Environmental Policy and Competitiveness: The Porter Hypothesis and the Composition of Capital 1

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1 Journal of Environmental Economics and Management 7, 65 8 Ž 999. Article ID jeem.998.6, available online at ttp: on Environmental Policy and Competitiveness: Te Porter ypotesis and te Composition of Capital Anastasios Xepapadeas Department of Economics, Uni ersity of Crete, Uni ersity Campus, Retymno 74, Crete, Greece and Aart de Zeeuw Department of Economics and CentER, Tilburg Uni ersity, P.O. Box 95, 5 LE Tilburg, Te Neterlands Received April, 998; revised October, 998 Te Porter ypotesis suggests a win win situation in te sense tat environmental policy improves bot environment and competitiveness. Te suggestion received strong criticism from economists driven by te idea tat if opportunities exist, firms do not ave to be triggered by an extra cost. In tis paper a model is developed wic confirms tis point but wic also draws attention to some general mecanisms tat relax te trade-off considerably. Downsizing and modernization of firms subject to environmental policy will increase average productivity and will ave positive effects on te marginal decrease of profits and environmental damage. 999 Academic Press. INTRODUCTION In an article tat attracted te attention of bot economists and policymakers, Porter 9 callenged te establised notion tat toug environmental policies imply private costs tat arm te competitiveness of a country s industry, by claiming precisely te opposite. For policymakers Že.g., Gore. 5 tis idea of a possible win win option was like manna from eaven, because it relieved tem of te difficult trade-off between environmental and oter economic targets. Economists, owever, are by nature sceptical about te idea of a free lunc, and some also critized tis so-called Porter ypotesis in te sense tat attention is distracted from te cost-benefit analysis of environmental policy, wic is in teir view te most important issue Že.g., Palmer, Oates, and Portney. 8. In sort Porter s argument is tat toug environmental regulation in te form of economic incentives can trigger innovation tat may eventually increase a firm s competitiveness and may outweig te sort-run private costs of tis regulation. Tis researc was initiated under te CM-programme Designing Economic Policy for te Management of Natural Resources and te Environment. Support from te researc programme PENED Ž No and from te Neterlands Organization for Scientific Researc Ž No is also acknowledged. We are very grateful for te comments of two anonymous referees $. Copyrigt 999 by Academic Press All rigts of reproduction in any form reserved.

2 66 XEPAPADEAS AND DE ZEEUW is argument is mainly supported by a large number of case studies were firms under strict environmental regulation prove to be very successful Žsee, e.g., Porter and van der Linde.. Empirical studies on competitiveness in te meaning of canges in te trade and investment patterns Že.g., Kalt 7, Tobey, Jaffe et al.. 6 do not find a significant adverse effect of more stringent environmental policies. Te existing data are of course limited in teir ability to measure te stringency of regulation but possible explanations mentioned are tat te compliance costs are only a small fraction of total costs of production, tat stringency differentials are small, and tat investments follow te current state-of-te-art in tecnology even if tis is not required by te environmental regulation in tat country. In te discussion following te appearance of te Porter ypotesis a number of attempts ave been made to identify te mecanisms tat can lead to a mitigation of te cost effect of environmental policy or can even lead to a win win situation. Te dominant argument is tat firms are not aware of certain opportunities and tat environmental policy migt open te eyes. Te revenues of tese opportunities can ten outweig te costs of compliance. One line of tougt is tat te external sock troug environmental regulation may reduce intrafirm inefficiencies and organizational failures Žsee, e.g., Gabel and Sinclair-Desgagne. 4, and may move te firm toward its production possibility frontier: te X-efficiency argument. A second idea is tat firms create a first-mover advantage by te development of environmental tecnology wic can be beneficial in later times wen oter countries also adopt a more stringent environmental policy. Te standard counterargument is, of course, tat in rational economic modelling it cannot be explained wy firms do not see tese opportunities by temselves, wic at least implies tat te argument does not ave a general validity. It can be te case tat innovation wit te aim to reduce environmental pollution also lowers production costs and can terefore even be beneficial witout considering environmental costs. For a rational firm, owever, te conclusion must be tat environmental policy is ten not needed to trigger tis innovation. Te only arguments tat remain in tis discussion are te possibility of positive externalities of te additional R & D and te reduction of uncertainty to te firms about policy trends. In te context of strategic trade models, were consumption takes place in a tird country, increased competitiveness means a sift of profits from te foreign firm to te ome firm. In a two-stage model were firms invest in R & D first and ten coose output, it is possible to construct specific examples in wic foreign R & D decreases and ome profits increase under an environmental tax, but again tis result as definitely no general validity ŽSimpson and Bradford III.. On te contrary, te basic story remains tat governments ave an incentive to distort te environmental tax downward from te Pigouvian level in order to lower te costs of te ome firm and to sift profits to te ome firm ŽBarrett, Ulp 4., wic is sometimes referred to as ecological dumping Že.g., Rauscer.. Te purpose of tis paper is to explore te validity of te Porter ypotesis by considering firms reactions wit respect to bot te type and te quantity of equipment in wic tey invest in response to canges in te production costs. First it is sown tat an increase in production costs, brougt about by environmental policy, triggers a restructuring of te capital stock in suc a way tat

3 ENVIRONMENT AND COMPETITIVENESS 67 average productivity increases. Tis can already be considered as an improvement of te competitiveness of te industry ŽPorter and van der Linde., so tat tis part of te paper gives a formal basis to tat point. It is, owever, more interesting to see wat appens to net profits, wic is te focus of te second part of te paper. Te analysis in te paper is based on a model were firms invest in macines of different ages. Younger macines are more productive and less polluting tan older macines, but are more costly to buy and to install in te capital stock. Stricter environmental regulation, in te form of an increase in te emission tax, will reduce te number of macines of all ages and terefore te size of te firm. owever, te same tax increase generally also reduces te average age of te capital stock and tus increases its productivity. It follows tat two effects can be distinguised: a downsizing effect and a modernization effect. Downsizing refers to te reduction of te total capital stock. Modernization refers to te reduction of te average age of tis capital stock. Environmental regulation accelerates te removal of older macines from te capital stock wic increases its productivity. 4 It is important to note ere tat in te actual practice of environmental policy, existing capital is often exempted from te new and stricter regulation. Te effects analysed in tis paper ten only occur for te ages of te capital stock on wic te iger tax is levied. As a consequence, modernization is less tan in case all ages of te capital stock are subject to environmental regulation Že.g., Ellerman.. Te extra tax burden and te sift in investments and output are not profitable for te firm. Tis cost of environmental regulation is, owever, mitigated by tree effects: downsizing leads to an upward pressure on prices, modernization leads to a iger productivity of te capital stock, and downsizing and modernization togeter lead to lower emissions, so tat an environmental target can be reaced wit a lower tax tan in te absence of tis effect. In tis paper a situation wit omogeneous capital, were only downsizing occurs, is compared to a situation wit eterogeneous capital, were also modernization occurs. It is sown tat te marginal decrease in profits is lower and te marginal decrease in emissions is iger in te second situation. Te implication for te debate on te Porter ypotesis is not tat a win win situation can be expected, but te trade-off between improving te environment and te competitiveness of te ome industry is not as grim as it is sometimes suggested because of favourable canges in te composition of te capital stock. Section presents te basic model and Section derives te optimal age distribution of te macines. In Section 4 te effects of an emission tax on productivity, profits, and emissions are given and a comparison is made wit te case of omogeneous capital. Section 5 concludes te paper. A better environment will also ave a positive effect on te productivity of oter factors troug clean air, clean water, improved ealt and so on, but tis aspect will not be considered ere. It is interesting to note ere tat Nabisco cairman and cief executive J. Greeniaus, wen announcing te firm s downsizing, stated tat it was necessary to improve te company s competitive position and to accelerate strong sustainable earning growt in te next century ŽFinancial Times, June 5, Environmental regulations in te 97s unintentionally accelerated te modernization of te U.S. steel industry, altoug tis does not mean tat te premature scrapping of obsolete capital is socially beneficial, because suc plants were presumably producing output wose value exceeded variable production costs ŽJaffe et al. 6, based on U.S. Office of Tecnology Assessment 5..

4 68 XEPAPADEAS AND DE ZEEUW. TE MODEL Consider a firm tat can invest in macines of different ages. Let y, denote te age of te macine and introduce te following notation: Ž y. is te output produced by a macine of age y, wit Ž y.. Tat is, a newer macine cannot produce less output tan an older macine. New macines are more productive because tey embody superior tecnology. cž y. is te running cost of a macine of age y, c Ž y.. sž y. are emissions of a macine of age y, s Ž y.. Older macines emit at least as muc as newer macines. Tis migt be te result of a natural deterioration in te condition of te macine wit te passage of time, and or te result of cleaner tecnologies being embodied in te new macines. Let xt, Ž y. be te number of macines of age y operating in year t. Ten total output produced in year t is defined as Q t y x t, y dy. Assume tat te firm as to pay an emission tax per unit emissions. Ten te cost of running one macine is: cž y. sž y.. Terefore total running costs for year t are defined as CŽ t. cž y. sž y. xž t, y. dy. In practice existing capital is often exempted from new and stricter environmental regulation. In te model tis would imply tat te tax is not levied on capital up to te maximum age, wic is analysed in tis paper, but only on capital up to te age k. As a result, te downsizing and modernization effects, wic are sown later on, only occur for tat part of te capital stock. In a world wit new source performance standards, k and te analysis in tis paper breaks down. If k te effects will be tere but will be smaller, and te older capital will not be affected. It follows tat te results of tis paper only apply to regulatory institutions were an emission tax is levied on all polluters or at least on te pollution of some part of te existing capital stock. Te last situation occurs, for example, wen regulations put a cap on te amount of money a firm may be required to spend to come into compliance wit a new standard. Because te size of te necessary expenditure is usually correlated wit te age of te capital stock, tis cap in fact implies tat capital above a certain age is exempted from te new regulation. Te previous model can be used, but te age sould ten be interpreted as te maximum age of macines on wic te emission tax is actually levied. Finally, note tat in practice economic incentive approaces to environmental regulation Ž primarily taxes and tradable permits. are gradually being adopted, so tat an analysis based on an emission tax fits well wit tis development. We assume tat markets exist for macines of any age from to. Tis is a strong assumption but it is somewat relaxed by introducing a capital adjustment cost later on. Let bž y. be te cost of buying a macine of age y, wit b Ž y. Ž older macines cannot be more expensive tan newer macines. and b Ža

5 ENVIRONMENT AND COMPETITIVENESS 69 macine at te maximum age is not wort anyting.. For te analysis in tis paper it is assumed tat te cost b of a used macine is given and tat tis cost does not depend on te oter parameters of te model and te emission tax. In fact, none of te parameters of te model depends on te emission tax so tat te firm can only react to te tax by adjusting te composition of te capital stock, wic is te focus of tis paper. Let už y, t. be te number of macines of age y bougt Žif už y, t.. or sold Žif už y, t.. in year t. Te total cost or revenue to te firm from transactions in te macine market is defined as b y u y, t u y, t, wit te second term reflecting te adjustment costs in buying or selling macines. Tese costs are, for example, adaptation costs or searc costs. Te quadratic form of tis cost term leads to a simple expression for optimal purcases wic is needed in order to make te rest of te analysis tractable. Te firm cooses to buy or to sell macines of different ages in order to maximize profits, wit p te price of output. Tat is, te firm cooses at eac point in time an age distribution of macines to maximize profits, 5 ut, Ž y.4 max p y x t, y c y s y x t, y b y u t, y u t, y dydt xž t, y. xž t, y. subject to už t, y., t y xž,., xž t, y., t, y. Tis is an infinite orizon optimal control problem wit transition dynamics described by a linear partial differential equation ŽCarlson, aurie, and Leizarowitz.. Te transition equation indicates tat te rate of cange in te number of macines of a given age, y, is determined by two factors. Tese are te reduction in te number of macines of tat age as macines become older Žte first term of te transition equation., and te reduction or increase in te number of macines brougt about by te sale or acquisition of macines of te given age y Žte second term of te transition equation.. Te number of macines of eac age at eac time as to be nonnegative, wile te initial condition on te number of macines implies tat te firm starts wit no new macines in te capital stock. Te generalized amiltonian function for tis problem is given as p y x t, y c y s y x t, y b y u t, y u t, y xž t, y. Ž t, y. už t, y.. y 5 We take a discount rate equal to zero because te analysis would oterwise become more complex witout adding anyting to te purpose of tis paper.

6 7 XEPAPADEAS AND DE ZEEUW Ž. Te first-order conditions for optimality, besides te transition dynamics in, are or, or už y, t. Ž y, t. bž y., u Ž y, t. x, x y, t x y x y y Ž y, t. Ž y, t. p Ž y. cž y. sž y.. t y In order to obtain tractable analytical results from te preceding optimality conditions, we consider te firm at te steady state, in wic case x t and t. By suppressing t and ten denoting y, and x y x, te optimality conditions at te steady state can be written as už y. Ž y. bž y., Ž y. p Ž y. cž y. sž y.,. Ž x y. už y... Te optimality conditions corresponding to te steady state are equivalent to te optimality conditions of te optimal steady-state problem Ž OSSP. associated wit problem Ž.. Te OSSP is defined ŽCarlson, aurie, and Leizarowitz. as max p y x t, y c y s y x t, y už y.4 b y u t, y u t, y dy subject to Ž x y. už y., x, xž y., y. Te OSSP problem is an optimal control problem defined over ages y,, wit as state variable te number of macines of a given age and as control variable te sales or acquisitions of macines of tis same age. Te OSSP problem can be tougt of as a situation were te firm cooses te optimal age distribution of te macines in steady state, wic results from some exogenous sock. In our model te exogenous sock is a cange in te emission tax tat canges te optimal age distribution of te macines. In order to determine te effects from canges in te tax parameter we examine next te optimal age distribution of te macines as determined by te optimality conditions Ž.,., and.. Integrating. we obtain. TE OPTIMAL AGE DISTRIBUTION y Ž y. p Ž. cž. sž. d A. Ž 4.

7 ENVIRONMENT AND COMPETITIVENESS 7 Te boundary condition of tis fixed-orizon optimal control problem,, yields te constant of integration in Ž. 4, Terefore, y is given by A p Ž. cž. sž. d. Ž y. p Ž. cž. sž. d. Ž 5. y Te value of as given by Ž. 5 reflects te benefits from installing one macine of age y and keeping it until it becomes of maximum age. From Ž. te optimal sales or acquisitions of macines of age y is given by u* Ž y. Ž y. bž y. p Ž. cž. sž. d bž y.. Ž 6. y Note tat u* Ž y., as Ž y. bž y., wic is intuitively clear because denotes te benefits and b denotes te price of new macines. Te stock of macines of age y is partly determined by sales and acquisitions of macines of tat age and partly inerited from sales and acquisitions in te past. Te set of stocks of all ages is te optimal age distribution of macines and can be calculated from.. Note tat te initial stock is and tat te result can be viewed as a function of te tax parameter. Tis yields y z x* Ž y,. p Ž. cž. sž. d bž z. dz. Ž 7. Te marginal canges of tese stocks wit respect to te tax rate are given by y x* y, sž. d dz. z Terefore, an increase in te emission tax reduces te number of macines of eac age in te capital stock, wic implies tat te age distribution of macines is sifted downward. Tis is te downsizing effect of te emission taxes. Furtermore, because total emissions are defined as we ave tat SŽ. sž y. x* Ž y,. dy, ds. d

8 7 XEPAPADEAS AND DE ZEEUW Te important questions, owever, are Ž. i weter tis downsizing effect is accompanied by a modernization effect, or a cange in te sape of te age distribution of macines, tat increases te productivity of te capital stock, and Ž ii. ow te increase in te emission tax affects firm s profits. 4. PRODUCTIVITY EFFECTS OF EMISSION TAXES Suppose tat te firm as optimized te age distribution of its capital stock, so tat te number of macines for eac age is given by Ž. 7. Te proportion of macines of age y in te aggregate optimal capital stock of te firm is defined as xž y,. fž y,.. xž y,. dy Note tat fž y,. is a density function, because fž y,.,, fž y,. dy. Te average age of te optimal capital stock is defined as yxž y,. dy g Ž. yf Ž y,. dy. xž y,. dy Te basic question is under wic conditions an increase in te tax rate reduces te average age of te capital stock, or dg d. PROPOSITION. A stricter en ironmental policy reduces te a erage age of te optimal capital stock if and only if te a erage age of te optimal capital stock before te tax increase is less tan te a erage age of te cange in te capital stock Žwic is a reduction as te firm downsizes in response to an increase in te tax rate., or yxž y,. dy yž xž y,.. dy. xž y,. dy Ž xž y,.. dy For a proof see te Appendix. Te proposition is intuitively clear, because removing on average more older macines reduces te average age, but te formulation is useful for wat follows. Under te condition of te foregoing proposition te downsizing of te firm also causes modernization of te capital stock. Te optimal average age is reduced, as te tax increase removes te relatively older macines from te capital stock.

9 ENVIRONMENT AND COMPETITIVENESS 7 To analyse te productivity effects from a reduction in te average age, we define te average productivity of te capital stock as Ž y. xž y,. dy Ž.. xž y,. dy Using a decreasing linear productivity function, defined as y y wit, we ave tat d d yxž y,. dy dgž.. d d d xž y,. dy In tat case, stricter environmental policy, in te form of a iger tax rate, increases te productivity of te capital stock wen te average age of te capital stock is reduced. Te earlier proposition gives te condition for tis to take place. We will investigate tis condition for general linear functional forms for te variables of te problem. Te linearity assumption migt not always be realistic but te analysis becomes already quite complex. To investigate weter te results are generalizable to nonlinear functional forms is left for furter researc. Consider te case were Ž y. a až y., cž y. c, bž y. bž y., sž y. s sy, were all te parameters are nonnegative and at least a or s is strictly positive. Tis implies tat acquisition costs b decline linearly wit age y of te macines and running costs c of te macines are constant. Output is linearly decreasing wit age y wile emissions s are linearly increasing, wit at least one of tem in a strict way. Te following proposition can ten be stated. PROPOSITION. Under te assumptions made earlier about te functional forms of output, running costs, acquisition costs, and emissions, an increase in te emission tax reduces te optimal a erage age of te capital stock and increases its a erage producti ity. For a proof see te Appendix. Tus wen te downsizing effect is accompanied by a modernization effect a stricter environmental policy can increase te average productivity of te capital stock. It sould be noticed, owever, tat te increase in productivity cannot be solely attributed to a stricter environmental policy. In case, for example, tat running costs c increase linearly wit age y of te macines, it can be sown tat in te absence of environmental policy, an exogenous upward sock to tese costs also increases productivity. Te result appears again because of a more general mecanism wic is associated wit a downsizing of te industry due to an increase

10 74 XEPAPADEAS AND DE ZEEUW in costs and an accompanying modernization of te capital stock in te course of te downsizing process. As wit X-efficiency, te positive effects may be caused by an external sock in general and not exclusively one in relation wit an environmental problem. A stricter environmental policy can tus increase te average productivity of capital and reduce emissions at te same time. Tese effects can, owever, not be regarded as a win win situation unless te effects of emission taxes on profits are positive as well. 5. PROFIT EFFECTS OF EMISSION TAXES In order to analyse te profit effects of emission taxes, we consider a case were te firm subject to te environmental tax represents te ome industry. Tis industry competes wit a similar industry in anoter country wic is not subject to te environmental tax. Given te price p and te steady-state optimal age distribution of macines given by Ž. 7 total output for te ome industry is given by y Ž y. x* Ž y,. dy Ž y. p Ž. cž. sž. d dz dy z y y b z dzdy. Suppose tat te demand for te output of te ome industry and te industry abroad comes from a tird country according to te linear demand scedule, p p y x* y, dy y x* y, dy. Te equilibrium price becomes were and p* p p, y p Ž y. cž. d dz dy Ž y. bž z. dzdy z p, y Ž y. Ž. d dz dy z y z y Ž y. sž. d dz dy p. Ž y. Ž. d dz dy z Using tese expressions te steady-state optimal age distribution of macines becomes y z x* Ž y,. p Ž. sž. d dz x* Ž y,., y

11 ENVIRONMENT AND COMPETITIVENESS 75 were y z x* Ž y,. p Ž. cž. d bž z. dz, y wit p Ž. sž. d dz z indicating te reduction in te capital stock of te ome industry due to te downsizing effect of te environmental tax. Te environmental tax as a price effect and a cost effect. Te cange in te steady-state profits can be split into two parts. A cange as a result of te canges in te price, te cost of emission taxes, and te age distribution of macines, and a cange as a result of te canges in te transactions on te macine market. Te first cange in profits becomes y z Ž. p Ž y. sž y. p Ž. sž. d dz dy y z p Ž y. cž y. p Ž. sž. d dz dy p y s y x* y, dy. Because te net result from transactions on te macine market is given by b Ž y. p Ž. cž. sž. d, te second cange in profits becomes y y p s d dy p Ž. sž. d p Ž. cž. d dy. y y In order to obtain a tractable expression for te total cange in profits Ž., Lemma from te Appendix is used. By renaming y into and by renaming z into y in te rigt-and side of Lemma it is easy to see tat te second term of and te second term of cancel out, and tat te total cange in te steady-state profits can be written as were Ž., Ž 8. y z p Ž y. sž y. p Ž. sž. d dz dy, and p Ž y. sž y. x* Ž y,. dy.

12 76 XEPAPADEAS AND DE ZEEUW Tus te cange in profits is a quadratic function of te environmental tax, wit Ž.. Wit an increasing environmental tax te profits decrease monotonically until te steady-state optimal age distribution of macines as decreased to zero. In te interval from until te value max, at wic te resulting macine distribution is zero, te cange in profits is negative and decreasing in te environmental tax, d Ž. p Ž y. sž y. x* Ž y,. dy. d Wit an increasing environmental tax total emissions S also decrease according to 6 y ds sž y. p Ž. sž. d dz dy. d z aving establised tat stricter environmental policy reduces bot profits and emissions in te ome industry, we now turn to examine te relative effects of a stricter environmental policy wen te downsizing of te ome industry is or is not accompanied by a modernization of te capital stock. We compare two cases: In te first, te bencmark case, te productivity of te macines is constant and terefore no modernization is possible. In te second case te newer macines ave a iger productivity so tat a stricter environmental policy can generate a modernization effect. Emissions are kept constant over age in te two cases. It would be more realistic to assume tat older macines emit more tan newer macines, but tis would only strengten te results tat follow. Consider as a bencmark te case were all macines ave te same productivity Ž y. a, te same running costs cž y. c Ž., te same emissions sž y. s, and acquisition costs bž y. b Ž y. to reflect tat newer macines last longer. Te bencmark is compared wit te case were te macines productivity decreases wit age according to Ž y. a a Ž y.. It is easy to sow tat tis specification leads to te same total output and equilibrium price p before tax as in te bencmark case, if te parameters of te specification satisfy and te acquisition costs become 8 a da, a Ž d. a, d,., bž y. b Ž y., b b Ž d. p a. 5 It is to be expected tat te parameter of te acquisition costs is iger for a downward sloping productivity tan for a constant productivity. From Proposition it follows tat an increase in te emission tax, for tese specifications, increases te average productivity of te capital stock troug te modernization effect. 6 Note tat in order to determine te optimal tax it is necessary to determine te costs of total emissions to society. Te purpose of tis paper is, owever, to analyse te effect of a nonomogeneous capital stock, for wic suc a valuation is not necessary.

13 ENVIRONMENT AND COMPETITIVENESS 77 Suppose tat now an environmental tax is levied. In te bencmark case te equilibrium price becomes p b p b p wit as b p, a wile for te varying productivity case te equilibrium price becomes p p p wit as p. Ž d. a 5 Using tis framework te following proposition can be stated b b PROPOSITION. Let ds d, ds d, and d d, d d denote te marginal decreases in emissions and profits by a stricter en ironmental policy in te ome country, in te bencmark and arying producti ity cases, respecti ely. Ten under te assumptions made pre iously, and. d d d d b b ds ds d d For a proof see te Appendix. Tus wen te industry can cange te composition of its capital stock by buying newer more productive macines, and tis action is induced by a stricter environmental policy te reduction in emissions is larger and te reduction in profits is smaller as compared to te case were no suc action is possible. Terefore it can be stated tat wen te downsizing of te ome industry due to a stricter environmental policy is accompanied by modernization of its capital stock, tere are smaller losses in profits and tere are greater gains in emission reductions relative to te case were modernization is not possible. 6. CONCLUSIONS Using a model in wic firms can invest in macines wit different caracteristics, were newer macines are more productive and cleaner but also more expensive tan older macines, we isolated two effects resulting from te introduction of a stricter environmental policy in te form of a tax on emissions: A productivity effect and a profit emission effect. Te productivity effect implies tat if te downsizing of te firm due to te stricter environmental policy is accompanied by a modernization effect, wic means a reduction in te average age of te capital stock, ten te average productivity of te capital stock increases. Te profit emission effect indicates tat profits and emissions decrease wit a stricter environmental policy. owever, in te case tat te capital stock can be composed of newer more productive macines and older less productive macines te effect of an environmental tax is better in two ways, as compared to te case were modernization of te capital stock is not possible: te marginal decrease in emissions is iger and te marginal decrease in profits is lower.

14 78 XEPAPADEAS AND DE ZEEUW Terefore, our results indicate tat altoug a stricter environmental policy cannot be expected to provide a win win situation in te sense of bot reducing emissions and increasing profitability in an industry, we may expect increased productivity of te capital stock along wit a relatively less severe impact on profits and more emission reductions, wen te stricter policy induces modernization of te capital stock. Te trade-off between environmental conditions and profits of te ome industry remains but is less sarp because of downsizing and modernization of te industry. Proof of Proposition. APPENDIX A Te proposition follows by taking te derivative, dg Ž. d yxž y,. dy d d xž y,. dy setting te numerator less tan zero and rearranging terms, were it sould be noted tat te cange in te capital stock is negative. LEMMA. Te following olds: y ž /ž / fž y. gž. d dz dy f Ž y. dy g Ž. d dz. z z z Proof. Cange te order of integration of z and y. Proof of Proposition. First, te terms of te two ratios of te condition of Proposition are developed separately. Te first term becomes y xž y,. dy p Ž. cž. sž. d dz dy z y bž z. dz dy. By Lemma and ten canging te order of integration, te first part of tis expression for can be written as z Ž z. p Ž. cž. sž. d dz Ž z. p Ž. cž. sž. dz d p Ž. cž. sž. d.

15 ENVIRONMENT AND COMPETITIVENESS 79 By canging te order of integration, te second part of y can be written as bž z. dz dy bž z. dy dz Ž z. bž z. dz. z Combining tese two results we obtain p Ž. cž. sž. Ž. bž. d. Similarly, te second term becomes yxž y,. dy Ž. p Ž. cž. sž. bž. d. Furtermore, xž y,. y sž. d dz dy, z or, by using Lemma and ten canging te order of integration, Similarly, z Ž z. sž. d dz Ž z. sž. dz d sž. d. xž y,. y dy 4 Ž. sž. d. It follows tat te condition of Proposition,, becomes 4 Ž. Ž. Ž. sž. d. Ž. sž. d p Ž. cž. bž. d p Ž. cž. Ž. bž. d For Ž. a, cž. c, bž. b Ž., and sž. s bot te left-and side and te rigt-and side of tis inequality are equal to 5 8. Furtermore, it is easy to see tat for sž. s s wit s te rigt-and side is larger tan 5 8 and tat for Ž. a a wit a te left-and side is smaller tan 5 8.

16 8 Proof of Proposition. XEPAPADEAS AND DE ZEEUW By straigtforward calculations we obtain wile b ds Ž. a s, d a ds Ž. Ž d. a s. 5 d Ž 5.Ž d. a Tus it follows tat te marginal decrease in total emissions is larger in te case wit te varying productivity tan in te bencmark case. Furtermore, straigtforward calculations sow tat in te bencmark case te marginal cange in steady-state profits becomes b b d d a a s s Ž p a c b., d d a a wile for te varying productivity case te result is were d Ž. d Ž. ˆ, d d Ž 5.Ž d. a 45 Ž 5.Ž d. a ˆ d p a s, and Ž d. a 5 s Ž 5.Ž d. a p a Ž 5.Ž d. a Ž c b.. Ž d. a 5 Tus it follows tat te marginal decrease in profits is already smaller for in te varying productivity case as compared to te bencmark, and te difference grows wit an increasing environmental tax. APPENDIX B: LIST OF SYMBOLS y age of a macine maximum age of a macine t time Ž y. output of a macine of age y a, a, d, a parameters of Ž y.

17 ENVIRONMENT AND COMPETITIVENESS 8 cž y. running cost of a macine of age y c parameter of cž y. sž y. emissions of a macine of age y s, s parameters of sž y. xt, Ž y. number of macines of age y operating in year t Qt Ž. total output in year t emission tax per unit emissions Ct Ž. total running costs for year t S total emissions bž y. buying cost of a macine of age y b, b parameters of bž y. už y, t. number of macines of age y bougt or sold in year t p price of output p, p parameters of te equilibrium price generalized amiltonian Ž y, t. adjoint state or benefits from installing one macine of age y at time t A constant of integration * optimal fž y. proportion of macines of age y in te optimal capital stock g average age of te optimal capital stock average productivity of te capital stock, productivity parameters cange profits, parameters of cange in steady-state profits b bencmark case varying productivity case REFERENCES. S. Barrett, Strategic environmental policy and international trade, J. Public Econom. 54, 5 8 Ž D. Carlson, A. aurie, and A. Leizarowitz, Infinite orizon Optimal Control, Springer-Verlag, Berlin Ž D. Ellerman, Note on te seemingly indefinite extension of power plant lives, a panel contribution, Energy J. 9Ž., 9 Ž L. Gabel and B. Sinclair-Desgagne, Te firm, its routines, and te environment, in Te International Yearbook of Environmental and Resource Economics ŽT. Tietenberg and. Folmer, Eds.., Edward Elgar, Celtenam, pp Ž A. Gore, Eart in te Balance, Eartscan, London Ž A. Jaffe, S. Peterson, P. Portney, and R. Stavins, Environmental regulation and te competitiveness of U.S. manufacturing: wat does te evidence tell us?, J. Econom. Literature, 6 Ž J. Kalt, Te impact of domestic environmental regulatory policies on U.S. international competitiveness, in International Competitiveness Ž M. Spence and. azard, Eds.., arper and Row, Cambridge, MA, pp. 6 Ž K. Palmer, W. Oates, and P. Portney, Tigtening environmental standards: te benefit-cost or te no-cost paradigm?, J. Econom. Perspect. 9Ž. 4, 9 Ž M. Porter, America s green strategy, Sci. Amer. 64Ž. 4, 96 Ž M. Porter and C. van der Linde, Toward a new conception of te environment-competitiveness relationsip, J. Econom. Perspect. 9Ž. 4,97 8 Ž 995..

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