RESEARCH ARTICLE Promoting energy-efficient products: voluntary or regulatory approaches? Rasha Ahmed Received: 16 August 2011 / Accepted: 28 February 2012 / Published online: 16 March 2012 Ó Springer 2012 Abstract Several product-related voluntary agreements (VAs) have emerged between firms to limit production of energy-consuming products, e.g., domestic appliances and automobiles. While some VAs have been successful in achieving their targets, others have failed. The paper identifies two factors that can explain the success or failure of product-related VAs. The first is a technological property of the product line: whether provision of energy-efficient products requires a quality compromise (quality–efficiency trade-off). The second is the type of the constraint imposed by the VA: a quota on the brown model or a VA based on an average efficiency standard. I show that VAs are more likely to be successful for products where there is no quality–efficiency trade-off than for products where there is such a trade-off. I also show that quantity-based VAs are more likely to emerge than VAs imposing an average efficiency standard. The findings provide a possible explanation for why the CECED appliances VAs have been successful in achieving the targets they set, while the ACEA agreement for automobiles has failed. Keywords Voluntary agreements Green products Average efficiency standard Quota Energy efficiency JEL Classification Q48 Q58 1 Introduction In several contexts where pollution stems from the use of the final product, voluntary agreements (VAs) have emerged. These agreements, most notably in Electronic supplementary material The online version of this article (doi:10.1007/s10018-012-0032-8) contains supplementary material, which is available to authorized users. R. Ahmed (&) Department of Economics, Trinity College, 300 Summit St., Hartford, CT 06106, USA e-mail: [email protected]123 Environ Econ Policy Stud (2012) 14:303–321 DOI 10.1007/s10018-012-0032-8
The second factor that I consider relates to the nature of the VA. I distinguish
between two types of VAs: (1) a VA that sets an average energy efficiency standard
across all models of a product produced and sold by a firm, and (2) a VA limiting
the output and sales of the polluting model. The European automobile VA is an
example of the former type of VA, while the washing machines agreement is an
example of the latter type. I show that the latter is more powerful in suppressing
competition between firms.4
The primary results can be summarized as follows. For products that do not exhibit a
quality–efficiency trade-off (such as most domestic appliances), an industry-wide VA
is always profitable regardless of whether it is based on an average efficiency standard
or a quota, provided the standard is not too stringent. When the standard becomes too
stringent, either type of VA will no longer benefit firms; however, the VA always
reduces energy consumption in this case. For products that exhibit a quality–efficiency
trade-off (such as automobiles or paper), as in the previous case, a VA that is based on a
quota is always profitable, provided the quota is not too stringent and will always
reduce energy consumption. However, in contrast to the previous case, an industry-
wide VA based on an average efficiency standard is not profitable for firms and may
result in increased energy consumption depending on the stringency of the standard.
This suggests that, for products with a quality–efficiency trade-off, a VA based on an
average efficiency standard is not likely to be successful in the absence of some
external incentive for firms to participate. This suggests that, for products that exhibit a
quality–efficiency trade-off, firms will not voluntarily participate in an agreement
based on an average efficiency standard in the absence of some external incentives. In
that case, regulation can be more effective in ensuring participation and reducing
energy consumption.
2 According to Ward’s Automotive Yearbook (2009), small cars have higher miles per gallon than luxury
cars; however, they are smaller in size and have a weaker horsepower than luxury cars. Also, the price of
small cars is less than the price of luxury cars. This suggests that consumers value inefficient cars more
than they value efficient cars, assuming a vertically differentiated product market.3 According to Consumer Reports (2011), front-loading washing machines rank higher than top-loading
machines in terms of energy and water efficiency. While the cycle time of front-loading machines is
longer, their overall ranking is still higher than the overall ranking of top loading machines, where overall
ranking is based on washing performance, gentleness, noise energy efficiency, water efficiency and cycle
time.4 Ahmed and Segerson (2011) only consider a quota-based VA applied to products that do not exhibit a
quality–efficiency trade-off. It analyzes participation incentives and highlights the need of an enforcement
device to ensure sufficient participation. This paper focuses instead on contexts where VAs are likely to
be profitable by considering the role of the standard implemented by the VA as well as the trade-off
between product quality and efficiency.
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Taken together, the results suggest a possible explanation for why appliance-
related VAs such as the CECED agreements have been successful, at least up to a
point, while success in using VAs for automobiles or paper recycling has been
limited. In particular, they suggest that the initial appliance-related VAs might
have provided firms with a profitable opportunity in this market, due to the nature
of the product and the structure of the VA. More specifically, the fact that
appliances do not generally exhibit a quality–efficiency trade-off and the use of a
quantity-based VA (thereby, directly limiting sales of the low-efficiency models)
combined to create the potential to simultaneously increase profits and reduce
energy consumption under the VA as long as the implied restrictions were not too
stringent. Thus, VAs imposing stringent standards are not likely to emerge which
explains, at least in part, the refusal of the CECED to continue to eliminate the
less efficient models through VAs. In contrast, our results suggest that the
European VA for automobiles might not have provided a profitable opportunity
for firms due, at least in part, to the combination of the quality–efficiency trade-
off and the use of a VA based on an average energy efficiency standard. The
combination of these two factors makes the VA costly to firms, regardless of the
stringency of the target set.
The organization of the paper is as follows. Section 2 presents the basic model
structure and the initial equilibrium. Section 3 presents the equilibrium analysis
under the average efficiency VA. Section 4 presents the equilibrium under the
quota-based VA. Section 5 concludes the study.
2 The model
I model a market for a vertically differentiated product. I assume that two models of
a given product are available, a green model (G) and a brown model (B). The
models vary with regard to two attributes, quality denoted by bs and lifetime energy
consumption denoted by Ls, where s = B or G. The combination of the two
attributes will determine the net benefit derived from each model and thus the
product ranking. To characterize the demand side of the market, I assume that there
is a unit mass of consumers of the product who vary in their valuation of the net
benefit derived from model s, denoted x, which is uniformly distributed on [0, 1].
Each consumer has the option to buy a single unit of the product or not to buy
at all.5 The utility of a consumer of type x who purchases one unit of model s is
given by
Vxs ¼ xðbs � peLsÞ � Ps; ð1Þ
where pe is the per unit price of energy and Ps is the price of the type-s model.
I assume that the total energy consumed by the green model is less than that
5 Alternatively, not buying a new model may mean that those consumers are holding onto their old
model. This will not significantly affect our results, except that (14) would be interpreted as energy
consumption from new models only.
Environ Econ Policy Stud (2012) 14:303–321 307
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consumed by the brown model, i.e., LB [ LG.6 For some products, it is possible that
bG [bB and so the green product has a higher quality or performs better than the
brown product. If on the other hand bG \bB, then the brown product has a higher
quality.7 Note that this specification does not embody ‘‘green’’ preferences; energy
consumption affects utility only through its impact on the variable cost of using the
product.8
The utility of a consumer of type x who buys model s simplifies to Vsx = asx -
Ps, where as = bs - peLs. The utility of a consumer who does not buy a new model
and holds onto the old model is normalized to zero. The parameter as reflects the net
benefit (the benefit net of energy cost) of model s and determines the product
ranking.
The characterization of the demand side of the market for a vertically
differentiated product will depend on the consumer ranking of the two products.
Two possible cases will be considered. Under the first case, aB [ aG and therefore
all consumers prefer the brown model over the green model (the brown model has a
higher ranking). Thus if both models are offered for sale at the same price, everyone
will buy the brown model. This will be true when bB - bG [ pe(LB - LG), i.e., the
gain from the higher quality outweighs the energy loss from switching to the brown
model. I refer to this case as the ‘‘trade-off’’ case to denote the trade-off between the
energy efficiency of the model and its ranking. This case represents, for example,
automobiles where luxury cars are preferred to small economy cars since they tend
to be safer and more powerful to drive. Under the second case, bB - bG \ pe(LB -
LG), and thus all consumers have a higher willingness to pay for the green model.
This will be true if the green model is of a higher quality, i.e., bB \bG, or if the
brown model is of a higher quality, i.e., bB [ bG; however, the energy savings from
switching to the green product are significant enough to outweigh any possible
quality loss. Clearly, in this case there is no trade-off between the product ranking
and its energy efficiency; the green product is the higher ranking product. An
example is washing machines, where the higher efficiency models rank higher than
the low-efficiency models.
The demand for each model will depend on the ranking of the two models. I will
use the subscript H to denote prices, quantities and net benefit of the higher ranking
product, while the superscript L denotes the corresponding values for the lower
ranking product. Under the trade-off market, the superscript H denotes values for
the brown product, while the superscript L denotes values for the green product. The
opposite will be true under the no trade-off case where the green product is the
higher ranking product. I will show that in equilibrium, PH [ PL. This has to be true
6 This is consistent with the empirical literature, which suggests that while the more efficient (green)
models are typically used more frequently, a phenomenon referred to as the rebound effect, the total
energy consumed by the energy-efficient model is less (see for example Small and Van Dender 2006).7 Although I simplify and assume that both bs and Ls are exogenous, they can both depend on the
frequency of use of each model. This specification will not change the results of the paper since the
frequency of use depends on exogenous product characteristics (e.g., energy efficiency and quality) and
energy price which is held constant.8 The model is an extension to Ahmed and Segerson (2011) where I model two product attributes that
consumers value, energy efficiency and product quality, instead of energy efficiency only.
308 Environ Econ Policy Stud (2012) 14:303–321
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to induce any consumers to buy the lower ranking product. Thus, when both models
are produced and hence available, the prices of the two models (along with other
parameter values) induce a partitioning of consumers as depicted in the upper part
of Figs. 1 and 2. Under this partitioning, a consumer of type x will buy the higher
ranking model if and only if
x�xH �PH � PL
aH � aL
; ð2Þ
while he will buy the low ranking model if and only if
PL
aL
� xL�x\xH: ð3Þ
Consumers for whom x\ xL choose not to buy the product at all.
0
10
1
Buy the brown modelBuy the green modelDo not buy
0TBω0T
GωPre-agreement
Quota
Average Efficiency Standard
TKGω TK
Bω
TZGω TZ
Bω
10
Fig. 1 Market segmentation for the trade-off market. The market segmentation under the averageefficiency standard represents values of Z where market output expands
0
10
1
Buy the green modelBuy the brown modelDo not buy
Pre-agreement
Quota
Average Efficiency Standard
10 0NGω0N
Bω
NKGωNK
Bω
NZBω NZ
Gω
Fig. 2 Market segmentation for the no trade-off market
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Given the distribution of x, the resulting demands when both models are offered
on the market are given by
QH ¼ 1� xH ð4Þ
and
QL ¼ xH � xL; ð5Þ
where Qs is the quantity demanded of model s. This implies the following inverse
demand functions:
PH ¼ aHð1� QHÞ � aLQL; ð6Þ
and
PL ¼ aLð1� QH � QLÞ: ð7ÞFinally, I assume that production costs are quadratic. This implies
Csðqis; bs; xsÞ ¼ csðbs; xsÞqi2
s ; ð8Þ
where qs is the quantity of model s produced by an individual firm.
I assume that the market is supplied by n multiproduct firms that have identical
costs and are Cournot competitors. Thus, given the inverse market demands in (6)
and (7), each firm seeks to maximize its profits by choosing its quantities of the two
models, i.e., its product line,9 given the quantities of the other firms. Thus, in the
absence of any commitments to reduce production of the polluting product, firm isimply chooses qB
i and qLi qG
i so as to maximize
Pi ¼ PBqiB þ PGqi
G � cBqi2B � cGqi2
G ð9Þ
where i = 1 to n. It is straightforward to show that the resulting Nash equilibrium
has the following properties (where the superscript ‘‘0’’ denotes the initial equi-
librium values prior to any commitments):
Proposition 1 (1) PG0 [ PB
0 only if aG [ aB, (2) qGi0 = qG
0 and qBi0 = qB
0 for alli = 1 to n.10
As expected, in equilibrium the green model will sell at a premium if its net
benefit is higher, i.e., aG [ aB, and the brown model must have a lower purchase
price to induce any consumers to buy it. In this case, as shown in Fig. 2, consumers
with high valuation of the product buy the green model. This contrasts with Fischer
(2005) where the energy-efficient model always sells at a premium and is bought by
the high-end consumers. That is because Fischer (2005) models one product
attribute, energy efficiency, which consumers value, as it results in a lower
operating cost. In this paper, I generalize by introducing two product attributes and a
trade-off between them. This gives rise to equilibrium outcomes where the green
model sells for a lower price, since product price is determined by both its energy
9 For product line models, see Brander and Eaton (1984), Champsaur and Rochet (1989), De Fraja (1996)
and Johnson and Myatt (2003).10 Proofs of all propositions are provided in the Appendix (Online Resource 1).
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efficiency and quality. If the trade-off between energy efficiency and product quality
is strong enough, then this gives rise to the trade-off case where the green model
sells for a lower price and consumers with strong valuation for the product buy the
inefficient model instead as shown in Fig. 1.
In addition, firms produce the same amount of each of the models, i.e., there is no
quality specialization. This is consistent with the observation that firms often
produce very similar product lines that include both environment friendly and less
friendly models, rather than specializing in the production of one or the other as
predicted by much of the quality choice literature (see Chen 2001).
Given a characterization of the initial equilibrium, I then turn to the equilibrium
under each type of VA. Participation in the VA represents a commitment by an
individual firm to an environmental standard that is not mandated by the regulation.
I analyze the conditions under which participation by all firms in the VA raises firm
profit. Under those conditions, full participation in the VA may not be a Nash
equilibrium, as individual firms have incentives to defect. This is possible given the
voluntary nature of the agreement and given that enforcement may be weak or
absent under the VA, unlike under government regulation. In this paper, I assume
that an enforcement mechanism exists that ensures collective commitment and focus
instead on the conditions under which industry participation in the VA raises
profit.11 I continue to model the output choices of firms as Nash equilibrium. I start
by analyzing the impact of a VA based on an average efficiency standard and then
turn to the impact of a quota-based VA. I consider the impact of each VA on the
market equilibrium for both the trade-off market and the no trade-off market. I show
that the nature of the agreement, as well as the existence of a trade-off, play a key
role in determining whether the VA can be profitable for firms. More specifically, I
show that, when a trade-off exists, a VA that imposes an average efficiency standard
will always reduce firm profit, while a VA that imposes a quota on sales of the
polluting product can be profitable. Since all equilibria considered are symmetric,
the superscript i will be dropped when defining the equilibrium under each
agreement.
3 The average efficiency standard
I first consider a VA based on an average efficiency standard. A VA of this type imposes
an upper limit on the average energy consumption across the models produced by each
firm. In terms of our model, the average efficiency standard is given by
LBqB þ LGqG
qB þ qG
� g ð10Þ
where LG B g\ g0 and g0 is the free market level of weighted average energy
consumption. An average efficiency VA is represented by a reduction in g by
11 Enforcement can be achieved if information about participation is made public and firms care about
their image, by the use of trigger strategies in repeated interactions, or by using a regulatory threat. For a
discussion of a firm’s incentive to free ride, the impact of free riding and possible enforcement
mechanisms, see Ahmed and Segerson (2011).
Environ Econ Policy Stud (2012) 14:303–321 311
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individual firms. Note that tightening g does not directly restrict production of any
model. Firms can freely set the quantities as long as the above constraint is satisfied.
The average efficiency constraint simplifies to a limit on the ratio of the output of
the brown to the green models that a firm produces as follows
qB
qG
� g� LG
LB � g: ð11Þ
Let Z ¼ g�LG
LB�g. Thus, a tighter standard, a lower g, is represented by a decrease in
Z. Note that setting g = LG, i.e., Z = 0, represents the agreement to eliminate the
brown product from the market. Under the VA, each firm maximizes profit in (9)
subject to the constraint that qB
qG¼ Z where Z 2 ½0; Z0Þ and Z0 is the free market ratio
of the two models.12 In the next section, I will analyze the impact of the average
efficiency VA on prices, output, firm profit and energy consumption. I will also
compare the impact of the average efficiency VA under the trade-off and the no
trade-off markets in an attempt to analyze the impact of the trade-off on the
likelihood that a VA imposing an average efficiency standard emerges and on its
effectiveness in reducing energy consumption. I will use the superscript TZ to
denote equilibrium values under the average efficiency VA for the trade-off market
and the superscript NZ to denote equilibrium values for the no trade-off market.
3.1 The trade-off market
The VA imposing an average efficiency standard is represented by a decline in
Z below the free market value Z0. The effect of a decline in Z on prices quantities
and firm profit is summarized in Proposition 2.
Proposition 2 Under the trade-off market (1)oqTZ
B
oZ [ 0, (2)oqTZ
G
oZ \0 if
(n ? 1)aG(aB - 2aG) ? 2aBcG \ 0, otherwise it reaches a maximum in Z at
Z \ Z0 (3) total market output reaches a maximum in Z at Z \ Z0, (4)oPTZ
B
oZ \0, (5)
PGTZ reaches a minimum in Z at Z \ Z0 and (6) opTZ
oZ [ 0.
Under the trade-off market, firms can meet the standard by expanding production
of the green product and/or by reducing production of the brown product. Based on
the market segmentation shown in Fig. 1, firms can increase sales of the green
product by attracting the consumers who buy the brown model, and/or by selling to
consumers who did not buy at all. Both changes take place under a mild standard
where production of the brown model shrinks resulting in an increase in its price and
causing some consumers to substitute toward the green model. Staring from the pre-
agreement equilibrium point, where Z = Z0, a marginal decline in Z raises the price
of the brown model and lowers the price of the green model as shown in Fig. 3a.
12 The average efficiency standard is usually specified as a limit on the average of energy efficiency
(energy consumed per use) across the models rather than the average of lifetime energy consumed. For
example, the ACEA agreement sets a limit on the average CO2 emissions per kilometer driven. However,
since the green model uses less energy per use and less in total, both specifications simplify to a limit on
the ratio of the brown to the green model as shown in the paper.
312 Environ Econ Policy Stud (2012) 14:303–321
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The decline in the price of the green model causes some consumers who did not buy
before to start buying the product, which results in an increase in total market output
under a mild standard as shown in Fig. 4a.13 Further tightening of the standard
always reduces production of the brown model and expands production of the green
model. Note that as the standard gets stringent enough, it is possible for firms to
meet the standard by reducing production of both models. This will depend on the
relative parameter values as indicated in the above proposition in (2).14
Firm profit is monotonic in Z, indicating that the VA based on an average
efficiency standard results in a lower industry profit relative to the pre-agreement
equilibrium for the trade-off case. This is illustrated in Fig. 5a which shows the
locus of equilibrium points in (qB, qG)-space for different values of Z. Figure 5a also
shows the iso-profit line through point O, the free market equilibrium point.15 Points
inside the iso-profit line represent market outcomes where profits are higher than the
pre-agreement point. Point C represents the outcome if firms were to collude. The
equilibrium locus under the average efficiency standard lies outside the iso-profit
line, indicating that all possible equilibrium points for the trade-off market result in
a lower profit level. This is because the average efficiency standard brings firms
further away from the collusion point.
More formally, I decompose the effect of changing Z on firm profit. Firm i’sprofit under the average efficiency standard is given by the Lagrangian function
TZBP
TZGP
0Zb The no tradeoff marketa The tradeoff market
NZGP
NZBP
0Z
Fig. 3 Prices under the average efficiency VA
13 A mild average efficiency standard can increase consumer surplus under the trade-off market. This is
because the gain to consumers from the reduction in the price of the green model outweighs the loss from
the increase in the price of the brown model. Note that for the no trade-off market, the consumer surplus
always declines regardless of the standard used. Similarly, consumer surplus always declines under the
quota regardless of the type of market. The changes in prices under these different cases will be explained
in the following sections.14 See proof of Proposition 2 for a detailed explanation.15 Derivation of the iso-profit line is shown in the Appendix (Online Resource 1).
Environ Econ Policy Stud (2012) 14:303–321 313
123
UiTZ ¼ PTZB qiTZ
B þ PTZG qiTZ
G � cBðqiTZB Þ
2 � cGðqiTZG Þ
2 þ q Z � qiTZB
qiTZG
� �ð12Þ
where q is the Lagrangian multiplier. The impact of a reduction in Z on firm profit is
Fig. 4 Market output under the average efficiency VA
TZBQ
TZGQ
The no tradeoff marketbThe tradeoff marketa
NZBQ
NZGQ
.C
.O
Iso-profit line
.C.O
Iso-profit line
Equilibrium locus under the quotaEquilibrium locus under the average efficiency standard
Fig. 5 The equilibrium locus under each VA
314 Environ Econ Policy Stud (2012) 14:303–321
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This decomposition shows that the agreement has two effects on firm profit:
a restriction effect and a strategic effect.16 The restriction effect, given by q,
represents the change in firm i’s profit as a result of changing its quantity
choices due to a marginal change in Z. The restriction effect is always positive
for Z \ Z0 (a marginal increase in Z has a positive impact on profit). This
indicates that setting Z at a value other than Z0, all else equal, is always
detrimental to profit. Thus, the restriction effect indicates that in the absence of
any strategic behavior, the agreement always reduces firm profit as in the
monopoly case.17
The strategic effect, on the other hand, represents the effect of a marginal change
in Z on firm i’s profit as a result of changing the quantity choices of its competitors.
The strategic effect captures the change in firm i’s profit as market prices change in
response to constraining the choices of other firms in the market. Thus, the strategic
effect captures the impact of the constraint on competition between firms.18 For the
trade-off market, a mild standard is associated with a positive strategic effect,
suggesting that the standard reduces firm profit. This is because the standard causes
other firms to expand total production and moves firms further away from the
collusion point. The expansion in production of the green model reduces its price
and, while it results in a higher price for the brown model, its net effect is a
reduction in firm i’s profit.
I turn next to the impact of the average efficiency VA on energy consumption.
Total energy consumption, E, is given by
E ¼ LBQB þ LGQG: ð14ÞA reduction in output of both models would unambiguously reduce energy
consumption. However, a one-to-one substitution toward the green model would
also reduce energy consumption since LB [ LG. The impact of the average
efficiency VA on energy consumption, ETZ, is summarized in the proposition below.
Proposition 3 ETZ reaches a maximum at a value of Z given by ZE, where0 \ ZE B Z0.
While the average efficiency VA results in a reduction in the output of the brown
model, it does not necessarily reduce total energy consumption. In the trade-off
market, total output increases under a mild standard. The increase in total output can
be strong enough to undermine the energy savings resulting from switching to the
green model. The combination of these two effects may result in an increase in total
energy consumption (this corresponds to the case where ZE \ Z0), which will
16 This is an application of the general principle that, in the presence of strategic behavior, the shadow
price of a constraint is not the Lagrange multiplier (see Caputo 2007).17 The effects of the agreements on output and prices in a market with n firms are qualitatively the same
as for the monopoly market. However, the impact on profit is different. The VA always leads to a decline
in monopoly profit.18 The sign of the strategic effect is generally ambiguous. The constraint can increase or decrease
competition depending on the specific demand functions as well as the type and stringency of the
restriction imposed on firms.
Environ Econ Policy Stud (2012) 14:303–321 315
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depend on the relative lifetime energy consumption of both models.19 Corollary 1
follows immediately:
Corollary 1 For products that have a quality–efficiency trade-off, the averageefficiency VA reduces firm profit and may increase energy consumption.20
3.2 The no trade-off market
Under the no trade-off market, consumers have a higher willingness to pay for the
green model. In this case, the gain in energy savings from switching to the green
model outweighs the potential loss from a lower product quality. The effect of the
average efficiency VA, represented by a decline in Z, on market values is
summarized in the proposition below.
Proposition 4 Under the no trade-off market (1)oqNZ
B
oZ [ 0, (2)oqNZ
G
oZ \0 if its cost is
low enough, otherwise it reaches a maximum in Z at Z \ Z0, (3) oQNZ
oZ [ 0, (4)oPNZ
B
oZ \0, (5)oPNZ
G
oZ \0, (6) pNZ reaches a maximum in Z at Z \ Z0 and (7) oENZ
oZ [ 0:
Under the no trade-off market, the standard results in an expansion in the green
product market. In contrast to the trade-off case, this expansion is only possible
through attracting some of the buyers of the brown model as clear from Fig. 2. This
takes place as the brown model becomes relatively more expensive inducing
consumers to substitute toward the green model. The average efficiency VA results
in an increase in both prices and reduces total output as shown in Figs. 3b and 4b,
respectively. The average efficiency VA induces a substitution toward the green
model without any reduction in the price of the green model or expansion in total
output, contrary to the trade-off case. This is due to the higher ranking of the green
model under the no trade-off market, and thus firms meet the target without having
to reduce the price of the green model. The green market will always expand under
the average efficiency VA regardless of the market type, although its maximum size
may not be reached at Z = 0. It is possible that further tightening of the standard,
beyond a certain point, may reduce production of the green model, an outcome that
depends on parameter values.
While the average efficiency VA always results in a substitution toward the green
model, its impact on firm profit will depend on the market type. Under the no trade-
off market, a mild average efficiency standard raises firm profit. This is shown in
Fig. 5b where part of the equilibrium locus under the average efficiency VA lies
inside the iso-profit line, indicating that higher profit equilibrium points can be
achieved. Under the no trade-off market, the agreement raises prices of both models
19 IfdQTZ
G
dQTZB
[ � LB
LG; then energy consumption decreases with a decline in Z.
20 The impact on social welfare is beyond the scope of analysis of this paper where the main concern is
the profitability of the VA and its impact on energy consumption. However, it can be shown that a mild
standard under the trade-off market increases the sum of consumers and producers surplus, as it expands
production in an imperfectly competitive market. Its impact on social welfare will depend on how the VA
affects energy consumption and on the stringency of the standard.
316 Environ Econ Policy Stud (2012) 14:303–321
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and a mild standard brings firms closer to the collusion equilibrium, an outcome that
was not possible under the trade-off market.21
A decomposition of the effect of the VA on firm profit as in (12) and (13) shows
that the VA has a negative strategic effect under the no trade-off market. This
suggests that, all else equal, a tight standard raises firm profit as it reduces
competition between firms. The standard reduces the output of competing firms and
raises both prices. Under a mild standard, the strategic effect outweighs the
restriction effect giving rise to a higher firm profit. The results are consistent with
the empirical evidence cited earlier showing that the European car agreement could
not meet the goals that were set, while the second washing machine agreement
was successful in meeting its goals. Both agreements adopted an average
efficiency standard; however, there is a quality–efficiency trade-off only in the
cars market.
The average efficiency VA always reduces energy consumption under the no
trade-off market. The agreement reduces total output and results in a substitution
toward the green model. Thus Corollary 2 follows.
Corollary 2 For products that do not have a quality–efficiency trade-off, aprofitable average efficiency VA exists that reduces energy consumption.
4 The quota
A quota-based VA is an agreement designed to limit production/sales of the brown
model. I capture the effect of the quota by imposing a constraint on each firm’s
production decision as follows
qiB ¼ K ð15Þ
where i = 1 to n. A value of K below qB0 represents an agreement to limit production
of the polluting model.22 Note that a value of K equal to zero represents the
agreement to completely eliminate the brown model from the market. Each firm
maximizes profit in (9) subject to the constraint in (15) where qGi is the only choice
variable.23 The equilibrium values under the quota will be denoted by the super-
script NK for the no trade-off market and TK for the trade-off market.
21 In Fischer (2005), the imposition of an average efficiency standard always reduces firm profit in
contrast to the results in this paper. That is because she considers a monopoly market and the standard
restricts the monopolist’s choices or reduces his ability to extract surplus from consumers. However, this
paper shows that in a market with n firms, it is possible that the standard reduces competition between
firms and thus results in a higher firm profit.22 This is the type of constraint used in the European washing machine agreement. The agreement also
had a target for average energy efficiency, but given the commitment to eliminate production and sales of
low-efficiency machines, the average efficiency target was not binding.23 The maximization problem under the average efficiency standard can also be written such that qB
i is
the only choice variable, since qiG ¼
qiB
Z . However, the fact that qGi is a function of qB
i under the average
efficiency standard, which is not true under the quota, makes the two problems totally different since the
choice of qBi directly affects the output of the other model.
Environ Econ Policy Stud (2012) 14:303–321 317
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4.1 The trade-off market
The effect of the quota on the trade-off market is summarized below.
Proposition 5 Under the trade-off market (1)oqTK
G
oK \0, (2) oQTK
oK [ 0, (3)oPTK
G
oK \0,
(4)oPTK
B
oK \0, (5) pTK is non-monotonic and reaches a maximum at a value of K given
by K*, where K* \ qB0 and (6) oETK
oK [ 0.
The quota-based VA limits the output of the brown model below the pre-
agreement equilibrium level resulting in a rise in its price. This causes some of the
consumers who used to buy the brown model to stop buying at all. The reduction in
price difference between the two models also encourages some consumers to switch
to the green model. The impact of the quota on the segmentation of consumers by
purchase decision is shown in Fig. 1. Due to the increased demand for the green
model, both its output and its price increase.
The impact of the quota-based VA on firm profit depends on the stringency of the
quota. A mild quota increases firm profit relative to the pre-agreement scenario,
although further restriction of the quota beyond a certain point would result in a
decline in profits. Figure 5a shows the equilibrium locus under the quota for the
trade-off market. Part of the equilibrium locus lies inside the iso-profit line that goes
through the pre-agreement equilibrium, point O. A relatively stringent quota would
result in an equilibrium point outside the iso-profit line, i.e., a lower profit
equilibrium.24
Decomposing the effect of changing K on firm profit, as under the average
efficiency standard, reveals two effects from the quota. Firm i’s profit is given by the
Lagrangian function
UiTK ¼ PGqiTKG þ PBqiTK
B � cGðqiTKG Þ
2 � cBðqiTKB Þ
2 þ eðK � qiTKB Þ ð16Þ
where e is the Lagrangian multiplier. The impact of a reduction in K on firm profit is
As discussed before, the restriction effect is always positive indicating that
limiting firm i’s choices, all else equal, is detrimental to its profit. The strategic
effect under the quota, on the other hand, is always negative suggesting that limiting
the quantity of the brown model produced by other firms has a positive impact on
24 Even though a profitable agreement exists, in the absence of an enforcement device, it is not a Nash
equilibrium, i.e., in the absence of the agreement, both firms would choose not to limit production of the
brown model on their own and hence the agreement constitutes a binding restriction on their choices.
318 Environ Econ Policy Stud (2012) 14:303–321
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firm i’s profit as it reduces competition between firms. The net effect on firm i’sprofit will depend on the value of K.25
4.2 The no trade-off market
The effect of the quota on prices and profit under the trade-off market is
qualitatively the same as that for the no trade-off market. Thus, the results in
Proposition 5 also hold for a product that involves no quality–efficiency trade-off.
The impact of the quota-based VA on market segmentation for the no trade-off
market is shown in Fig. 2.
It is important to note that total energy consumption under the quota-based VA
always declines regardless of the market type, since total output declines and some
consumers switch to the green model. Corollary 3 follows.
Corollary 3 There always exists a profitable VA imposing a quota on the brownmodel that reduces energy consumption.26
5 Conclusion
It is important to understand the conditions under which a VA is likely to emerge
and achieve its target and the conditions under which mandatory standards are
needed to improve energy efficiency. The paper focuses on two important factors,
summarized in Table 1, which determine the profitability of VAs and thus the
likelihood of their success. The first factor is the nature of the product and whether
there is a quality–efficiency trade-off. The second factor is the nature of the
constraint imposed on firms. Two types of VAs are considered: a quota-based VA
and a VA based on an average efficiency standard.
The results indicate that a quota-based VA can always raise firm profit provided
it is not too stringent. This is because the quota reduces competition between firms
Table 1 Summary of results
The no trade-off market The trade-off market
Quota-based VA A profitable VA exists A profitable VA exists
Energy consumption declines Energy consumption declines
Average efficiency VA A profitable VA exists A profitable VA does not exist
Energy consumption declines Energy consumption may increase
25 This can explain why the European Committee of Domestic Equipment Manufacturers has decided in
April 2007 not to update their VAs on product energy efficiency (CECED 2007). While enforcement
problems could be a possible reason behind not updating the VAs as the CECED claims, it is also possible
that the agreement has limited production of the inefficient model, such that further reductions would
reduce industry profit as explained in Proposition 5.26 The quota-based VA always reduces the sum of consumer and producer surplus as it exacerbates the
underproduction problem. Whether it raises social welfare or not will depend on the magnitude of
environmental damages from energy consumption.
Environ Econ Policy Stud (2012) 14:303–321 319
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and can result in an equilibrium that is closer to the collusion outcome. This result is
true regardless of whether a trade-off exists or not. In addition, the quota-based VA
always results in a reduction in energy consumption and thus provides a win–win
opportunity for the industry and the environment. Alternatively, an average
efficiency VA, while giving firms more flexibility in choosing their product mix,
does not necessarily result in a higher profit level or less energy consumption. This
will depend on whether a trade-off exists or not. When a trade-off exists, the average
efficiency VA always reduces firm profit and may increase energy consumption if
the green model is not significantly energy efficient.
The poor performance of automobile fuel efficiency VAs has led policy makers
to conclude that VAs in general are not an effective tool in limiting pollution and
has led many countries to move toward government regulation instead. The results
here suggest that the success of a VA depends on the specific context. The failure of
automobile fuel efficiency VAs is due to the use of an average efficiency standard
applied to a product with a quality–efficiency trade-off, which is a costly
combination to firms. Thus, under these conditions, in the absence of a strong
regulatory threat, the prospects for a successful VA might be less promising.
However, the failure of VAs to improve automobile fuel efficiency does not imply
that VAs in general are not effective. The European washing machine agreement is
an example of a successful VA that achieved its targets. This VA used a quota-based
restriction applied to a product that does not involve a quality–efficiency trade-off.
The results indicate that this combination yields a VA that is relatively less costly to
firms. This suggests that in the future, we might continue to see successful VAs for
appliances, but regulatory solutions to reducing energy consumption for products
such as automobiles.
Acknowledgments I am grateful to Shunsuke Managi, the journal co-editor, and to two anonymous
referees for their comments and suggestions.
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