Bi =0 Ri (τ ) − ri (τ )
(7)
The second part of the Lemma is trivial, by (3).
Lemma 3 The set of isocost curves of a firm of type i consists of weakly increasing
functions in (S, τ ) space, differentiable in every point except on the adoption barrier Bi =
0, and such that costs (weakly) fall with lower taxes and higher subsidies. Also, at any
(S, τ ) such that Bi > 0 for all i, the corresponding isocost curve for a firm of type i is
strictly steeper than that of a firm of type j if Vi R < Vj R for all R ∈ (0, 1] .
Proof. Using (1) and (2), we have ∂Ki /∂τ = (1 − φi ) (1 − ri ) + φi (1 − Ri ) > 0 and
16
∂Ki /∂S = −φi ≤ 0. Setting dKi = 0, we have
0
dτ =
1
>0
dS dKi =0
1−Ri (τ )
if φi = 0
.
if φi = 1
(8)
To prove the second part of the lemma, note that Vi R < Vj R for all R ∈ (0, 1]
implies Ri (τ ) > Rj (τ ) for all τ , by (2) . Therefore, we have
φi = φj = 1.
dτ dS dKi =0
>
dτ dS dKj =0
> 0 if
In Figure 2 we depict an example of the adoption barrier and one isocost curve for each
firm type for the case (a) (C1 − V1 ) C2 V2 < (C2 − V2 ) C1 V1 and (b) V1 R < V2 R
for all R ∈ (0, 1].11 For type i, barrier Bi = 0 divides the set of policies into two regions.
To its right, type i’s net benefits of adoption are positive (Bi ≥ 0) and the firm decides to
adopt (φi = 1); to its left, the net adoption benefits are negative and the firm decides not
to adopt (Bi < 0; φi = 0). Increasing either the tax rate (along the vertical axis) or the
subsidy level (along the horizontal axis) makes adoption more attractive. And (a) implies
that type 1’s adoption boundary is located to the right of that of type 2 (by Lemmas 1
and 2).12
The isocost curves are strictly upward sloping in each type’s adoption region, and
horizontal in its non—adoption region (as the firms are not entitled to receive any subsidies
when they do not adopt); see Lemma 3. The further to the South—East an isocost curve
is located, the lower the associated total costs (lower taxes, or larger subsidies). And (b)
implies that for any tax/subsidy combination in the full adoption region (B1 (S, τ ) ≥ 0,
11
Our assumptions regarding the curvature of the abatement cost functions are such that the iso-cost
curves and adoption barriers are, in fact, convex functions in (S, τ ) space. We have simplified this figure
by drawing them as straight lines, but this does not affect the interpretation of the results in any way.
12
The only point of intersection of the two firm types’ adoption barriers is at τ = 0, since Z1 (0) =
Z2 (0) = 0. Equation (3) then implies that Si = I for i = 1, 2.
17
τ
K1
K2
Decrease in
firms’ costs
(S1, τ1)
(0, τ2)
B2=0
B1=0
I
S
Figure 2: The adoption boundaries and isocost curves, and a separating policy (for the
case where V1 (R̄) > V2 (R̄) and (C1 − V1 ) C2 V2 < (C2 − V2 ) C1 V1 ).
i.e. where φ1 = φ2 = 1), the corresponding isocost curve of type 1 is strictly steeper than
that of type 2 (see Lemma 3). The economic interpretation is the following. Consider a
one dollar increase in the amount of subsidies offered. Given this one dollar increase, the
type that is ultimately most efficient (that is, when using the new technology) can incur a
larger increase in the tax level and still remain at the same isocost curve. Emission taxes
are paid over the amount of unabated emissions (1 − Ri ), and these are smallest (all else
equal) for the type that is most efficient in abatement upon adoption.
Figure 2 can be used to identify uniform policies as well as sets of separating policies
that induce full adoption and are incentive compatible. Any uniform tax/subsidy combination on or to the northeast of the adoption barrier B1 = 0 will induce both firms to
adopt. An example of a separating policy is the menu (S1 , τ 1 ) and (0, τ 2 ). Here, both firm
18
types are indifferent between the two tax/subsidy combinations and hence, by assumption, each firm chooses the combination targeted at its type.13 So, (S1 , τ 1 ) and (0, τ 2 ) are
an example of a separating policy menu, where the type that needs largest subsidies to
adopt (type 1) also ends up receiving the largest amount of subsidies.
4
Separating or uniform policies?
The regulator has to find the combination of taxes and subsidies that minimizes the social
cost function (4) , ensuring that both types adopt the new technology (φ1 = φ2 = 1), and
that the incentive compatibility constraint (6) is met. The complete information policy is
trivial. Since τ < τ E , the sum of abatement costs and external damages decreases if the
tax is increased towards the Pigovian level, and hence τ c1 = τ c2 = τ (where superscript c
denotes the optimal solution under complete information). And to ensure full adoption
at minimum subsidies, Sic = max{0, I − Zi (τ )}. But clearly, this policy is not incentive
compatible in case of asymmetric information: all firms would prefer the contract with
the largest subsidy, since the tax rate τ is the same in both contracts.
Under asymmetric information, the incentive compatibility constraint is trivially met
when imposing a uniform policy where τ 1 = τ 2 = τ ∗ and S1 = S2 = S ∗ . Taxes should be
set such that they give the maximum incentive to abate and adopt, and hence τ ∗ = τ .
To ensure full adoption, we need S ∗ = I − min{Zi (τ ) , Zj (τ )}, so one firm type ends up
obtaining windfall profits.14
13
The assumption of ‘in case of indifference, firms choose the policy combination targeted at their type’
is made for expositional simplicity only. To make firms strictly prefer the policy aimed at their type, we
only need to move (S1 , τ 1 ) infinitesimally to the North-East into the region between K1 and K2 .
14
For example, in Figure 2 B2 = 0 is located to the South—West of B1 = 0. For any given tax rate,
uniform subsidies need to be such that type 1 firms are indifferent between adopting and not adopting.
19
We now ask whether it is possible to reduce social costs (and therefore, total windfall profits) by designing a separating policy, such that each firm actually prefers the
tax/subsidy combination targeted at its type. That is, we ask whether an incentive—
compatible separating policy menu can be socially preferred to the optimal uniform policy.
As shown in Section 3, the two crucial characteristics for separation are (i) which type
is the most efficient upon adoption (as identified in Lemma 3), and (ii) which type gains
most upon adoption (see Lemma 1). Because we arbitrarily assumed that type 1 has the
lowest marginal abatement costs when using the old technology, we are left with three
cases: (a) type 1 gains least when adopting but remains most efficient upon adoption,
(b) type 1 gains most from adoption and also remains most efficient upon adoption, and
(c) type 2 gains most when adopting and also becomes most efficient when adopting.
These three cases can be labelled convergence, divergence and overtaking, respectively,
for reasons that become obvious momentarily. The case of convergence (a) is presented in
Section 4.1, and divergence (b) and overtaking (c) are discussed in Section 4.2. Practical
issues regarding the implementation of separating policies are discussed in Section 4.3.
4.1
The case of convergence
Under convergence, the initially most efficient firm type (type 1) remains the most efficient
one upon adopting (that is, it has the lowest marginal abatement costs when using the
new technology, V1 R̄ < V2 R̄ ), but its private benefits of adoption are smaller than
type 2’s (that is, (C1 − V1 ) C2 V2 < (C2 − V2 ) C1 V1 ). This is illustrated in Figure 3.
Hence, uniform policies need to be located on type 1’s adoption barrier (B1 = 0), which implies that type
2 firms receive a windfall profit.
20
$
C 2’
C1’
V2’
V1’
t
r2(t )
r1(t ) R2(t ) R1(t )
1
1-e
Figure 3: The case of convergence.
Here, when both types adopt, type 2 is still less efficient in abatement than type 1 but the
difference in efficiency is smaller than before adoption; the two types’ abatement levels
converge (that is, r1 − r2 > R1 − R2 ). And the adoption benefits of type 1 firms (Z1 )
equal the sum of the black and dark—grey areas, whereas the adoption benefits of type 2
firms (Z2 ) equal the sum of the dark—grey and light—grey areas (cf. Figure 1).
Differences in abatement levels tend to fall when a technology matures, and hence
convergence is likely to reflect the type of technological progress if there is a technical
maximum to emission abatement. The closer one operates to this maximum, the smaller
the gains that can be obtained from adoption (as is the case with incremental technological
progress, as opposed to technological breakthroughs; cf. Antonelli [3]). An example of
21
convergence is provided by Jaffe and Stavins [17]. They estimate how the level of insulation
implemented in housing by building firms in the 48 lower States of the US in the period
1979—1988 varies with a series of control variables, including lagged levels of insulation.
The coefficient on the lagged insulation level is positive but less than 1 (it ranges between
0.3 and 0.4), implying that if the difference in insulation levels installed between two
states is 1 unit in a specific year, the difference is smaller in the next year — all else
equal. So, Jaffe and Stavins find that the building firms that initially install higher levels
of insulation in new homes and buildings than other firms, still install higher insulation
levels ten years later, but that the gap with other firms is reduced.
Within the convergence case, two situations are possible. “Leapfrogging” implies that
it is possible that firms of type 2 abate more in absolute terms than do firms of type 1,
but only if they have adopted the new technology and firms of type 1 have not (R2 > r1 ).
This is in fact the case presented in Figure 3. Alternatively, “closing the gap” implies
that firms of type 1 always abate more, irrespective of the technology used by each type
(r1 > R2 ). In terms of Figure 3, this would be the case where C1 and V2 swap location.
Regarding the locations and shapes of the adoption barriers and the isocost functions
of the two types in case of convergence, Lemmas 1—3 imply that B1 (S, τ ) ≥ B2 (S, τ ) and
dτ dS dK1 =0
>
dτ dS dK2 =0
> 0 for all (S, τ ) where B1 (S, τ ) > 0; see Figure 4.15 Here, (S ∗ , τ )
is the optimal uniform policy, and the first thing to note is that it cannot be part of a
separating menu. A separating policy including (S ∗ , τ ) would have (0, τ 2 ) as its second
policy combination, where (S ∗ , τ ) is intended for type 1 firms and (0, τ 2 ) for type 2 firms.
15
Note that when explaining the adoption barriers and iso—cost functions in Section 3, we actually used
the case of convergence, cf. Figure 2.
22
τ
K1’
K1
K2
(S*,τ)
τ
K2’
(S1, τ)
(0,τ2’)
(S2, τ2)
B2=0
B1=0
I
S
Figure 4: Incentive—compatible separating policies around the least—cost uniform policy
in case of convergence.
Type 2 firms are indifferent between the two (as both policy points are located on K2 ) and
hence are assumed to choose the latter. But type 1 firms strictly prefer not to adopt and
choose (0, τ 2 ) because (S ∗ , τ ) is located strictly above K1 , the isocost function through
(0, τ 2 ).
Because (S ∗ , τ ) cannot be part of a separating policy, any attempt to decrease social
costs by decreasing the amount of subsidies offered to type 2 firms necessarily goes at the
expense of paying larger subsidies to type 1 firms. In other words, the policy targeted
at type 1 firms should be located in their strict adoption region (B1 > 0) in order to be
able to locate the policy targeted at type 2 firms in the non—adoption region of type 1
firms (B1 < 0 ≤ B2 ). Thus, starting from the uniform policy (S ∗ , τ ), the policy targeted
at type 1 firms should include a (possibly infinitesimal) increase in the subsidy only; the
23
tax rate remains at τ . The tax cannot be increased, and it is not socially optimal to
reduce it because of the associated increase in the sum of abatement costs and external
damages. Since both types prefer this new policy (S1 , τ ) to the uniform one, the policy
for type 2 firms should be adjusted to satisfy the incentive compatibility constraint (6).
For policy (S1 , τ ), an incentive—compatible tax/subsidy combination targeted at type 2
firms is (S2 , τ 2 ). Both types are indifferent between (S1 , τ ) and (S2 , τ 2 ), and hence they
are assumed to choose the policy targeted at their type.16
Note that increasing the subsidy for type 1 firms and decreasing the tax for type 2 firms
increase social costs. However, decreasing the subsidy for type 2 firms decreases social
costs. Therefore, separation is socially desirable if the latter effect dominates the former.
The following proposition gives a sufficient condition for separating to be preferred to the
uniform policy.
Proposition 1 Under costly subsidies (F > 0) and convergence of the types’ abatement
technologies, separating reduces social costs if the following condition holds:
q1
1
(τ − D ) R2
<
(r1 − R2 ) +
q2
1 − R1
F
(9)
evaluated at the uniform policy (S ∗ , τ ) .
Proof: see Appendix 2.
So, the relevant factors include the number of firms of each type (q1 and q2 ), their
abatement levels before (ri ) and after adoption (Ri ), the marginal social costs of raising
funds (F (•)), and the difference between the maximum tax rate (τ ) and the actual
16
For any policy point in the region B1 (S, τ ) > 0, a second policy point can be found such that the
two form a separating policy. That means that there are infinitely many separating policies; (S1 , τ̄ ) and
(S2 , τ 2 ) is just one of them.
24
marginal damage, D . The first observation we can make from Proposition 1 is that
because R1 < 1, τ < D , R2 > 0 and F > 0, r1 − R2 should be positive and sufficiently
large in order for condition (9) to hold. That means that separation can only be socially
preferred in case of “closing the gap” (see above). But this is a necessary condition, and
not a sufficient one. If “closing the gap” is met, separation is more likely to be preferred
(i) the larger the number of type 2 firms and the smaller the number of type 1 firms
(resulting in q1 /q2 being smaller), (ii) the smaller the environmental distortion (D − τ )
and the larger the marginal social costs of raising subsidies (F ), and (iii) the larger the
difference in efficiency in using the new technology (such that R1 >> R2 or, alternatively,
R1 close to 1).
Regarding (i), clearly the proportion of firms of each type matters. Separation reduces
the amount of windfall profits received by the type 2 firms, but at the cost of giving
sufficiently generous subsidies to firms of type 1 to bring them strictly into their adoption
region. If there are relatively many firms of the former type, separating can be socially
preferred to the least—cost uniform policy. Regarding (ii), the smaller D − τ , the less
subsidies are required as higher taxes provide stronger incentives to adopt.17 But if the
marginal social costs of raising subsidies are negligible (F close to zero), subsidies are
virtually transfers and hence there is not much use in trying to reduce the amount of
subsidies provided. Finally, concerning (iii), the relevance of a larger R1 and a smaller R2
is clear from Figure 4. R1 (R2 ) being large (small) implies K1 (K2 ) being steep (flat) —see
Lemma 3— which allows τ 2 to be close to τ and S1 to be close to S ∗ .
17
Alternatively, the smaller τ , the less likely it is that separation is optimal. In the limiting case of
τ = 0, both types need S = I to adopt and there is neither means nor reason to induce separation.
25
4.2
The cases of divergence and overtaking
Let us now analyze the cases of divergence and overtaking. Divergence occurs if the
initially most efficient firm type (type 1) remains the most efficient one upon adopting
(that is, V1 R̄ < V2 R̄ ) and its private benefits of adoption are larger than type 2’s
(that is, (C1 − V1 ) C2 V2 > (C2 − V2 ) C1 V1 , see Lemma 1). This is the case where the
old (new) marginal abatement cost function of type 1 in Figure 3 is shifted up (down)
sufficiently so that the horizontal distance between the two firm types’ new marginal
abatement cost functions is larger than the horizontal distance between their old functions
(i.e., r1 − r2 < R1 − R2 ). In other words, the difference in efficiency increases upon
adoption. This case may arise, for example, if the labor force that uses the old technology
most efficiently have skills that better match the requirements associated with using the
new technology, so that they are able to make better use of the new technology than their
peers. Divergence may therefore occur if existing know—how plays an important role in
technology use.
In contrast, overtaking occurs if the initially least efficient firm type becomes most
efficient upon adoption (V1 R̄ > V2 R̄ ) — by definition it is then also the type that
gains most from adoption. In terms of Figure 3 this case can be represented by swapping
the labels of V1 and V2 (so that r1 − r2 > 0 > R1 − R2 ). This situation may occur if
firms need to invest in learning how to use the new technology. Whereas the expected
benefits for the “technological leader” (type 1) are too small to invest in developing this
knowledge, they are likely to be much larger for the “lagging firm” (type 2), and hence
the latter ends up running the new technology (much) more efficiently than the former
26
(for a similar argument see for example Brezis et al. [7]). Or it may be the case that
abatement technologies are run on the basis of rules of thumb rather than that operating
procedures are continuously re—optimized, with the shock of using a new technology being
sufficiently large for the type 2 firms’ managers to thoroughly reconsider their modes of
operation, but not for those of type 1 firms (cf. Porter and van der Linde [39]).
Examples of both divergence and overtaking can be found in the literature. Kerr
and Newell [22] analyze how the US lead phasedown policy induced adoption of cleaner
technologies (specifically the adoption of the so—called pentane—hexane isomerization technology). Using panel data on US refineries in the period 1971—1995, they find that initially
low—cost abatement firms gain more from adopting cleaner technologies than the initially
high—cost abatement firms, which they attribute to marginal abatement cost functions
shifting out in a fashion we have labeled divergence (see also their Figure 1 on page 319,
which is a specific case of our Figure 1). They find that refineries using relatively complex
technologies beforehand (more specifically, those that had catalytic reforming capacity in
1971) are more prone to adopting the new technology because of the in—house availability
of specialized knowledge.
An example of overtaking is the case of Flue Gas Desulfurization (FGD) as presented
by Bellas [5]. Tabulating the data of sulfur content in units with and without FGD, Bellas
finds that the propensity to adopt FGD technology is higher for the firms with the higher
initial levels of average sulfur content (see his Table 1 on page 330). Assuming continuous
marginal abatement cost functions, we can infer that the firms with the lower initial
marginal abatement costs (resulting in lower emission levels) are less prone to adopt the
new abatement technology, resulting in the least efficient firms becoming most efficient
27
upon adopting.
Let us now analyze how our results change under these two alternative cases. They
have in common that the ultimately most efficient type also has the largest benefits of
adopting. Because it faces the lowest marginal abatement costs when using the new
technology it is more prone to choosing the high tax/subsidy combination, whereas it is
actually the type that needs least subsidies to adopt. As a result, we find that separating
policies are always more costly than the best uniform policy in case of either divergence,
or overtaking.
We show this graphically in Figure 5. In this figure, j identifies the firm type that uses
the new technology most efficiently and also gains most when adopting (and i the other
firm type). In case of overtaking i = 1 and j = 2; under divergence, i = 2 and j = 1.
Separation can be induced by increasing the subsidy offered to the ultimately most efficient
type from S ∗ to Sj and by offering a second tax/subsidy combination along Ki (Sj , τ ) to
the South—West of (Sj , τ ). Obviously this second tax/subsidy combination cannot be in
the region Bi < 0 because then type i would not adopt. The least cost approach is then to
locate (Si , τ i ) on Bi = 0 (to the South—East of (S ∗ , τ )). As a result, in case of divergence
and overtaking separation always requires an increase in the total amount of subsidies
provided (Sj > Si > S ∗ ) and with lower incentives to actually abate for the ultimately
least efficient type (τ i < τ ), thus exacerbating the environmental distortion.
4.3
Separating policies in practice
Having derived the conditions for separating policies to be socially preferred, the next
question is how the regulator can obtain the required information to construct these
28
τ
Kj
Ki
(S*,τ)
τ
(Sj, τ)
(Si, τi)
Bj=0
Bi=0
I
S
Figure 5: The cases of divergence (i=2, j=1) and overtaking (i=1, j=2).
policies. The analysis in this subsection gives insight into the steps the regulator needs
to take to obtain such information.
First of all, the regulator should determine what case of technological progress is
relevant. This is not hard to determine; engineers will be able to give an assessment
what firms are likely to gain most when adopting the new technology — the ones that are
currently most efficient in abatement, or the ones that are least. For example, if the new
technology is very complicated to operate requiring a high level of specific knowledge,
it is likely that either divergence or overtaking is the relevant case. Divergence because
the firms currently using fairly advanced technologies have the in—house knowledge to
successfully run the new technology (as is the case with the pentane—hexane isomerization
technology as analyzed by Kerr and Newell [22]), or overtaking because the firms using
29
fairly advanced technologies stand to gain fairly little from using the new technology
so that they decide not to invest in acquiring the knowledge needed to run the new
technology (as in the case of the FGD technology analyzed by Bellas [5]). The analysis in
Section 4.2 shows that in the case of pentane—hexane isomerization and FGD technologies,
uniform policies are preferred to separating policies. This is relevant information for
regulators in various countries where governments use (or have used) subsidies (oftentimes
in combination with taxes) to phase out lead in gasoline (cf. Lovei [29]: 23) and/or to
reduce emissions of SO2 (Bohi and Burtraw [6]: 74).
Separating by means of tax/subsidy menus may be socially preferred, however, in
case of convergence (as shown in Section 4.1), and this may well be the case that occurs
with a higher frequency than either divergence or overtaking. An example of convergence
was provided by Jaffe and Stavins [17] as their regression results suggest that insulation
levels installed by construction firms converge over time. Again, many countries use
subsidies to increase insulation levels in new residences and buildings (OECD/IEA [36]),
and for these governments the relevant next question is whether technological progress is
‘closing the gap’ or of the leapfrogging type. An example in point is Spain that tries to
stimulate residential insulation by offering a combination of minimum standards regarding
energy savings (insulation, the use of solar power) and investment subsidies to building
corporations (OECD/IEA [36]).
Whereas engineers are likely to readily assess (or even infer from the literature as in the
cases described above) whether a specific technology is expected to give rise to divergence,
convergence or overtaking, determining whether convergence results in leapfrogging or
closing the gap is much more information intensive. To assess this, information is needed
30
about the pre— and post—adoption abatement levels of the various types. Indeed, a necessary condition for separating to be preferred to uniform policies is that r1 > R2 . Again,
regulators may be able to learn from other countries’ experience. For example, tradable
permit systems implemented in other jurisdictions can reveal which types of firms tend to
adopt the new technologies and whether they become net suppliers or buyers of permits
(see also Malueg [31]). But in some instances site visits may be the only way to obtain
such information.18
If regulators cannot draw on other countries’ experiences, the analysis in Section 4.1
suggests that the least—cost approach is then to next assess how likely it is that separating
will provide savings — by assessing whether condition (9) is likely to hold. That means
that the regulator needs to assess (i) how large the marginal costs of raising funds are,
(ii) how large the marginal damages are (or, more specifically, how large the difference
is between marginal damages and the maximum tax rate that she can impose), and (iii)
how large the share is of the currently most efficient firms. If it is likely that condition (9)
holds, it is expected to be worthwhile to send engineers to firms for extensive site visits in
order to determine whether technological progress is likely to result in ‘closing the gap’ or
‘leapfrogging’, and also what the expected abatement levels are of the various firms types
when using the new technology (i.e., R1 , R2 and R2 ; see condition (9)).
18
From all the possible policy instruments implemented by other countries, tradable permits convey the
most information to other regulators because they reveal both adoption behavior as well as the relative
positions of the marginal abatement cost functions across types (because some firms will become net
buyers and others net sellers of permits). But there are also other sources of information. For example,
Jaffe and Stavins [17] include the price of energy in their regression analysis explaining insulation levels,
and thus information is available about the relationship between energy prices changes (caused by international price developments, or by energy taxes) on the level of insulation installed — information which
can be used to trace the firms’ marginal abatement cost functions. To the extent that the application of
insulation techniques is sufficiently similar across jurisdictions, studies that analyze the determinants of
technology adoption also contain useful information for regulators.
31
Clearly, auditing a sample of firms in the regulated industry is costly. However, the
savings in the social costs of raising funds may well be such that the information collection
effort is a profitable investment.
5
Robustness of the results
In the previous section we have identified the necessary condition for separation to be
the least—cost solution; technological progress should “close the gap” but even then the
uniform policy may still be socially preferable. We derive these conclusions using a simple
model; most of the assumptions serve the purpose of making the model easier but are not
crucial to our results. In this section we show the robustness of our results against relaxing
some of them.
First, we consider what happens if we relax the assumption that all firms face the same
investment costs. The direct consequence of relaxing this assumption is that the horizontal
intercepts for the adoption barriers in (S, τ ) space no longer coincide (see Figure 2, 4 or
5), resulting either in (i) the one barrier being located strictly to the North—East of the
other for all τ ≥ 0 (rather than weakly), or (ii) the two adoption barriers intersecting
in (S, τ ) space. Clearly, case (i) leaves our analysis unaffected; the resulting situation
can still be classified as convergence, divergence, or overtaking. Case (ii) is a little more
subtle, because the resulting situations can then no longer be globally referred to with
labels such as convergence, divergence and overtaking. But these labels are still relevant
locally: for a given set of adoption barriers and isocost functions, the relevant case may
be convergence for a specific level of τ̄ but divergence if the tax threshold is slightly higher
or lower. And hence all our analyses remain valid; all that matters is whether or not the
32
type that needs the largest adoption subsidies (when confronted with tax rate τ̄ ) is also
the one that is more prone to choosing the high tax/subsidy combination.
Also, making the costs of raising funds dependent on the net subsidies provided (that
is, the total subsidies paid minus the tax revenues raised) does not fundamentally affect
our results. Our analysis in Sections 3 and 4 uses the gross subsidy specification, and
hence reducing the tax rate (i.e., below τ̄ ) for the type that uses the new technology less
efficiently is costly only because it gives lower incentives to abate at the margin. If we use
the net subsidy specification there is the additional cost in the form of raising less funds
to cover the cost of subsidization, and hence separation is even less likely to be socially
preferred. That means that assuming that the costs of raising funds are a function of net
subsidies instead of gross subsidies reduces the probability that separating policies prove
to be welfare enhancing.
Our conclusion that separation is always feasible but may not be desirable is again
reinforced when allowing for three firm types — or more. Let us assume that type 3 firms
are the ones that gain least from adoption. Considering the consequences of having three
types in the regulated industry, two cases are relevant here: (a) the third type should
not be induced to adopt (i.e., partial adoption is optimal), or (b) it should. In (a), the
presence of type 3 firms does not affect the location of the uniform policy (S ∗ , τ̄ ). At this
policy point type 3 firms strictly prefer not to adopt. So they are charged tax rate τ̄ but
do not collect subsidy S ∗ .
Because the uniform policy is the least costly option in case of divergence and overtaking, the presence of a third type does not affect any of the results in these two cases.
But it will have an impact in case of convergence, because overinvestment needs to be
33
prevented. The separating policy should be such that type 3 firms do not want to adopt
and hence also do not claim a subsidy. If (S1 , τ̄ ) in Figure 4 is located in the B3 < 0
region (not shown), type 3 firms prefer the other policy point (S2 , τ 2 ) and hence offering
an additional tax/subsidy combination (0, τ 2 ) results in complete separation of the three
types.
If (S1 , τ̄ ) is located in the B3 ≥ 0 region, type 3 firms need to be induced not to select
this policy, and this may even require offering a third policy combination (0, τ 3 ), with
τ 3 < τ 2 — if K3 is sufficiently steep and/or B3 = 0 is sufficiently close to B1 = 0. In either
case there is an additional welfare cost as compared to the uniform policy because type
3 firms are charged a tax rate below τ̄ . And hence the likelihood of separating being the
least—cost option is smaller if partial adoption is optimal.19
If the third type should be induced to adopt (case (b)), separation is again always
feasible, but may or may not be desirable. Here, the uniform policy is affected, obviously,
because of the presence of firms of type 3 that need larger subsidies to adopt. In principle,
this raises the stakes of being able to separate the three types. And separation is still
always feasible. But it would require offering even larger subsidies to the type that is most
efficient upon adopting and also reducing the tax rates faced by the other two types. If
the type that is ultimately most efficient in using the new technology is not the one that
needs the largest subsidies to adopt (cf. divergence and overtaking), separating is again
never the least—cost solution. If this ultimately most efficient type does need the largest
subsidies, however, separation may be welfare enhancing, and similar considerations play
19
Note that partial adoption in the two-types model is trivial. By offering policies (0, τ̄ ) and (S, τ̄)
—where S = I − max{Z1 (τ̄), Z2 (τ̄)}— the two types are separated efficiently.
34
a role as in Proposition 1.
6
Conclusions
We have analyzed the problem that (lump—sum) investment subsidies can be highly effective in inducing adoption of new technologies —e.g., emission abatement equipment— but
that such subsidies may result in some firms earning windfall profits (or informational
rents). Firms differ with respect to the private benefits they reap from switching to a
new technology, and hence a subsidy that renders adoption weakly profitable for some
firms results in positive net gains for others. Given that providing subsidies is socially
costly, the question arises whether the regulator can design a menu of policies consisting
of taxes and subsidies that induces firms to self—select according to the minimum amount
of money they need to adopt the new technology.
Using a stylized model of two types of firms, we show that the ultimately most efficient firms are (weakly) more likely to prefer higher tax/subsidy combinations than the
ultimately least efficient ones. That means that for policy menus to be incentive compatible, the regulator should offer larger subsidies to (but also impose higher tax rates on)
those firms that are more efficient in emission abatement upon adoption —irrespective of
whether these firms are indeed the ones that need the largest subsidy to adopt. But only
when these ultimately most efficient types are also the ones that gain least upon adopting,
separating policy schemes may be socially preferred to uniform policies.
This incentive compatibility condition enables us to identify the situations in which
a separating policy scheme results in lower social costs than the best uniform scheme.
Here, the differences in marginal abatement costs within and between firms play a key
35
role. In fact, we find that separating policies are socially preferred neither if full adoption
results in a divergence of the firms’ levels of abatement efficiency, nor in case of overtaking.
In those cases, incentive compatibility requires giving a larger subsidy to the type that
gains most when adopting, which is not cost—effective. Then, uniform policies are always
cheaper.
Separating policies can be socially preferred in case of convergence of abatement efficiencies. Here, the initially most efficient type is also most efficient upon adopting, but
its private adoption benefits are smaller than those for the initially least efficient type.
We find that a necessary condition for separation to be least cost is that the initially
most efficient firm type always has lower marginal abatement costs than the other type,
even when the latter invests and the former does not (i.e., under “closing the gap”). If
this necessary condition is met, we find that separation is more likely to be least cost (i)
the smaller the share of ultimately most efficient type in the industry, (ii) the closer the
emission tax rate can be set to actual marginal damage, and (iii) the larger the difference
in abatement efficiencies upon adopting.
Whereas we find that uniform policies are better than separating policies in two out of
three cases, it may well be the case that convergence occurs much more frequently than
divergence or overtaking. That means that regulators need to assess, on a technology—
to—technology basis, whether it is worthwhile to invest in collecting the data needed to be
able to construct separating policy menus. Our analysis suggests that in some instances
information is readily available in the environmental economics literature obviating the
necessity to collect the data because the technology under consideration gives rise to divergence or overtaking (e.g., Kerr and Newell [22] and Bellas [5]). If not, a sample of
36
firms may need to be audited to be able to identify firm types and to infer the slopes
and locations of the various types’ marginal abatement cost functions (before and after
adoption). Clearly, the costs of auditing a sample of firms in the regulated industry can
be considerable, and this paper identifies the steps that need to be taken to ensure information is collected cost—effectively. Ultimately, the savings in the social costs of raising
funds may well be such that the information collection effort is a profitable investment.
7
Appendix 1
Table of symbols.
Bi (S, τ )
Ci (ri )
D (E)
ei
2
E=
qi ei
Firm type i’s net benefits of adoption
Abatement costs of a firm of type i under the old technology
External damages associated with total emissions in the industry
Emission level of a firm of type i
Total emissions in the industry
i=1
φi
F (ST )
I
Ki (S, τ )
qi
ri
Ri
Si
2
ST =
qi φi Si
Variable indicating whether type i adopts (φi = 1), or not (φi = 0)
Social costs of raising subsidies
Costs of adopting the new technology
The minimum total abatement costs
Number of firms of type i
Emission abatement level of a firm of type i under the old technology
Emission abatement level of a firm of type i under the new technology
Subsidy level intended for a firm of type i
Total amount of subsidies provided in the industry
i=1
τi
τE
τ
Vi (Ri )
Zi (τ i )
Tax rate intended for a firm of type i
Pigovian tax rate
Tax rate below (above) which the political economy costs
of taxation are zero (infinite), τ < τ E
Abatement costs of a firm of type i under the new technology
Variable cost savings of adoption for a firm of type i
37
τ
K1
τ
dτ2
τ2
dS1
1 dS1’
(S1, τ)
(S*,τ)
(S2, τ2)
K2
(S*+1, τ2)
dS2
B2=0
S*
B1=0
I
S*+1
S
Figure 6: Graphical representation of the approach taken for the proof of Proposition 1.
8
Appendix 2
Proof of Proposition 1.
We present the proof with the help of Figure 6. Starting
from the uniform policy (S ∗ , τ ), we identify a separating menu of policies such as (S1 , τ )
and (S2 , τ 2 ) intended for type 1 and 2 firms respectively. The social cost consequences of
moving from (S ∗ , τ ) to (S1 , τ ) and (S2 , τ 2 ) depends on dτ 2 and dS1 (which increase social
costs) as well as on dS2 (which reduces social costs).
To induce separation, we start by increasing the subsidy intended for type 1 firms by
a very small amount; say one dollar (S ∗ + 1). The corresponding decrease in the tax (dτ 2 )
that still induces adoption by type 1 firms is given by (7):
dτ 2 = −
1
< 0.
R1 − r1
38
(10)
The extra subsidy that type 1 firms (dS1 = 1 + dS1 ) require to be indifferent between
the policies (S ∗ + 1, τ 2 ) and (S1 , τ ) can be obtained by using (8) and (10):
dS1 = 1 + dS1 = 1 +
1 − R1
1 − r1
=
> 0.
R1 − r1
R1 − r1
(11)
We can now construct (S2 , τ 2 ). First note that type 2 firms’ costs in (S1 , τ ) are lower
than under the uniform policy; dK2 = −dS1 . To find S2 , type 2 firms must be indifferent
between policies (S1 , τ ) and (S2 , τ 2 ). Therefore, the cost saving associated with moving
to (S2 , τ 2 ) should also be −dS1 :
∂K2
∂K2
dτ 2 +
dS2 = −dS1 .
∂τ
∂S
(12)
By (1), ∂K2 /∂S = −1 and ∂K2 /∂τ = 1 − R2 . Substituting these expressions in (12),
and using (10) and (11), we obtain:
dS2 =
R2 − r1
,
R1 − r1
(13)
which is negative if and only if R2 < r1 .
We now consider the corresponding change in social costs due to the changes (dτ 2 , dS1 , dS2 ),
evaluated at the uniform policy (S ∗ , τ ) :
dSC = q2 (τ − D ) R2 dτ 2 + F [q1 dS1 + q2 dS2 ] .
(14)
Substituting (10) , (11) and (13) in (14), we have:
dSC =
1
{−q2 (τ − D ) R2 + F [q1 (1 − R1 ) + q2 (R2 − r1 )]} ,
R1 − r1
which is negative if:
F [q1 (1 − R1 ) + q2 (R2 − r1 )] < q2 (τ − D ) R2 .
Rearranging terms, we obtain the desired result.
39
(15)
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