Theoretical Economics Letters, 2013, 3, 297-301
Published Online December 2013 (http://www.scirp.org/journal/tel)
http://dx.doi.org/10.4236/tel.2013.36050
Open Access TEL
Environmental Regulation, Technology Innovation, and
Profit: A Perspective of Production Cost Function*
Ming-Chung Chang
Department of Banking and Finance, Kainan University, Chinese Taipei
Email: changmc@mail.knu.edu.tw
Received October 17, 2013; revised November 17, 2013; accepted November 24, 2013
Copyright © 2013 Ming-Chung Chang. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In accor-
dance of the Creative Commons Attribution License all Copyrights © 2013 are reserved for SCIRP and the owner of the intellectual
property Ming-Chung Chang. All Copyright © 2013 are guarded by law and by SCIRP as a guardian.
ABSTRACT
The Porter hypothesis asserts that a stricter environmental regulation stimulates firms to conduct innovation and in-
crease their profit. This paper uses a theoretical framework to examine the Porter hypothesis. W e conclude that although
a stricter environmental regulation can increase profit, it does not stimulate innovation in a firm.
Keywords: Porter Hypothesis; Environmental Regulation; Innovation
1. Introduction
There was a controversy on whether stringent environ-
mental regulations enhance pollution-reducing innova-
tion and increase firms’ benefits or not. In the opinion of
Porter and van der Linde [1], the enforcement of envi-
ronmental regulations not only reduces environmental
damage, but also stimulates pollution-reducing innova-
tion and increases firms’ profit. This comes to be the
renowned Porter hypothesis. Many case studies after Por-
ter and van der Linde [1] support the Porter hypothesis,
but they have been criticized by economists for lack of
rigorous theoretical fo undations. Hence, this p aper uses a
theoretical framework to examine the Porter hypothesis.
In the case of a game without environmental regula-
tion, we consider a model with a single monopoly firm
producing a dirty product. For maximizing monopoly
profit, a monopoly firm determines the product’s envi-
ronmental performance at stage 1 and sets the price at
stage 2. In the case of a game with environmental regula-
tion, we consider two agents in the economy: a single
monopoly firm deciding a product’s environmental per-
formance and a price to maximize profit and a regulator
deciding an environmental regulation (an emission stan-
dard) to control th e emission quantity.
The paper closest to our own is Ambec and Barla [2],
who concluded that the Porter hypothesis can hold when
the product’s marginal environmental damage is small.
In contrast, we find that a strict environmental regulation
benefits a firm’s profit, but this cannot stimulate it to con -
duct innovation. This result comes from a difference on
the set-up of the cost function. The cost function in Am-
bec and Barla [2] is separated into the production cost and
R&D cost , and both are add ible. However, the cost func -
tion in this paper integrates the pro duction cost and R&D
cost. Other papers that seek to justify the Porter hypothe-
sis include Greaker [3], Hart [4], Mohr [5], and more.
The remainder of this paper is organized as follow.
Section 2 is the model set-up. Section 3 presents the case
of a game without environmental regulation. Section 4
presents the case of a game with environmental regula-
tion. Section 5 offers a comparison of the equilibrium
results of the two different games. Section 6 concludes
this paper.
2. The Model
We consider two agents in an economy. One is a firm (F),
and the other is an environmental regulator (R). The firm
produces an amount q of a good that generates a level e
of pollution. We connect quantity and environmental
quality here thro ugh a pollu tant emissions fun ction as e =
f(q)/θ. The emission function is increasing and convex in
q, where f(0) = 0, f'(q) > 0, and f''(q) 0 shows a positive
relationship between the output and the pollution. Pa-
rameter θ is an index for the product’s environmental
*The author appreciates the part of financial support from National
Science Committee (N S C 102-2410-H-424-02 0-).
M.-C. CHANG
298
performance. A product with a large θ means that it gen-
erates less environmental harm, i.e., a “green” product,
where θ (0, ). A firm’s cost function is described as
c(q,
), with c(0,
) = 0, c
(q,
) > 0, c

(q,
) > 0, cq(q,
)
> 0, and cqq(q,
) 0, where the subscripts stand for par-
tial derivatives, pollution abatement costs are increas-
ingly costly, and marginal production costs are non-de-
creasing. A firm’s cost function in our model also satis-
fies the traditional hypothesis in the environmental eco-
nomics literature by Palmer et al. [6], i.e., cq
(q,
) > 0.
Polluting emissions damage the global environment
and personal health due to the ingestion of polluted air,
water, and food. We denote the social cost D(e) as the
global environmental damage, and denote the private
cost d(e) as the personal health damage. The consumers
are a continuous distribution over [0, 1]. A consumer of
type s has a maximized willingn ess to pay for the product
to be s, and each consumer purchases at most one unit of
the product at price p. Since the global environmental
damage is the same for each buyer and each non-buyer, it
does not affect our analytic result. A buyer’s net utility is
s d(e) D(e) p, while a non-buyer’s net utility is
D(e). We assume that d(0) = 0, d' (e) > 0, and d''(e) 0.
3. Game without Environmental Regulation
The game without environmental regulation is a two-
stage game. At stage 1, the firm determines the product’s
environmental performance. At stage 2, the firm sets the
price. We use backward induction to obtain a sub-game
perfect Nash equilibrium (SPNE).
sU is assigned as the marginal consumer who is indif-
ferent to buy produ cts or not. The superscript “U” sta nds
for the case of a game without environmental regulation.
sU is solved through the Eq uation (1) as follow:


1sdf sp
0. (1)
From Equation (1), we have sU = sU(p, θ), where sU
[0, 1], and from Equation (1), we obtain the relationship
between sU and p by the Implicit Function Theorem as:

1
1
U
p
sdf

 0
,
. (2)
The result of Equation (2) tells us when price (p) in-
creases, it induces the critical point sU to shift to right and
it approaches 1. In other words, when price increases, it
makes the demand quantity (1 sU) decrease. Hence,
consumer behavior satisfies the demand law.
The demand function that firm faces is qU = 1 sU,
and the firm’s profit function is:
 
,, ,
UU
ppqpcqp
 

. (3)
Deriving Equation (3) with respect to parameter p and
let it be zero, we have the result in Stage 2 as:
0
UU
qU
pqs c. (4)
From Equation (1), we also obtain the relationship
between sU and θ by the Implicit Function Theorem as:
10
U
s
, (5)
where 22
011dfdfqd f
 
 0
 ,
and 2
1q
qcdf
2
 . The sign of U
s
is de-
cided by the sign of 1. When the product’s marginal
environmental damage is large enough, i.e.,
2
q
dqc f
 , it induces 1 < 0 and 0
U
s
. This
implies that given one unit of emission with large health
damage to consumers, an increase in a product’s envi-
ronmental performance induces the product’s demand
quantity to increase.
We next examine the relationship between price (p)
and the product’s environmental performance (θ). The
comparative static result in Equation (4) is:

22
2
0,
for.
U
q
q
pdfqdfq
sc
dqc f





 



(6)
This tells us that the clearer the product is, the higher
the price will be when the product’s marginal environ-
mental damage is large enough. There are two negative
effects in a consumer’s utility: a large marginal environ-
mental damage of the product and the high price. How-
ever, the product’s marginal environmental damage can
be mitigated by increasing its environmental perform-
ance. Hence, when the product’s marginal environmental
damage is large, the consumers are willing to spend a lot
more to purchase the product with high environmental
performance. Some studies on marketing research pro-
vide various evidence to support our finding such as
Cairncross [7], and Cason and Gangadharan [8]. They
concluded that some consumers are willing to pay a
higher price on biodegradable and 3R (Reduce, Reuse
and Recycle) products. We propose this as:
Proposition 1. In a game without environmental regu-
lation, when the products marginal environmental da-
mage is large, the consumers are willing to pay a high
price to purchase the product with a high environmental
performance.
We solve the equilibrium solution at stage 1. Recall
the firm’s profit function in Equation (3). Derive Equa-
tion (3) with respect to parameter θ and let it be zero. We
obtain the optimal product’s environmental performance
θU that maximizes the firm’s profit. Substitute θU into
Equation (4) and Equation (3), and the equilibrium solu-
tions in the game without environmental regulation are
{θU, pU,
U, eU}.
4. Game with Environmental Regulation
We now introduce an environmental regulation into the
game. At stage 0, the regulator sets the emission standard
Open Access TEL
M.-C. CHANG 299
eR. The superscript “R” stands for the case with environ-
mental regulation. Since the regulator must consider the
influence of environmental emission damage on social
welfare, the regulator manages a firm’s activity by fixing
an upper bound on emission quantity, i.e., eR < eU. The
regulator’s two behavior assumptions are:
Assumption 1 The regulator does not consider the
number of purchases when it regulates the emission stan-
dard, i.e., eR/s = 0.
Assumption 2 The emission standard becomes not
strict when a firm promotes the product’s environmental
performance, and both of them have a linear relationship,
i.e., eR/θ > 0 and 2eR/θ2 = 0. This assumption satis-
fies the claim by Porter and van der Linde [1] that envi-
ronmental regulation leads to a firm’s innovation.
We now go to the game analysis. The game structure
in this section is the same as the game without environ-
mental regulation. A marginal consumer defined as sR is
indifferent to buy products or not. Solve sR by the equa-
tion:


,
R
sdesp
0
,
. (7)
From Equation (7), we have sR = sR(p, θ), where sR
[0, 1], and from Equation (7), we obtain the relationship
between sR and p by the Implicit Function Theorem as:
10
R
p
s . (8)
Since an increase in price makes the critical point of
marginal consumer move to the right, i.e., the demand
quantity deceases, Equation (8) shows that the con-
sumer’s behavior satisfies the demand law. The demand
function that the firm faces is qR = 1 sR, and the firm’s
profit function is:
 

,, ,
RR
ppqpcqp
 

. (9)
Deriving Equation (9) with respect to parameter p and
letting it be zero, we have the equilibrium result in Stage
2 as:
0
R
qR
pq c . (10)
From Equation (7), we obtain the relationship between
sR and θ as:

RR
sdep

. (11)
The sign of
R
s
cannot be confirmed here until the
next context since we need to confirm a relationship be-
tween p and
. Deriving Equation (10) with respect to
,
we have:


20
R
qR
pde c
 
. (12)
We find that there is a direct relationship between p
and
, implying the consumer is willing to pay a high
price to purchase green products. This is because the
consumer can increase utility by paying a high price to
get a green product. Hence, we have a proposition as
follow:
Proposition 2. Under an environmental regulation,
the consumer is willing to pay a high price to get green
products.
We now recall Equation (11) to examine the sign of
RR
sde p
. Since eR/
> 0 and p/
> 0, the sign of
R
s
is positive. It shows that when the
product’s environmental performance increases, the num-
ber of consumers who purchase the product will decrease.
This result comes from a high product price.
At stage 1, the firm decides the product’s environmen-
tal performance. Substituting Equ ation (10) into Equation
(9) and deriving it with respect to θ, we have:
 
1
RR
des c


0
 . (13)
Equation (13) shows that the product with a low envi-
ronmental performance will create a high profit for the
firm. Hence, θR = 0 maximizes the firm’s profit. Substi-
tuting θR = 0 into Equation (10) and Equation (9), the
equilibrium solutions in the game with environmental
regulation are {θR = 0, pR,
R}.
5. Comparison Two Outcomes and
Examination of Porter Hypothesis
We now compare the outcomes of the two different
games and examine the implication of the Porter hy-
pothesis by assuming e = q/θ, c = q(θ2/2), d = e2/2. The
cost function here captures the characteristic that there is
no cost when the firm produces the lowest environmental
performance of a product, i.e., θ = 0. By simple calcula-
tion, we get the equilibrium solutions in the game with-
out environmental regulation as follow:
12
U
, (14a)
58
U
p, (14b)
18
U
, (14c)
12
U
e. (14d)
We next solve the equilibrium solutions in the game
with environmental regulation. Since the regulator sets
the emission standard eR, the environmental damage
function is d = (1/2)eR2. Letting s d(eR) p = 0, the
marginal consumer is sR = (1/2)eR2 + p, and the demand
quantity is q = 1 sR. Substituting q into the cost func-
tion c = q(θ/2)2, we have
= pq c. By backward induc-
tion, we get the equilibrium solutions:
0
R
, (15a)
0,0 . 5
R
p, (15b)
Open Access TEL
M.-C. CHANG
300
0,0.25
U
, (15c)
0, 2
R
e
. (15d)
A comparison in two different games shows in Table 1.
We next use the figure below to illustrate the firm’s
equilibrium profits in two different games. In Figure 1
we find that when the regulator sets an emission standard
(eR) lower than the emission quantity under the game
without environmental regulation (eU = 0.5), the firm’s
profit (
R) is higher than that under the game without
environmental regulation (
U). However, it does not
benefit the firm to promote a product’s environmental
performance since the product’s environmental perform-
ance under the game with environmental regulation (θR =
0) is lower than that of the game without environmental
regulation (θU = 0.5). This result is different from Ambec
and Barla (2002). They concluded that when the mar-
ginal environmental damage of a product is small, an
environmental regulation can enhance pollution-reducing
innovation and in creases the firm’s profit. The difference
between their conclusion and ours comes from the inde-
Table 1. A comparison in equilibrium result.
No
Environmental
Regulation
Implementation
Environmental
Regulation
Product’s Environmental
Performance (
) 1/2 0
Product’s Price (p) 5/8 [0, 0.5]
Firm’s Profit (
) 1/8 [0, 0.25]
Pollutant Emissions (e) 1/2 0, 2


0.5
0.25
0.125
0
π
π
U
e
R
π
R
2
Figure 1. Comparison of profits in two different games.
pendence between their production cost and innovation
cost. These two costs are relative in ours. Hence, we have
the proposition as fo llow.
Proposition 3. When the production cost and innova-
tion cost are relative, a stringent environmental regula-
tion can increase the firms profit, but it cannot enhance
pollution-reducing innovation.
6. Concluding Remarks
Many papers seek to justify the Porter hypoth esis, which
claims that a stringent environmental regulation will in-
crease a firm’s profit and enhance innovation. We use a
theoretical framework to examine the Porter hypothesis.
The closest article to ours is Ambec and Barla [2], who
concluded that when the product’s marginal environ-
mental damage is small, the Porter hypothesis holds. The
production co st and R&D cost in th eir paper are additive.
However, these two costs in our paper are relative. Hence,
our conclusion is different from Ambec and Barla [2].
We conclude that although a stringent environmental
regulation can increase the firm’s profit, it cannot en-
hance its innovation.
REFERENCES
[1] M. E. Poter and C. van der Linde, “Toward a New Con-
ception of the Environment Competitiveness Relation-
ship,” Journal of Economic Perspectives, Vol. 9, No. 4,
1995, pp. 97-118. http://dx.doi.org/10.1257/jep.9.4.97
[2] S. Ambec and P. Barla, “A Theoretical Foundation of the
Porter Hypothesis,” Economics Letters, Vol. 75, 2002, pp.
355-360.
http://dx.doi.org/10.1016/S0165-1765(02)00005-8
[3] M. Greaker, “Spillovers in the Development of New Pol-
lution Abatement Technology: A New Look at the Porter
Hypothesis,” Journal of Environmental Economics and
Management, Vol. 52, No. 1, 2006, pp. 411-420.
http://dx.doi.org/10.1016/j.jeem.2006.01.001
[4] R. Hart, “Growth, Environment and Innovation—A
Model with Production Vintages and Environmentally
Oriented Research,” Journal of Environmental Economics
and Management, Vol. 48, No. 3, 2004, pp. 1078-1098.
http://dx.doi.org/10.1016/j.jeem.2004.02.001
[5] R. D. Mohr, “Technical Change, External Economies, and
the Porter Hypothesis,” Journal of Environmental Eco-
nomics and Management, Vol. 43, No. 1, 2002, pp. 158-
168. http://dx.doi.org/10.1006/jeem.2000.1166
[6] K. Palmer, W. E. Oates and P. R. Portney, “Tightening
Environmental Standards: The Benefit Cost or the No-
Cost Paradigm?” Journal of Economic Perspectives, Vol.
9, 1995, pp. 119-132.
http://dx.doi.org/10.1257/jep.9.4.119
[7] F. Cairncross, “Costing the Earth,” Harvard University
Press, Cambridge, 1992.
[8] T. N. Cason and L. Gangadharan, “Environmental Label-
Open Access TEL
M.-C. CHANG
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301
ling and Incomplete Consumer Information in Laboratory
Experiments,” Journal of Environmental Economics and
Management, Vol. 43, 2002, pp. 113-134.
http://dx.doi.org/10.1006/jeem.2000.1170