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Strategic environmental policy; eco-dumping or a green strategy?
Journal of Environmental Economics and Management 45 (2003) 692–707
Strategic environmental policy; eco-dumping or a green strategy? Mads Greaker Statistics Norway, P.O. Box 8131 Dep., 0033 Oslo, Norway
Abstract The Porter hypothesis claims that a strong environmental policy best serves the interests of a nation’s export industry. While this hypothesis seems to be based on some form of bounded rationality, this paper argues that governments may have good reasons for setting an especially strong environmental policy even though firms are fully rational. If the available abatement technology turns the environment into an ‘‘inferior input’’, competitiveness is spurred by a strong environmental policy. The government should take advantage of this, and set an especially strict emission quota or an especially high emission tax. The findings in the paper also has consequences for the desirability of international cooperation with respect to national environmental policy. If a strict environmental policy spurs competitiveness, the environment is better protected without cooperation. r 2003 Published by Elsevier Science (USA). JEL classification: H7; Q2; R3 Keywords: Environmental policy; Strategic trade theory
1. Introduction Export firms are frequently given various kinds of subsidies, either openly as production subsidies or, more difficult to discover, as cheap government provided inputs or as tax reductions. One rationale for this line of thought can be found in the strategic trade theory literature. This literature explores how governments can help their national firms to steal profits from foreign competitors by making it possible for their firms to commit to a more aggressive strategy, see for instance [6]. While the literature on this subject dealt primarily with traditional industrial policy tools such as the ones mentioned above, it has during the 90s been extended to the field of
E-mail address: [email protected]. 0095-0696/03/$ - see front matter r 2003 Published by Elsevier Science (USA). doi:10.1016/S0095-0696(02)00053-0
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environmental policy. The question has been to what extent a government should provide its export industry with a weak environmental policy as a sort of hidden subsidy. Weak environmental policies which purposely seek to promote the competitiveness of the export industry, could be characterized by the term ‘‘eco-dumping’’. The prospect of eco-dumping has been a major issue in the trade-environment debate, see for example [1,26]. Because the current GATT treaty prohibits the use of traditional industrial policy tools like export subsidies and restricts the use of other subsidies like R&D subsidies, eco-dumping could become even more attractive. However, the prospect of eco-dumping presupposes that a strong environmental policy hampers competitiveness. Empirical research indicates that this may not always be the case. An econometric study from Norway by Golombek and Raknerud [9] suggests that a strong environmental policy spurred employment and induced a lower probability of exit from some industries notably pulp and paper and iron, steel and ferroalloys. Porter and von der Linde [17] refer to various case studies where a strong environmental policy lead to decreased production cost and/or higher value products. The idea that a strong environmental policy will improve the general performance of firms is the so-called Porter hypothesis, which we will refer to as a ‘‘green strategy’’. The Porter hypothesis is disputed among economists, see for example Palmer et al. [16]. Further, Porter and von der Linde [17] do not provide us with an unambiguous definition of the term green strategy. In this paper a green strategy will be defined as an environmental policy where marginal abatement cost exceeds marginal environmental damage, and vice versa, ecodumping will be defined as an environmental policy where marginal abatement cost falls short of marginal environmental damage.1 Regarding eco-dumping and a green strategy, we will deal with two questions in the paper. Firstly, we will analyze how environmental policy affects marginal production costs, and secondly, we will see how this affects the question of optimal policy. A majority of the articles about eco-dumping do not explicitly treat the issue on how environmental policy affects cost, but assumes that both total cost and marginal cost is increasing in the stringency of environmental policy (see for example [2,3,7,18]). This paper shows that although total cost increases, it is not necessarily the case that marginal cost increases. If the environment is an inferior input for some levels of environmental policy, marginal production cost will decrease for these levels of policy. The development of a cost model of end-of pipe cleaning further indicates that the inferior input case is likely if there is economics of scale in abatement technology. Economics of scale seems to be a feature of many abatement technologies. In an econometric estimation of abatement cost for the cement, pulp and paper and iron and steel sector Hartman et al. [12] find that ‘‘average abatement cost drops sharply as abatement volume increases’’. Scale economics in abatement is also suggested by the US Environmental Protection Agency [23,24]. Ulph [22], Bradford and Simpson [4] and Ulph and Ulph [21] also contain a model of abatement where marginal production cost may be decreasing in the stringency of environmental policy. In these models the firms undertake environmental R&D before they compete in the market. The result that marginal production cost may be decreasing in the stringency of 1
The literature also compares the non-cooperative environmental standards with the cooperative environmental standards. This comparison is also made in this paper, but it is not used to define a green strategy or eco-dumping.
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environmental policy therefore appears to be dependent on the sequential timing of the R&D decision and the output decision. However, this paper shows that this result alternatively can be explained by the inferior input concept independent of the timing of decisions. Regarding optimal policy, all authors find that eco-dumping is optimal when the firms compete in quantities and when abatement is decided simultaneously with output [2,3,7,18]. For the contributions of A. Ulph [20], D. Ulph [22], Bradford and Simpson [4] and Ulph and Ulph [21] with environmental R&D, the results are more ambiguous, however, no unambiguous support for a green strategy can be found. Hence, the Porter hypothesis is not confirmed in the theoretical literature apart from the Bertrand situation where the government purposely hurts the competitiveness of its firm in order to soften competition (see [3]). This paper shows that if emissions are an inferior input, the government should use a green strategy when abatement and output are decided simultaneously. This is also very likely to hold when abatement effort is decided separately from output. Cases where emissions can be both an inferior and a normal input are explored through a numerical example. In these cases the resulting strategy is sensitive to market size. Since it is scale economics in abatement which leads to the inferior input case, environmental policy will be stronger and emissions smaller the bigger the market.
2. A simple model of strategic environmental policy The model includes two countries; one domestic and one foreign. There is one nationally owned firm in each of the countries. Both firms pollute, and the governments use an emission tax to regulate emissions. The firms export to a third market, compete by choosing output levels, and take the emission taxes in the two countries as given. It is assumed that environmental damage is national, and that the environmental performance of the industries has no effect on demand. Denote the domestic firm’s output by q; the domestic emission tax rate by t and let cðq; tÞ be the domestic firm’s cost function. Emissions can be interpreted as an input, and the tax rate as the price of this input. It then follows from standard production theory that costs are increasing in the tax rate. Denoting derivatives by subscripts, we have c1 40 and c2 40: Uppercase letters denote corresponding magnitudes for the foreign firm, with C1 40 and C2 40: Total revenues of the domestic and foreign firms are rðq; QÞ and Rðq; QÞ respectively. Assuming that the two products are substitutes yields; r2 ; R1 o0: It is also assumed that r12 and R21 are negative in order to ensure that the outputs of the two firms are strategic substitutes. Profits of the home and foreign firms are given by pðq; QÞ ¼ rðq; QÞ cðq; tÞ
ð1Þ
Pðq; QÞ ¼ Rðq; QÞ CðQ; TÞ;
ð2Þ
and
respectively. Each firm chooses its output taking the emission tax and the output of the other firm as given. The first-order conditions are p1 ¼ r1 c1 ¼ 0
ð3Þ
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and P2 ¼ R2 C1 ¼ 0:
ð4Þ
The two first-order conditions determine the Nash-equilibrium output quantities given the emission taxes. It is assumed that the second-order conditions for profit maximum hold, i.e. that p11 ; P22 o0: Further, we assume that the uniqueness criterion for the Cournot–Nash equilibrium is fulfilled, i.e. that ðp11 P22 p12 P21 Þ40:2 The output quantities can then be written as functions of the emission tax rates; q ¼ qðt; TÞ and Q ¼ Qðt; TÞ: In order to study the two functions; qðt; TÞ and Qðt; TÞ; we look at the comparative statics of the Nash equilibrium. Total differentiation of systems (3) and (4) yields: p11 dq þ p12 dQ c12 dt ¼ 0; P21 dq þ P22 dQ ¼ 0: We have from the second equation that dQ=dq ¼ P21 =P22 : Inserting this into the first equation we obtain dQ ¼ c12 P21 =ðp11 P22 p12 P21 Þ: dt Combining this with the expression for dQ=dq we also obtain dq ¼ c12 P22 =ðp11 P22 p12 P21 Þ: dt The denominator in both expressions is positive, while both P22 and P21 are negative. The signs dq on dQ dt and dt are thus dependent on c12 : dq ð5Þ Sign ¼ Sign½c12 ; dt dQ ð6Þ ¼ Sign½c12 : Sign dt Note that the derivatives have opposite signs reflecting that the two outputs are strategic substitutes. If marginal cost is increasing in the emission tax rate, the domestic firm would like to supply less the higher the emission tax rate for a given output of the foreign firm. Hence, its reaction curve shifts inward if the emission tax rate is increased. In the new Nash equilibrium the foreign firm has increased its output, while the domestic firm has reduced its output. This is the normal case analyzed in the literature, see for example [18]. However, the sign on c12 is by no means given from economic theory alone, even though c2 40: Denoting emission by s; we have from Young’s equality and Shepard’s lemma: @c2 ðq; tÞ @c2 ðq; tÞ @s ¼ ¼ : ðc12 ¼Þ @t@q @q@t @q 2
ðq;tÞ Thus, the cross-derivative @c@q@t tells us how emissions change with an increase of output for given input prices including the emission tax rate. Hence, the normal case depends on emissions 2
See the discussion about uniqueness in [19, pp. 225–226].
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@s being a normal input, i.e. @q 40: If on the contrary, emissions are an inferior input, an increase in the emission tax rate would lead to lower marginal cost, and thus an expansion of domestic output. In order for emissions to be an inferior factor, the firm must be able to abate emissions. Further, the technology must be such that the firm chooses to abate more of the emissions, the higher the output. Total emissions can then be decreasing in output. The mechanism with respect to costs is as follows: Marginal production cost of the regulated firm consists of two parts; firstly, the extra input needed for production of an additional unit, and secondly, the emission tax payments resulting from the extra emissions created by the production of an extra unit. Imagine then that the government increases the tax rate. This makes the firm increase its abatement effort, which implies that one additional unit of output creates less extra emissions. If this reduction in emissions per unit effect dominates the direct effect of the increased tax rate, marginal production cost will be decreasing in the emission tax rate. The first proposition then follows directly from standard production theory. @s 40; the domestic firm will reduce its output as a Proposition 1. If emissions are a normal input, i.e. @q
response to a higher emission tax rate, i.e. dq dt o0: In the new Nash equilibrium the foreign firm will dQ produce more, i.e. dt 40: If emissions are an inferior input both effects are reversed. Emissions cannot be an inferior input for all t: Since total cost is given by the area under the marginal cost curve, the marginal cost curve has to shift up for some t—for example by a discontinuous jump when t is just above 0.3 Net surplus generated by the home firm is given by w: w ¼ rðqðt; TÞ; Qðt; TÞÞ cðqðt; TÞ; tÞ þ ts dðsÞ;
ð7Þ
where the two first terms represent the profit of the firm as a function of t and T: The third element is the firm’s tax payment. Since the tax payment is a pure transfer, and since it is included implicitly in the cost function cðq; tÞ; we have to explicitly add it in the welfare expression. The last element dðÞ is the environmental damage caused by the firm. The function dðÞ is assumed to be increasing reflecting that higher emissions increases environmental damage. The government of the home country maximizes the net surplus taking the emission tax of the other country as given. A first order condition for maximizing national product obtains when dw dt ¼ 0: dw dq dQ dq dq ¼ ðr1 c1 Þ þ r2 c2 þ c2 þ t c22 þ c21 d1 c22 þ c21 ¼ 0; dt dt dt dt dt where by Shepard’s lemma; s ¼ @cðq;tÞ @t ¼ c2 : 3
Dijkstra [8] mentions the possibility of the inferior input case, but does not analyse it any further.
ð8Þ
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The first term is zero by the firm’s first-order condition for profit maximum (3), and the third and the fourth term cancel out. By rearranging terms we get d1 t ¼
r2 dQ dt
ð9Þ
: c22 þ c21 dq dt
The term in the nominator r2 dQ dt is the strategic effect of the environmental policy. Since r2 is negative, the strategic effect is negative if emissions are a normal input and positive if emissions are an inferior input. The first term in the denominator c22 is negative or zero by the concavity of the cost function. In 2
ðq;tÞ Þ refers again to the properties of emissions as an input. the next term the derivative c21 ð¼ @c@q@t Thus we can have two cases for the left-hand side of (9). dq dq If emissions are a normal input; c21 40; then r2 dQ dt o0; dt o0 and c22 þ c21 dt o0 which implies dq dq that d1 t40: If emissions are an inferior input c21 o0; then r2 dQ dt 40; dt 40 and c22 þ c21 dt o0 which implies that d1 to0: We know that the firm sets marginal abatement cost equal to the tax rate. Hence, we have the following proposition:
Proposition 2. If emissions are a normal input d1 4t: If emissions are an inferior input
@s @qo0;
@s @q40;
the government will prefer eco-dumping, i.e.
the government will prefer a green strategy, i.e. d1 ot:
In the ‘‘green strategy’’ case the government fixes an emission tax rate which exceeds marginal environmental damage. Since this forces marginal cost of the domestic firm to decrease, the firm will want to produce more even if total cost goes up. The high tax rate works as a commitment to increase output. In the case of eco-dumping, it is easy to show that profit increases compared with the situation where the tax rate is set equal to marginal environmental damage. The firm gets both reduced cost and a higher market share. In the green strategy case profit can go both ways; on the one hand, the firm gets higher market share and hence, higher revenues, on the other hand the firm gets higher total cost. In a non-cooperative equilibrium both governments use their emission tax strategically. In order to see that this leads to a sort of a Prisoners dilemma we will take a look at the cooperative equilibrium. We assume that the two countries and the two firms are symmetric in all aspects, and that they maximize joint welfare with respect to a common emission tax rate. The maximization problem can then be written: maxfw þ W ¼ 2½rðqðt; tÞ; Qðt; tÞÞ cðqðt; tÞ; tÞ þ tc2 dðc2 Þg; t
which after some rearranging yields the following first-order condition: d1 t ¼
@Q r2 ð@Q @t þ @T Þ
ðc22 þ c21 dq dt Þ
:
ð10Þ
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@Q @Q 4 The nominator at the left-hand side of (10) is dominated by @Q @T because we have j@T j4j @t j: @Q Hence, the term r2 ð@Q @t þ @T Þ will be negative when emissions are an inferior input, and the term will be positive when emissions are a normal input. Since ðc22 þ c21 dq dt Þo0; the following proposition follows.
Proposition 3. In the cooperative solutions the results are reversed: If emissions are an inferior input @s @s @qo0; the governments will prefer eco-dumping, i.e. d1 4t; and if emissions are a normal input @q40; the governments will prefer a green strategy, i.e. d1 ot: Contrary to the popular view, cooperation may lead to a less stringent environmental policy. The reason is that a stringent environmental policy makes the firms more aggressive in the inferior input case, and that the governments want to ‘‘soften’’ competition in order to turn the two firms into a sort of ‘‘world monopoly’’.
3. Inferior input cases Norway has a considerable aluminium industry which exports almost all of its production, and studies have indicated that the industry has some degree of market power (see for example [15]). There are two ways of smelting primary aluminium; the old Soderbergh method and the new Prebake method. The Prebake method is in general superior with regard to emissions; it implies lower local emission of hazardous gasses and particles, uses less energy per ton aluminium produced, etc. [25, p. 263]. On the other hand, the Prebake method requires a separate facility for ‘‘baking’’ the electrodes in addition to the production unit. In Norway, tough environmental regulation seems to have accelerated the shift from Soderbergh technology to Prebake technology. At a major production site where a switch of technology is currently taking place, total emissions are being cut, while production capacity is being increased. The increased capacity could be a sign that the tough environmental regulation has made the Norwegian producer more aggressive as the theory about inferior inputs above predicts. However, since the increased capacity may have other explanations, this paper also includes a formal abatement cost model based on the engineering literature about end-of-pipe cleaning where emissions may be an inferior input. Many processes, for example cement production, lead to emissions of airborne particles which represents a potential, local health hazard. The abatement of particles implies the installing of filters at different point sources in the production process— there are typically many point sources at each production line. Total particle removal efficiency is hence enhanced by increasing the number of point sources with filters.5 4 That the effect on foreign output of the foreign emission tax is greater than the effect on foreign output of the domestic emission tax follows from the assumption about Nash-equilibrium uniqueness and the assumption about symmetry. 5 The model is also based on a visit to a cement factory in Norway. In the factory there were 14 point sources with filters, and practically all particle emissions were removed.
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The filters can be of many types of which; electrostatic precipitators and baghouses are the most effective—most modern designs remove 99.9% of all the particles from a given flow [24]. The cost of cleaning can be measured by the number of filters and the capacity of each filter [23]. Since gross emissions of particles are in most cases positively related to output, the capacity of the filters must also be positively related to output. Let one unit of output correspond to one unit of gross emissions, i.e. gross emissions are equal to output; q: Let further n denote the number of filters, and aðqÞ the cost of a typical filter. A certain number of filters installed will imply that a fraction bðnÞ of gross emissions are removed, and that a cost naðqÞ is incurred. If the local environmental protection agency levies a particle tax t on net emissions from the industry, we have that the cost function of the domestic firm can be written: cðq; t; nÞ ¼ cðqÞ þ tð1 bðnÞÞq þ naðqÞ
ð11Þ
where we have b0 ; a0 40 and b00 o0: Further, we assume a00 p0:6,7 The industry decides on the number of filters to install. From cost minimisation we obtain an optimal number of filters; n ¼ nðt; qÞ: This function can be substituted back into the cost function. ds : The extent to which emissions are an inferior input is determined by the sign on the derivative dq ds d½ð1 bðnðt; qÞÞÞq @b dn ¼ ¼1bq : dq dq @n dq
ð12Þ
ds dn The term q @b @n is positive, and hence, a necessary condition for obtaining dqo0; is dq40; i.e. the firms must increase their use of filters when they increase output for a constant emission tax rate. For the derivative dn dq we have
dn b0 aðqÞ aðqÞ 0 a ¼ 00 X0; since a0 p when a00 p0: dq b aðqÞ q q
ð13Þ
Hence, scale advantages in abatement technology, ensures that the firm will choose to increase its use of filters if output is increased. By inserting, we finally obtain ds q ð1 bÞaðqÞ 00 aðqÞ 0 2 0 ¼ b þ a ðb Þ : ð14Þ dq aðqÞb00 q q aðqÞ q 0 2 ð1bÞaðqÞ 00 ds 0 Since aðqÞb jb j: 00 o0; we have dqo0; if ½ q a ðb Þ 4 q Lastly, by experimenting with different functional forms for bðnÞ and aðqÞ we find for example that all bðnÞ ¼ ðnn%Þl ; lo1; where n% is the number of filters which remove practically all particle ds o0 for some t emissions, in combination with all aðqÞ ¼ nnqy ; yo1; where n is a parameter, yield dq (see the appendix). 6
A more detailed derivation of the cost model can be found in the appendix. Kohn [13] and Hartford [11] also contain a model of end-of-pipe cleaning, however, their model does not entirely comply with the facts about the abatement technology that we have gathered. 7
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Table 1 ðy; MÞ
tn
d0
ð1 bðnÞÞq
q qþQ
naðqÞ cðq;tÞ
ð12; 5Þ ð12; 20Þ ð1; 5Þ ð1; 20Þ
0.266 0.174 0.261 0.410
0.281 0.140 0.322 0.419
0.703 0.351 0.804 1.048
48:2% 50:1% 45:1% 48:7%
7.1% 9.9% 5:1% 8:4%
4. A numerical example In this section we will look at a numerical example based on the model of end-of-pipe cleaning discussed in the former Section. By this we want to illustrate that the strategic effect can have a significant impact on the resulting net emissions. Further, we want to draw attention to an effect which is more complicated to demonstrate in the general model. When there is scale advantages in abatement, a big market leads to a more stringent environmental policy. In the example the firms and the countries have identical cost- and environmental damage functions. The costfunction is given by: cðqÞ ¼ c0 q; bðnÞ ¼ ðnn%Þl ; lo1; and aðqÞ ¼ nnqy ; yp1: Further, demand is given by: p ¼ M q Q where p is the market price and M the market size. And lastly, the environmental damage function is given by: d ¼ d0 ½ð1 bðnÞÞq2 :8 In Table 1 a simulation of the optimal environmental tax rate tn for a given predetermined T (otn ), and for different values of y and M is presented. The model is calibrated so that abatement cost does not make up more than 10% of total cost (the last column below). The following 9 parameter values are used; T ¼ 0; 1; l ¼ 23; ðnnÞ % ¼ 0; 3; c0 ¼ 1; d0 ¼ 0; 2: Firstly, note that in a model with simultaneous abatement–output decisions marginal abatement cost is equal to the tax rate. When y ¼ 12; emissions become an inferior input for bðnÞ40; 5: However, as long as the market is small ðM ¼ 5Þ; it is not optimal for the government to exploit this, and we consequently have that tn od 0 : The situation changes when the market is big ðM ¼ 20Þ: We then have that tn 4d 0 ; and that net emissions actually have decreased compared to the situation in the small market. This is clearly an effect of the increasing returns to scale property of the abatement technology. Note that in this q ¼ case the domestic firm succeeds in increasing its market share compared to the t ¼ T case ðqþQ 50:1%Þ (Table 1). In the two last rows we have removed the scale effect, and hence, emissions can no longer be an inferior input. Consequently, the governments sets tn od 0 irrespective of market size. The optimal level of net emissions are also increasing in the market size. Note that net emissions are considerably higher in the case with y ¼ 1 than with y ¼ 12: In Table 2 we present the non-cooperative policy equilibrium, i.e. the subgame—perfect equilibrium of the two stage game in which both governments simultaneously maximize welfare in 8 The simulation has also shown that an interior welfare maximum does not always exist. For example the case with constant marginal environmental damage does not yield an interior maximum. 9 l ¼ 23 and y ¼ 12 (or y ¼ 1) makes it possible to solve the model exact for the Nash-equilibrium output levels.
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Table 2
Non-cooperative Cooperative
t
T
d0
ð1 bðnÞÞq
w
w:w
0:174 0:172
0:174 0:172
0:142 0:197
0:355 0:492
39:5302 39:5344
158:7386 158:7322
the first stage, and the firms maximize profits in the second stage. Further, we compare the noncooperative equilibrium to a cooperative equilibrium where joint welfare is maximized under the condition that t ¼ T: For the parameters we have M ¼ 20; y ¼ 12; and the rest as before. All figures are for the domestic country except for the foreign tax rate and the last column: w.w. Note that net emissions are lower in the non-cooperative equilibrium than in the cooperative equilibrium. The reason is that a high emission tax rate makes the companies more aggressive, and hence, output is higher and emissions lower. On the other hand, domestic welfare is higher in the cooperative equilibrium. Because tod 0 in this equilibrium, the firms are less aggressive, total output is lower, and total oligopoly profits are higher. In the last column we display world welfare ðw:wÞ; i.e. the sum of domestic welfare, foreign welfare and consumer surplus in the third market. We note that from the point of view of the world the competitive policy equilibrium is preferred. Since total output is higher, consumer surplus in the third market has increased.
5. The use of other instruments An obvious question is whether the results change with the type of instrument. Consider for example an emission cap, i.e. the firm is only permitted to emit a certain load in a given period irrespective of output. The firms cost minimization problem can then be solved by the Langrange method where the emission cap places a constraint on the use of emissions as input. From the Langrange method we obtain a shadow price on emissions. This shadow price plays exactly the same role as the emission tax from the former section. Since reducing the emission cap implies an increase in the shadow price on emissions, we get the same results with respect to the effect on marginal production cost. A smaller emission cap, may reduce marginal production cost for some intervals of the emission cap. This can be explained intuitively by the following example. We compare the cost of increasing output for two levels of the emission cap. Given a high emission cap, the firm would like to invest in few filters and clean a small fraction of the emissions—say 25%. An increase in output would then imply a high increase in emissions, and consequently, the firm would have to increase the fraction cleaned by many %-points—if output goes from 10 to 11—by 7%-points. Given a low emission cap, the firm would on the other hand have to invest in many filters and clean a large fraction—say 75%. The same increase in output would then imply a smaller total increase in emissions. Thus, the firm would not have to increase the fraction cleaned as much as in the case for a high emission cap—if output goes from 10 to 11—by 2%-points. This could imply that it is less costly to increase output when the emission cap is low than when the emission cap is high, and consequently, the firm becomes more aggressive.
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It is also easy to show that as long as marginal cost is decreasing in the stringency of the environmental policy instrument, an optimal policy will imply a green strategy in the strategic environmental policy situation. Thus, the analysis yields the same results with an emission cap as with an emission tax. This is also showed explicitly in Greaker [10]. The situation changes when the government uses a technology mandate or demands a certain emission/output fraction. In the simplified model from Section 3 these two instruments have identical effects on costs. A technology mandate would imply a certain number (and type) of filters, as would a certain emission/output fraction. Marginal production cost is then strictly increasing in the policy instrument. In order to increase output the firm would have to increase the capacity of each filter. The more filters the firm is required to have, the more the firms’ capacity cost would increase with an increase in output. Hence, we would expect the government to ecodump if the government uses a technology mandate or demands a certain emission/output fraction.
6. Sequential abatement/output decisions So far we have assumed that output and abatement is decided simultaneously. In Ulph [22], Ulph and Ulph [21], Ulph [20] and Bradford and Simpson [4] abatement is R&D of cleaner production processes, and abatement and output is decided sequentially. The following discussion will focus on Ulph [22] who makes use of a cost function that has close similarities to the cost function which was developed for the end-of-pipe cleaning case. Change the definition of n; and let n now denote the amount of R&D. The cost function of Ulph [22] can then be written cðq; tÞ ¼ c0 q þ t½1 bðnÞq þ n: We have b0 40 and b00 o0 as in the model of Section 3. Since abatement takes the form of R&D, there is no capacity part of abatement cost—just n: Ulph [22] finds that marginal cost will be decreasing in t if the R&D technology satisfies the following condition: 1 ½ð1 bÞb00 ðb0 Þ2 o0: b00
ð15Þ
The condition appears to be dependent on the sequential timing of R&D and output decisions. However, by comparing Eq. (15) with Eq. (14) we discover that the condition also would have applied if R&D and output were decided simultaneously. Hence, if the firms decided R&D levels by just minimizing cost, we would still have that marginal cost is decreasing in t as long as condition (15) holds. Characterizing the optimal policy is considerably harder in the sequential version of the strategic environmental policy situation. Because the firms also compete in R&D levels, the firms over-invest in R&D and set marginal abatement cost above the emission tax rate, see also [5]. It is therefore misleading to evaluate the environmental policy by comparing marginal environmental damage with the emission tax rate as we can do for the two-stage version of the game.
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This has implications for the interpretation of the results in the articles of Ulph [22] (and Ulph and Ulph [21]). If marginal environmental damage were compared directly to marginal abatement cost, we would find that results tended to follow the simpler two-stage model. In the working paper version of this paper [10] the three stage game of Ulph [22] is solved in order to carry out such a comparison. When ½ð1 bÞb00 ðb0 Þ2 ¼ 0; marginal production cost is independent of the emission tax rate, and the government sets marginal abatement cost equal to marginal environmental damage. This is done by letting the tax rate fall short of marginal environmental damage. But because the firm overinvests in abatement, marginal abatement cost will be equal to marginal environmental damage anyhow. Greaker [10] also deals with the two other cases for the term; ½ð1 bÞb00 ðb0 Þ2 : Qualitatively, the results tend to follow those obtained from the two stage game. If emissions are a normal input, eco-dumping is the preferred policy, and if emissions are an inferior input, a green strategy is the preferred policy. The sufficient, but not necessary condition is: That the elasticity of marginal cost with respect to output is smaller than the inverse total cost share of total environmental taxes.10 The reason for the ambiguity is that the emission tax has two effects in the three stage game: It works as an export tax which is always bad when we have Cournot competition in the market game. However, it also influences marginal production cost of the foreign firm. Generally, the domestic government would like the marginal production cost of the foreign firm to rise, which also happens as long as emissions are an inferior factor.
7. Concluding remarks This paper has not treated other forms of competition. The introduction of Bertrand competition would turn all the conclusions around in the simple two-stage model where emissions are either inferior or normal. However, we would argue that the two-stage version of the game is less appropriate for Bertrand competition. Clearly, prices can be changed a lot easier than abatement technology. An emission cap could therefore work as a capacity constraint. This could yield the Cournot outcome of the Bertrand game as in Kreps and Scheinkman [14]. For a discussion of this case, see the working paper version of this paper [10]. It is argued in this paper that profit may rise as a result of a stronger environmental policy if competition is imperfect (compared to a weak level of environmental policy). The question is then why companies often resist stronger environmental regulation. Does this mean that emissions are very seldom an inferior input? This is probably to jump to conclusions. Firstly, profit is likely to decrease in the whole interval of the emission tax rate even if emissions are an inferior input for some interval of the emission tax rate. In the model total cost always increases. Thus, if the profit shift does not make up for the increase in total cost, profit is hampered.11 10
I.e. if emission taxes makes up 10% of total cost, the elasticity of output on marginal cost has to be less than 10 in Nash equilibrium. 11 At least profit must be decreasing for the optimal tax rate, if not, the government should increase the tax rate even further.
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Secondly, the firm’s point of reference could be no environmental policy, i.e. t ¼ 0: Then profit is bound to decrease at least in the end-of-pipe abatement cost model. In this model marginal production cost cannot be lower with regulation than without regulation. Consequently, the maximal profit shift cannot exceed the cost effect. Lastly, the model of a simultaneous game between two firms in both abatement and output may not be a good description of the actual situation. One could think of a lot of other alternative sequences of decisions. If for example one of the firms is told to install end-of-pipe equipment, it could act before its competitors had time to react. Ex post the investments in abatement should sometimes be treated as sunk costs hampering profit, but not altering the Cournot–Nash output levels. The paper should not be regarded as a general recommendation for strategic environmental policy. As the discussion in Section 3 has shown it is very difficult to know a priori whether emissions are an inferior or normal input. Further, we do not know a priori how competition in a particular market works. Thus, the policy implication of the paper is that governments should not distort their environmental policy for strategic reasons. However, given that emissions may be an inferior factor, politicians should a priori be less afraid of introducing a sufficiently stringent environmental policy.
Acknowledgments I am very grateful for the advice and comments I have received from my supervisor Nils Henrik von der Fehr. I would also like to thank Jon Vislie, Andrea Bigano and two anonymous referees for very valuable inputs. Lastly, I would like to thank the Norwegian Research Council for financial support. Appendix A. Derivation of the end-of-pipe abatement cost model Facts about end-of-pipe abatement technology can be found in the EPA Air Pollution Technology Fact Sheets [24], the EPA OAQPS Control Cost Manual [23] and the World Bank Pollution Prevention and Abatement Handbook [25]. The gross emissions of particles is in most cases directly related to output: sg ¼ Eq;
ðA:1Þ
where E is a given parameter, which for our purpose can be normalized to one. Abatement of gross emissions implies the installing of filters at different point sources in the production process. Total particle removal efficiency is hence enhanced by increasing the number of point sources with filters. Let n denote the number of filters. A certain number of filters installed will then imply that a certain fraction bðnÞ of the gross emissions; sg is removed. Net emissions; sn can then be written: sn ¼ ½1 bðn; s1g ; y; sng Þsg ;
ðA:2Þ
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with the following derivatives: @b @2b X0; o0; 2 @n (@n 0 for sig ps%ig @b ¼ @sig o0 for sig 4s%ig
8i ¼ 1; y; n;
where sig is the particle flow passing through filter i; and s%ig is the capacity of filter i: Since increasing the fraction cleaned for a given gross emissions implies adding new filters to 2 less pollution intensive point sources, we assume @@nb2 o0: Further, since the firm chooses its output, the number of filters and the capacity of each filter simultaneously, we also assume that sig ¼ s%ig 8i ¼ 1; y; n: Hence, the arguments s1g ; y; sng can be removed from the b-function. The cost of cleaning, i.e. the abatement cost a; can be measured by the number of filters and the capacity of each filter (see the EPA OAQPS Control Cost Manual, from pp. 6–46 of [23]): a¼
n X
ai ðs%ig Þ;
ðA:3Þ
i¼1
where the function ai ðs%ig Þ gives the cost of filter i as a function of the capacity. A continuous representation of (A.3) should take into account that the capacity of filter n; s%ng is likely to decrease as the number of filters n are increased, i.e. new filters are placed at less pollution intensive point sources. Further, since the capacity of at least one filter must be increased when output is increased, the continuous representation of (A.3) must be increasing in q: a ¼ aðn; qÞ
with an ; aq 40; ann ; aqq p0
and anq 40:
The first-order derivatives should be un-problematic. The cross-derivative is positive, because with a higher number of filters, an increase in output is likely to lead to increased capacity on more filters. The capacity cost of the filters is dependent of the gas volume flow rate because a higher gas volume flow rate will require a higher collection plate area. Further, since the gas volume flow rate will be proportional to output, we have that higher output will imply a larger collection plate area. From Fig. 6.5 on page 6–41 in EPA Control Cost Manual [23] we note that costs per squarefoot collection plate area decreases. This suggests that we have aqq p0: We also quote the EPA Air Pollution Technology Fact Sheets [24], Electrostatic Precipitators; ‘‘in general, smaller units controlling a low concentration waste stream will not be as cost effective as a large unit cleaning a high pollutant load flow’’. Thus, if higher output among others, implies a higher concentration of particles in the gas flow, this also indicates that we have aqq p0: Lastly, the reason for ann p0 is already mentioned. In Section 3 we have just used a ¼ naðqÞ; and hence, we have ignored the possibility that ann o0: Taking this into account would have reduced the convexity of the ‘‘emission-reduction’’ cost function. Thus, assuming a ¼ naðqÞ actually makes the inferior factor case less likely.
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With the specified functional forms the domestic firm solves the following cost minimization problem: n l q þ unqy ; min cðq; t; nÞ ¼ c0 q þ t 1 n n% where we have; l; yo1; and which yields the following solution for n: 1 lt 1l 1y n ¼ n% q1l : nu % The solution for n is then inserted back into the cost function, and we have l
l
1
1ly
cðq; tÞ ¼ c0 q þ tq ½1 lnu % 1l l1l t1l q 1l : For the derivatives we have 2 3 l 1l lly @cðq; tÞ 4 lt ¼ 1 q 1l 5qX0 @t nu % l
lly
lt 1l 1l q ; since bðnÞ ¼ ½nu %
and @c2 ðq; tÞ 1 ly ¼ 1 bðnÞ ‘0 @t@q 1l since
1ly 1l 41
as long as yo1; ½bðnÞ1ly 1l will exceed 1 for some t as bðnÞ goes towards 1.
References [1] C. Arden-Clarke, Environment, Competitiveness and Countervailing Measures, WWF, Switzerland, 1993. [2] W. Althammer, W. Buchholtz, Strategic trade incentives in environmental policy, Finanzarchiv 52 (3) (1995) 293– 305. [3] S. Barret, Strategic environmental policy and international trade, J. Public Econom. 54 (1994) 325–338. [4] R.L. Bradford, R.D. Simpson, Taxing variable cost: environmental regulation as industrial policy, J. Environ. Econom. Manage. 30 (1996) 282–300. [5] J. Brander, B. Spencer, Strategic commitment and R&D: the symmetric case, Bell J. Econom. 14 (1983) 225–235. [6] J. Brander, B. Spencer, Export subsidies and international market share rivalry, J. Internat. Econom. 18 (1985) 83–100. [7] K. Conrad, Optimal Environmental Policy for Oligopolistic Firms under Intra-Firm Trade, Nota Di Lavoro, Fondazione Eni Enirico Mattei, Milano, 1994. [8] B. Dijkstra, The Political Economy of Environmental Policy, Edward Elgar, Cheltenham, UK, 1999. [9] R. Golombek, A. Raknerud, Do environmental standards harm manufacturing employment?, Scand. J. Econom. 99 (1) (1997) 29–44. [10] M. Greaker, Strategic environmental policy; eco-dumping or a green strategy, memorandum 03/2000, Department of Economics, University of Oslo, 2000. [11] J.D. Hartford, Efficient scale of the pollution-abating firm, Land Econom. 65 (1989) 413–416. [12] R.S. Hartman, D. Wheeler, M. Singh, The cost of air pollution abatement, Applied Economics 29 (1997) 759–774. [13] R.E. Kohn, Pollution and the Firm, Edward Elgar, Cheltenham, UK, 1998.
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[14] D.M. Kreps, J.A. Scheinkman, Quantity precommitment and Bertrand competition yield Cournot outcomes, Bell J. Econom. 14 (1983) 326–337. [15] K.-G. Lindquist, Testing for market power in the Norwegian primary aluminium industry, Discussion paper, Statistics Norway, No. 132, 1994. [16] K. Palmer, W.E. Oates, P.R. Portney, Tightening environmental standards: the benefit–cost or the no-cost paradigm?, J. Econom. Perspec. 9 (1995) 119–132. [17] M.E. Porter, C. von der Linde, Green and competitive, Harvard Business Rev. September/October (1995) 120–134. [18] M. Rauscher, On Ecological Dumping. Nota Di Lavoro, Fondazione Eni Enrico Mattei, Milano, 1993. [19] J. Tirole, The Theory of Industrial Organization, The MIT Press, Cambridge, MA, 1997. [20] A. Ulph, Environmental policy and international trade when governments and producers act strategically, J. Environ. Econom. Manage. 30 (1996) 265–281. [21] A. Ulph, D. Ulph, Trade, Strategic Innovation and Strategic Environmental Policy: A General Analysis, Nota Di Lavoro, Fondazione Eni Enrico Mattei, Milano, 1995. [22] D. Ulph, Strategic innovation and strategic environmental policy, in: C. Carraro (Ed.), Trade, Innovation, Environment, Kluwer Academic Publishers, Dordrecht, 1994. [23] US Environmental Protection Agency, OAQPS Control Cost Manual, 5th Edition, Http://www.epa.gov/, 1996. [24] US Environmental Protection Agency, Air Pollution Technology Fact Sheets, Http://www.epa.gov/, 2000. [25] World Bank, Pollution Prevention and Abatement Handbook, The World Bank Group, Washington DC, 1998. [26] World Trade Organization, Special Studies 4—Trade and the Environment, Http://www.wto.org/, 1999.
Strategic environmental policy; eco-dumping or a green strategy? Mads Greaker Statistics Norway, P.O. Box 8131 Dep., 0033 Oslo, Norway
Abstract The Porter hypothesis claims that a strong environmental policy best serves the interests of a nation’s export industry. While this hypothesis seems to be based on some form of bounded rationality, this paper argues that governments may have good reasons for setting an especially strong environmental policy even though firms are fully rational. If the available abatement technology turns the environment into an ‘‘inferior input’’, competitiveness is spurred by a strong environmental policy. The government should take advantage of this, and set an especially strict emission quota or an especially high emission tax. The findings in the paper also has consequences for the desirability of international cooperation with respect to national environmental policy. If a strict environmental policy spurs competitiveness, the environment is better protected without cooperation. r 2003 Published by Elsevier Science (USA). JEL classification: H7; Q2; R3 Keywords: Environmental policy; Strategic trade theory
1. Introduction Export firms are frequently given various kinds of subsidies, either openly as production subsidies or, more difficult to discover, as cheap government provided inputs or as tax reductions. One rationale for this line of thought can be found in the strategic trade theory literature. This literature explores how governments can help their national firms to steal profits from foreign competitors by making it possible for their firms to commit to a more aggressive strategy, see for instance [6]. While the literature on this subject dealt primarily with traditional industrial policy tools such as the ones mentioned above, it has during the 90s been extended to the field of
E-mail address: [email protected]. 0095-0696/03/$ - see front matter r 2003 Published by Elsevier Science (USA). doi:10.1016/S0095-0696(02)00053-0
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environmental policy. The question has been to what extent a government should provide its export industry with a weak environmental policy as a sort of hidden subsidy. Weak environmental policies which purposely seek to promote the competitiveness of the export industry, could be characterized by the term ‘‘eco-dumping’’. The prospect of eco-dumping has been a major issue in the trade-environment debate, see for example [1,26]. Because the current GATT treaty prohibits the use of traditional industrial policy tools like export subsidies and restricts the use of other subsidies like R&D subsidies, eco-dumping could become even more attractive. However, the prospect of eco-dumping presupposes that a strong environmental policy hampers competitiveness. Empirical research indicates that this may not always be the case. An econometric study from Norway by Golombek and Raknerud [9] suggests that a strong environmental policy spurred employment and induced a lower probability of exit from some industries notably pulp and paper and iron, steel and ferroalloys. Porter and von der Linde [17] refer to various case studies where a strong environmental policy lead to decreased production cost and/or higher value products. The idea that a strong environmental policy will improve the general performance of firms is the so-called Porter hypothesis, which we will refer to as a ‘‘green strategy’’. The Porter hypothesis is disputed among economists, see for example Palmer et al. [16]. Further, Porter and von der Linde [17] do not provide us with an unambiguous definition of the term green strategy. In this paper a green strategy will be defined as an environmental policy where marginal abatement cost exceeds marginal environmental damage, and vice versa, ecodumping will be defined as an environmental policy where marginal abatement cost falls short of marginal environmental damage.1 Regarding eco-dumping and a green strategy, we will deal with two questions in the paper. Firstly, we will analyze how environmental policy affects marginal production costs, and secondly, we will see how this affects the question of optimal policy. A majority of the articles about eco-dumping do not explicitly treat the issue on how environmental policy affects cost, but assumes that both total cost and marginal cost is increasing in the stringency of environmental policy (see for example [2,3,7,18]). This paper shows that although total cost increases, it is not necessarily the case that marginal cost increases. If the environment is an inferior input for some levels of environmental policy, marginal production cost will decrease for these levels of policy. The development of a cost model of end-of pipe cleaning further indicates that the inferior input case is likely if there is economics of scale in abatement technology. Economics of scale seems to be a feature of many abatement technologies. In an econometric estimation of abatement cost for the cement, pulp and paper and iron and steel sector Hartman et al. [12] find that ‘‘average abatement cost drops sharply as abatement volume increases’’. Scale economics in abatement is also suggested by the US Environmental Protection Agency [23,24]. Ulph [22], Bradford and Simpson [4] and Ulph and Ulph [21] also contain a model of abatement where marginal production cost may be decreasing in the stringency of environmental policy. In these models the firms undertake environmental R&D before they compete in the market. The result that marginal production cost may be decreasing in the stringency of 1
The literature also compares the non-cooperative environmental standards with the cooperative environmental standards. This comparison is also made in this paper, but it is not used to define a green strategy or eco-dumping.
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environmental policy therefore appears to be dependent on the sequential timing of the R&D decision and the output decision. However, this paper shows that this result alternatively can be explained by the inferior input concept independent of the timing of decisions. Regarding optimal policy, all authors find that eco-dumping is optimal when the firms compete in quantities and when abatement is decided simultaneously with output [2,3,7,18]. For the contributions of A. Ulph [20], D. Ulph [22], Bradford and Simpson [4] and Ulph and Ulph [21] with environmental R&D, the results are more ambiguous, however, no unambiguous support for a green strategy can be found. Hence, the Porter hypothesis is not confirmed in the theoretical literature apart from the Bertrand situation where the government purposely hurts the competitiveness of its firm in order to soften competition (see [3]). This paper shows that if emissions are an inferior input, the government should use a green strategy when abatement and output are decided simultaneously. This is also very likely to hold when abatement effort is decided separately from output. Cases where emissions can be both an inferior and a normal input are explored through a numerical example. In these cases the resulting strategy is sensitive to market size. Since it is scale economics in abatement which leads to the inferior input case, environmental policy will be stronger and emissions smaller the bigger the market.
2. A simple model of strategic environmental policy The model includes two countries; one domestic and one foreign. There is one nationally owned firm in each of the countries. Both firms pollute, and the governments use an emission tax to regulate emissions. The firms export to a third market, compete by choosing output levels, and take the emission taxes in the two countries as given. It is assumed that environmental damage is national, and that the environmental performance of the industries has no effect on demand. Denote the domestic firm’s output by q; the domestic emission tax rate by t and let cðq; tÞ be the domestic firm’s cost function. Emissions can be interpreted as an input, and the tax rate as the price of this input. It then follows from standard production theory that costs are increasing in the tax rate. Denoting derivatives by subscripts, we have c1 40 and c2 40: Uppercase letters denote corresponding magnitudes for the foreign firm, with C1 40 and C2 40: Total revenues of the domestic and foreign firms are rðq; QÞ and Rðq; QÞ respectively. Assuming that the two products are substitutes yields; r2 ; R1 o0: It is also assumed that r12 and R21 are negative in order to ensure that the outputs of the two firms are strategic substitutes. Profits of the home and foreign firms are given by pðq; QÞ ¼ rðq; QÞ cðq; tÞ
ð1Þ
Pðq; QÞ ¼ Rðq; QÞ CðQ; TÞ;
ð2Þ
and
respectively. Each firm chooses its output taking the emission tax and the output of the other firm as given. The first-order conditions are p1 ¼ r1 c1 ¼ 0
ð3Þ
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and P2 ¼ R2 C1 ¼ 0:
ð4Þ
The two first-order conditions determine the Nash-equilibrium output quantities given the emission taxes. It is assumed that the second-order conditions for profit maximum hold, i.e. that p11 ; P22 o0: Further, we assume that the uniqueness criterion for the Cournot–Nash equilibrium is fulfilled, i.e. that ðp11 P22 p12 P21 Þ40:2 The output quantities can then be written as functions of the emission tax rates; q ¼ qðt; TÞ and Q ¼ Qðt; TÞ: In order to study the two functions; qðt; TÞ and Qðt; TÞ; we look at the comparative statics of the Nash equilibrium. Total differentiation of systems (3) and (4) yields: p11 dq þ p12 dQ c12 dt ¼ 0; P21 dq þ P22 dQ ¼ 0: We have from the second equation that dQ=dq ¼ P21 =P22 : Inserting this into the first equation we obtain dQ ¼ c12 P21 =ðp11 P22 p12 P21 Þ: dt Combining this with the expression for dQ=dq we also obtain dq ¼ c12 P22 =ðp11 P22 p12 P21 Þ: dt The denominator in both expressions is positive, while both P22 and P21 are negative. The signs dq on dQ dt and dt are thus dependent on c12 : dq ð5Þ Sign ¼ Sign½c12 ; dt dQ ð6Þ ¼ Sign½c12 : Sign dt Note that the derivatives have opposite signs reflecting that the two outputs are strategic substitutes. If marginal cost is increasing in the emission tax rate, the domestic firm would like to supply less the higher the emission tax rate for a given output of the foreign firm. Hence, its reaction curve shifts inward if the emission tax rate is increased. In the new Nash equilibrium the foreign firm has increased its output, while the domestic firm has reduced its output. This is the normal case analyzed in the literature, see for example [18]. However, the sign on c12 is by no means given from economic theory alone, even though c2 40: Denoting emission by s; we have from Young’s equality and Shepard’s lemma: @c2 ðq; tÞ @c2 ðq; tÞ @s ¼ ¼ : ðc12 ¼Þ @t@q @q@t @q 2
ðq;tÞ Thus, the cross-derivative @c@q@t tells us how emissions change with an increase of output for given input prices including the emission tax rate. Hence, the normal case depends on emissions 2
See the discussion about uniqueness in [19, pp. 225–226].
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@s being a normal input, i.e. @q 40: If on the contrary, emissions are an inferior input, an increase in the emission tax rate would lead to lower marginal cost, and thus an expansion of domestic output. In order for emissions to be an inferior factor, the firm must be able to abate emissions. Further, the technology must be such that the firm chooses to abate more of the emissions, the higher the output. Total emissions can then be decreasing in output. The mechanism with respect to costs is as follows: Marginal production cost of the regulated firm consists of two parts; firstly, the extra input needed for production of an additional unit, and secondly, the emission tax payments resulting from the extra emissions created by the production of an extra unit. Imagine then that the government increases the tax rate. This makes the firm increase its abatement effort, which implies that one additional unit of output creates less extra emissions. If this reduction in emissions per unit effect dominates the direct effect of the increased tax rate, marginal production cost will be decreasing in the emission tax rate. The first proposition then follows directly from standard production theory. @s 40; the domestic firm will reduce its output as a Proposition 1. If emissions are a normal input, i.e. @q
response to a higher emission tax rate, i.e. dq dt o0: In the new Nash equilibrium the foreign firm will dQ produce more, i.e. dt 40: If emissions are an inferior input both effects are reversed. Emissions cannot be an inferior input for all t: Since total cost is given by the area under the marginal cost curve, the marginal cost curve has to shift up for some t—for example by a discontinuous jump when t is just above 0.3 Net surplus generated by the home firm is given by w: w ¼ rðqðt; TÞ; Qðt; TÞÞ cðqðt; TÞ; tÞ þ ts dðsÞ;
ð7Þ
where the two first terms represent the profit of the firm as a function of t and T: The third element is the firm’s tax payment. Since the tax payment is a pure transfer, and since it is included implicitly in the cost function cðq; tÞ; we have to explicitly add it in the welfare expression. The last element dðÞ is the environmental damage caused by the firm. The function dðÞ is assumed to be increasing reflecting that higher emissions increases environmental damage. The government of the home country maximizes the net surplus taking the emission tax of the other country as given. A first order condition for maximizing national product obtains when dw dt ¼ 0: dw dq dQ dq dq ¼ ðr1 c1 Þ þ r2 c2 þ c2 þ t c22 þ c21 d1 c22 þ c21 ¼ 0; dt dt dt dt dt where by Shepard’s lemma; s ¼ @cðq;tÞ @t ¼ c2 : 3
Dijkstra [8] mentions the possibility of the inferior input case, but does not analyse it any further.
ð8Þ
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The first term is zero by the firm’s first-order condition for profit maximum (3), and the third and the fourth term cancel out. By rearranging terms we get d1 t ¼
r2 dQ dt
ð9Þ
: c22 þ c21 dq dt
The term in the nominator r2 dQ dt is the strategic effect of the environmental policy. Since r2 is negative, the strategic effect is negative if emissions are a normal input and positive if emissions are an inferior input. The first term in the denominator c22 is negative or zero by the concavity of the cost function. In 2
ðq;tÞ Þ refers again to the properties of emissions as an input. the next term the derivative c21 ð¼ @c@q@t Thus we can have two cases for the left-hand side of (9). dq dq If emissions are a normal input; c21 40; then r2 dQ dt o0; dt o0 and c22 þ c21 dt o0 which implies dq dq that d1 t40: If emissions are an inferior input c21 o0; then r2 dQ dt 40; dt 40 and c22 þ c21 dt o0 which implies that d1 to0: We know that the firm sets marginal abatement cost equal to the tax rate. Hence, we have the following proposition:
Proposition 2. If emissions are a normal input d1 4t: If emissions are an inferior input
@s @qo0;
@s @q40;
the government will prefer eco-dumping, i.e.
the government will prefer a green strategy, i.e. d1 ot:
In the ‘‘green strategy’’ case the government fixes an emission tax rate which exceeds marginal environmental damage. Since this forces marginal cost of the domestic firm to decrease, the firm will want to produce more even if total cost goes up. The high tax rate works as a commitment to increase output. In the case of eco-dumping, it is easy to show that profit increases compared with the situation where the tax rate is set equal to marginal environmental damage. The firm gets both reduced cost and a higher market share. In the green strategy case profit can go both ways; on the one hand, the firm gets higher market share and hence, higher revenues, on the other hand the firm gets higher total cost. In a non-cooperative equilibrium both governments use their emission tax strategically. In order to see that this leads to a sort of a Prisoners dilemma we will take a look at the cooperative equilibrium. We assume that the two countries and the two firms are symmetric in all aspects, and that they maximize joint welfare with respect to a common emission tax rate. The maximization problem can then be written: maxfw þ W ¼ 2½rðqðt; tÞ; Qðt; tÞÞ cðqðt; tÞ; tÞ þ tc2 dðc2 Þg; t
which after some rearranging yields the following first-order condition: d1 t ¼
@Q r2 ð@Q @t þ @T Þ
ðc22 þ c21 dq dt Þ
:
ð10Þ
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@Q @Q 4 The nominator at the left-hand side of (10) is dominated by @Q @T because we have j@T j4j @t j: @Q Hence, the term r2 ð@Q @t þ @T Þ will be negative when emissions are an inferior input, and the term will be positive when emissions are a normal input. Since ðc22 þ c21 dq dt Þo0; the following proposition follows.
Proposition 3. In the cooperative solutions the results are reversed: If emissions are an inferior input @s @s @qo0; the governments will prefer eco-dumping, i.e. d1 4t; and if emissions are a normal input @q40; the governments will prefer a green strategy, i.e. d1 ot: Contrary to the popular view, cooperation may lead to a less stringent environmental policy. The reason is that a stringent environmental policy makes the firms more aggressive in the inferior input case, and that the governments want to ‘‘soften’’ competition in order to turn the two firms into a sort of ‘‘world monopoly’’.
3. Inferior input cases Norway has a considerable aluminium industry which exports almost all of its production, and studies have indicated that the industry has some degree of market power (see for example [15]). There are two ways of smelting primary aluminium; the old Soderbergh method and the new Prebake method. The Prebake method is in general superior with regard to emissions; it implies lower local emission of hazardous gasses and particles, uses less energy per ton aluminium produced, etc. [25, p. 263]. On the other hand, the Prebake method requires a separate facility for ‘‘baking’’ the electrodes in addition to the production unit. In Norway, tough environmental regulation seems to have accelerated the shift from Soderbergh technology to Prebake technology. At a major production site where a switch of technology is currently taking place, total emissions are being cut, while production capacity is being increased. The increased capacity could be a sign that the tough environmental regulation has made the Norwegian producer more aggressive as the theory about inferior inputs above predicts. However, since the increased capacity may have other explanations, this paper also includes a formal abatement cost model based on the engineering literature about end-of-pipe cleaning where emissions may be an inferior input. Many processes, for example cement production, lead to emissions of airborne particles which represents a potential, local health hazard. The abatement of particles implies the installing of filters at different point sources in the production process— there are typically many point sources at each production line. Total particle removal efficiency is hence enhanced by increasing the number of point sources with filters.5 4 That the effect on foreign output of the foreign emission tax is greater than the effect on foreign output of the domestic emission tax follows from the assumption about Nash-equilibrium uniqueness and the assumption about symmetry. 5 The model is also based on a visit to a cement factory in Norway. In the factory there were 14 point sources with filters, and practically all particle emissions were removed.
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The filters can be of many types of which; electrostatic precipitators and baghouses are the most effective—most modern designs remove 99.9% of all the particles from a given flow [24]. The cost of cleaning can be measured by the number of filters and the capacity of each filter [23]. Since gross emissions of particles are in most cases positively related to output, the capacity of the filters must also be positively related to output. Let one unit of output correspond to one unit of gross emissions, i.e. gross emissions are equal to output; q: Let further n denote the number of filters, and aðqÞ the cost of a typical filter. A certain number of filters installed will imply that a fraction bðnÞ of gross emissions are removed, and that a cost naðqÞ is incurred. If the local environmental protection agency levies a particle tax t on net emissions from the industry, we have that the cost function of the domestic firm can be written: cðq; t; nÞ ¼ cðqÞ þ tð1 bðnÞÞq þ naðqÞ
ð11Þ
where we have b0 ; a0 40 and b00 o0: Further, we assume a00 p0:6,7 The industry decides on the number of filters to install. From cost minimisation we obtain an optimal number of filters; n ¼ nðt; qÞ: This function can be substituted back into the cost function. ds : The extent to which emissions are an inferior input is determined by the sign on the derivative dq ds d½ð1 bðnðt; qÞÞÞq @b dn ¼ ¼1bq : dq dq @n dq
ð12Þ
ds dn The term q @b @n is positive, and hence, a necessary condition for obtaining dqo0; is dq40; i.e. the firms must increase their use of filters when they increase output for a constant emission tax rate. For the derivative dn dq we have
dn b0 aðqÞ aðqÞ 0 a ¼ 00 X0; since a0 p when a00 p0: dq b aðqÞ q q
ð13Þ
Hence, scale advantages in abatement technology, ensures that the firm will choose to increase its use of filters if output is increased. By inserting, we finally obtain ds q ð1 bÞaðqÞ 00 aðqÞ 0 2 0 ¼ b þ a ðb Þ : ð14Þ dq aðqÞb00 q q aðqÞ q 0 2 ð1bÞaðqÞ 00 ds 0 Since aðqÞb jb j: 00 o0; we have dqo0; if ½ q a ðb Þ 4 q Lastly, by experimenting with different functional forms for bðnÞ and aðqÞ we find for example that all bðnÞ ¼ ðnn%Þl ; lo1; where n% is the number of filters which remove practically all particle ds o0 for some t emissions, in combination with all aðqÞ ¼ nnqy ; yo1; where n is a parameter, yield dq (see the appendix). 6
A more detailed derivation of the cost model can be found in the appendix. Kohn [13] and Hartford [11] also contain a model of end-of-pipe cleaning, however, their model does not entirely comply with the facts about the abatement technology that we have gathered. 7
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Table 1 ðy; MÞ
tn
d0
ð1 bðnÞÞq
q qþQ
naðqÞ cðq;tÞ
ð12; 5Þ ð12; 20Þ ð1; 5Þ ð1; 20Þ
0.266 0.174 0.261 0.410
0.281 0.140 0.322 0.419
0.703 0.351 0.804 1.048
48:2% 50:1% 45:1% 48:7%
7.1% 9.9% 5:1% 8:4%
4. A numerical example In this section we will look at a numerical example based on the model of end-of-pipe cleaning discussed in the former Section. By this we want to illustrate that the strategic effect can have a significant impact on the resulting net emissions. Further, we want to draw attention to an effect which is more complicated to demonstrate in the general model. When there is scale advantages in abatement, a big market leads to a more stringent environmental policy. In the example the firms and the countries have identical cost- and environmental damage functions. The costfunction is given by: cðqÞ ¼ c0 q; bðnÞ ¼ ðnn%Þl ; lo1; and aðqÞ ¼ nnqy ; yp1: Further, demand is given by: p ¼ M q Q where p is the market price and M the market size. And lastly, the environmental damage function is given by: d ¼ d0 ½ð1 bðnÞÞq2 :8 In Table 1 a simulation of the optimal environmental tax rate tn for a given predetermined T (otn ), and for different values of y and M is presented. The model is calibrated so that abatement cost does not make up more than 10% of total cost (the last column below). The following 9 parameter values are used; T ¼ 0; 1; l ¼ 23; ðnnÞ % ¼ 0; 3; c0 ¼ 1; d0 ¼ 0; 2: Firstly, note that in a model with simultaneous abatement–output decisions marginal abatement cost is equal to the tax rate. When y ¼ 12; emissions become an inferior input for bðnÞ40; 5: However, as long as the market is small ðM ¼ 5Þ; it is not optimal for the government to exploit this, and we consequently have that tn od 0 : The situation changes when the market is big ðM ¼ 20Þ: We then have that tn 4d 0 ; and that net emissions actually have decreased compared to the situation in the small market. This is clearly an effect of the increasing returns to scale property of the abatement technology. Note that in this q ¼ case the domestic firm succeeds in increasing its market share compared to the t ¼ T case ðqþQ 50:1%Þ (Table 1). In the two last rows we have removed the scale effect, and hence, emissions can no longer be an inferior input. Consequently, the governments sets tn od 0 irrespective of market size. The optimal level of net emissions are also increasing in the market size. Note that net emissions are considerably higher in the case with y ¼ 1 than with y ¼ 12: In Table 2 we present the non-cooperative policy equilibrium, i.e. the subgame—perfect equilibrium of the two stage game in which both governments simultaneously maximize welfare in 8 The simulation has also shown that an interior welfare maximum does not always exist. For example the case with constant marginal environmental damage does not yield an interior maximum. 9 l ¼ 23 and y ¼ 12 (or y ¼ 1) makes it possible to solve the model exact for the Nash-equilibrium output levels.
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Table 2
Non-cooperative Cooperative
t
T
d0
ð1 bðnÞÞq
w
w:w
0:174 0:172
0:174 0:172
0:142 0:197
0:355 0:492
39:5302 39:5344
158:7386 158:7322
the first stage, and the firms maximize profits in the second stage. Further, we compare the noncooperative equilibrium to a cooperative equilibrium where joint welfare is maximized under the condition that t ¼ T: For the parameters we have M ¼ 20; y ¼ 12; and the rest as before. All figures are for the domestic country except for the foreign tax rate and the last column: w.w. Note that net emissions are lower in the non-cooperative equilibrium than in the cooperative equilibrium. The reason is that a high emission tax rate makes the companies more aggressive, and hence, output is higher and emissions lower. On the other hand, domestic welfare is higher in the cooperative equilibrium. Because tod 0 in this equilibrium, the firms are less aggressive, total output is lower, and total oligopoly profits are higher. In the last column we display world welfare ðw:wÞ; i.e. the sum of domestic welfare, foreign welfare and consumer surplus in the third market. We note that from the point of view of the world the competitive policy equilibrium is preferred. Since total output is higher, consumer surplus in the third market has increased.
5. The use of other instruments An obvious question is whether the results change with the type of instrument. Consider for example an emission cap, i.e. the firm is only permitted to emit a certain load in a given period irrespective of output. The firms cost minimization problem can then be solved by the Langrange method where the emission cap places a constraint on the use of emissions as input. From the Langrange method we obtain a shadow price on emissions. This shadow price plays exactly the same role as the emission tax from the former section. Since reducing the emission cap implies an increase in the shadow price on emissions, we get the same results with respect to the effect on marginal production cost. A smaller emission cap, may reduce marginal production cost for some intervals of the emission cap. This can be explained intuitively by the following example. We compare the cost of increasing output for two levels of the emission cap. Given a high emission cap, the firm would like to invest in few filters and clean a small fraction of the emissions—say 25%. An increase in output would then imply a high increase in emissions, and consequently, the firm would have to increase the fraction cleaned by many %-points—if output goes from 10 to 11—by 7%-points. Given a low emission cap, the firm would on the other hand have to invest in many filters and clean a large fraction—say 75%. The same increase in output would then imply a smaller total increase in emissions. Thus, the firm would not have to increase the fraction cleaned as much as in the case for a high emission cap—if output goes from 10 to 11—by 2%-points. This could imply that it is less costly to increase output when the emission cap is low than when the emission cap is high, and consequently, the firm becomes more aggressive.
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It is also easy to show that as long as marginal cost is decreasing in the stringency of the environmental policy instrument, an optimal policy will imply a green strategy in the strategic environmental policy situation. Thus, the analysis yields the same results with an emission cap as with an emission tax. This is also showed explicitly in Greaker [10]. The situation changes when the government uses a technology mandate or demands a certain emission/output fraction. In the simplified model from Section 3 these two instruments have identical effects on costs. A technology mandate would imply a certain number (and type) of filters, as would a certain emission/output fraction. Marginal production cost is then strictly increasing in the policy instrument. In order to increase output the firm would have to increase the capacity of each filter. The more filters the firm is required to have, the more the firms’ capacity cost would increase with an increase in output. Hence, we would expect the government to ecodump if the government uses a technology mandate or demands a certain emission/output fraction.
6. Sequential abatement/output decisions So far we have assumed that output and abatement is decided simultaneously. In Ulph [22], Ulph and Ulph [21], Ulph [20] and Bradford and Simpson [4] abatement is R&D of cleaner production processes, and abatement and output is decided sequentially. The following discussion will focus on Ulph [22] who makes use of a cost function that has close similarities to the cost function which was developed for the end-of-pipe cleaning case. Change the definition of n; and let n now denote the amount of R&D. The cost function of Ulph [22] can then be written cðq; tÞ ¼ c0 q þ t½1 bðnÞq þ n: We have b0 40 and b00 o0 as in the model of Section 3. Since abatement takes the form of R&D, there is no capacity part of abatement cost—just n: Ulph [22] finds that marginal cost will be decreasing in t if the R&D technology satisfies the following condition: 1 ½ð1 bÞb00 ðb0 Þ2 o0: b00
ð15Þ
The condition appears to be dependent on the sequential timing of R&D and output decisions. However, by comparing Eq. (15) with Eq. (14) we discover that the condition also would have applied if R&D and output were decided simultaneously. Hence, if the firms decided R&D levels by just minimizing cost, we would still have that marginal cost is decreasing in t as long as condition (15) holds. Characterizing the optimal policy is considerably harder in the sequential version of the strategic environmental policy situation. Because the firms also compete in R&D levels, the firms over-invest in R&D and set marginal abatement cost above the emission tax rate, see also [5]. It is therefore misleading to evaluate the environmental policy by comparing marginal environmental damage with the emission tax rate as we can do for the two-stage version of the game.
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This has implications for the interpretation of the results in the articles of Ulph [22] (and Ulph and Ulph [21]). If marginal environmental damage were compared directly to marginal abatement cost, we would find that results tended to follow the simpler two-stage model. In the working paper version of this paper [10] the three stage game of Ulph [22] is solved in order to carry out such a comparison. When ½ð1 bÞb00 ðb0 Þ2 ¼ 0; marginal production cost is independent of the emission tax rate, and the government sets marginal abatement cost equal to marginal environmental damage. This is done by letting the tax rate fall short of marginal environmental damage. But because the firm overinvests in abatement, marginal abatement cost will be equal to marginal environmental damage anyhow. Greaker [10] also deals with the two other cases for the term; ½ð1 bÞb00 ðb0 Þ2 : Qualitatively, the results tend to follow those obtained from the two stage game. If emissions are a normal input, eco-dumping is the preferred policy, and if emissions are an inferior input, a green strategy is the preferred policy. The sufficient, but not necessary condition is: That the elasticity of marginal cost with respect to output is smaller than the inverse total cost share of total environmental taxes.10 The reason for the ambiguity is that the emission tax has two effects in the three stage game: It works as an export tax which is always bad when we have Cournot competition in the market game. However, it also influences marginal production cost of the foreign firm. Generally, the domestic government would like the marginal production cost of the foreign firm to rise, which also happens as long as emissions are an inferior factor.
7. Concluding remarks This paper has not treated other forms of competition. The introduction of Bertrand competition would turn all the conclusions around in the simple two-stage model where emissions are either inferior or normal. However, we would argue that the two-stage version of the game is less appropriate for Bertrand competition. Clearly, prices can be changed a lot easier than abatement technology. An emission cap could therefore work as a capacity constraint. This could yield the Cournot outcome of the Bertrand game as in Kreps and Scheinkman [14]. For a discussion of this case, see the working paper version of this paper [10]. It is argued in this paper that profit may rise as a result of a stronger environmental policy if competition is imperfect (compared to a weak level of environmental policy). The question is then why companies often resist stronger environmental regulation. Does this mean that emissions are very seldom an inferior input? This is probably to jump to conclusions. Firstly, profit is likely to decrease in the whole interval of the emission tax rate even if emissions are an inferior input for some interval of the emission tax rate. In the model total cost always increases. Thus, if the profit shift does not make up for the increase in total cost, profit is hampered.11 10
I.e. if emission taxes makes up 10% of total cost, the elasticity of output on marginal cost has to be less than 10 in Nash equilibrium. 11 At least profit must be decreasing for the optimal tax rate, if not, the government should increase the tax rate even further.
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Secondly, the firm’s point of reference could be no environmental policy, i.e. t ¼ 0: Then profit is bound to decrease at least in the end-of-pipe abatement cost model. In this model marginal production cost cannot be lower with regulation than without regulation. Consequently, the maximal profit shift cannot exceed the cost effect. Lastly, the model of a simultaneous game between two firms in both abatement and output may not be a good description of the actual situation. One could think of a lot of other alternative sequences of decisions. If for example one of the firms is told to install end-of-pipe equipment, it could act before its competitors had time to react. Ex post the investments in abatement should sometimes be treated as sunk costs hampering profit, but not altering the Cournot–Nash output levels. The paper should not be regarded as a general recommendation for strategic environmental policy. As the discussion in Section 3 has shown it is very difficult to know a priori whether emissions are an inferior or normal input. Further, we do not know a priori how competition in a particular market works. Thus, the policy implication of the paper is that governments should not distort their environmental policy for strategic reasons. However, given that emissions may be an inferior factor, politicians should a priori be less afraid of introducing a sufficiently stringent environmental policy.
Acknowledgments I am very grateful for the advice and comments I have received from my supervisor Nils Henrik von der Fehr. I would also like to thank Jon Vislie, Andrea Bigano and two anonymous referees for very valuable inputs. Lastly, I would like to thank the Norwegian Research Council for financial support. Appendix A. Derivation of the end-of-pipe abatement cost model Facts about end-of-pipe abatement technology can be found in the EPA Air Pollution Technology Fact Sheets [24], the EPA OAQPS Control Cost Manual [23] and the World Bank Pollution Prevention and Abatement Handbook [25]. The gross emissions of particles is in most cases directly related to output: sg ¼ Eq;
ðA:1Þ
where E is a given parameter, which for our purpose can be normalized to one. Abatement of gross emissions implies the installing of filters at different point sources in the production process. Total particle removal efficiency is hence enhanced by increasing the number of point sources with filters. Let n denote the number of filters. A certain number of filters installed will then imply that a certain fraction bðnÞ of the gross emissions; sg is removed. Net emissions; sn can then be written: sn ¼ ½1 bðn; s1g ; y; sng Þsg ;
ðA:2Þ
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with the following derivatives: @b @2b X0; o0; 2 @n (@n 0 for sig ps%ig @b ¼ @sig o0 for sig 4s%ig
8i ¼ 1; y; n;
where sig is the particle flow passing through filter i; and s%ig is the capacity of filter i: Since increasing the fraction cleaned for a given gross emissions implies adding new filters to 2 less pollution intensive point sources, we assume @@nb2 o0: Further, since the firm chooses its output, the number of filters and the capacity of each filter simultaneously, we also assume that sig ¼ s%ig 8i ¼ 1; y; n: Hence, the arguments s1g ; y; sng can be removed from the b-function. The cost of cleaning, i.e. the abatement cost a; can be measured by the number of filters and the capacity of each filter (see the EPA OAQPS Control Cost Manual, from pp. 6–46 of [23]): a¼
n X
ai ðs%ig Þ;
ðA:3Þ
i¼1
where the function ai ðs%ig Þ gives the cost of filter i as a function of the capacity. A continuous representation of (A.3) should take into account that the capacity of filter n; s%ng is likely to decrease as the number of filters n are increased, i.e. new filters are placed at less pollution intensive point sources. Further, since the capacity of at least one filter must be increased when output is increased, the continuous representation of (A.3) must be increasing in q: a ¼ aðn; qÞ
with an ; aq 40; ann ; aqq p0
and anq 40:
The first-order derivatives should be un-problematic. The cross-derivative is positive, because with a higher number of filters, an increase in output is likely to lead to increased capacity on more filters. The capacity cost of the filters is dependent of the gas volume flow rate because a higher gas volume flow rate will require a higher collection plate area. Further, since the gas volume flow rate will be proportional to output, we have that higher output will imply a larger collection plate area. From Fig. 6.5 on page 6–41 in EPA Control Cost Manual [23] we note that costs per squarefoot collection plate area decreases. This suggests that we have aqq p0: We also quote the EPA Air Pollution Technology Fact Sheets [24], Electrostatic Precipitators; ‘‘in general, smaller units controlling a low concentration waste stream will not be as cost effective as a large unit cleaning a high pollutant load flow’’. Thus, if higher output among others, implies a higher concentration of particles in the gas flow, this also indicates that we have aqq p0: Lastly, the reason for ann p0 is already mentioned. In Section 3 we have just used a ¼ naðqÞ; and hence, we have ignored the possibility that ann o0: Taking this into account would have reduced the convexity of the ‘‘emission-reduction’’ cost function. Thus, assuming a ¼ naðqÞ actually makes the inferior factor case less likely.
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With the specified functional forms the domestic firm solves the following cost minimization problem: n l q þ unqy ; min cðq; t; nÞ ¼ c0 q þ t 1 n n% where we have; l; yo1; and which yields the following solution for n: 1 lt 1l 1y n ¼ n% q1l : nu % The solution for n is then inserted back into the cost function, and we have l
l
1
1ly
cðq; tÞ ¼ c0 q þ tq ½1 lnu % 1l l1l t1l q 1l : For the derivatives we have 2 3 l 1l lly @cðq; tÞ 4 lt ¼ 1 q 1l 5qX0 @t nu % l
lly
lt 1l 1l q ; since bðnÞ ¼ ½nu %
and @c2 ðq; tÞ 1 ly ¼ 1 bðnÞ ‘0 @t@q 1l since
1ly 1l 41
as long as yo1; ½bðnÞ1ly 1l will exceed 1 for some t as bðnÞ goes towards 1.
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