Location Decisions of a Polluting Firm and the Time Consistency of Environmental Policy Emmanuel Petrakis and Anastasios Xepapadeas University of Crete This paper analyzes and compares delocation decisions of a monopolist, who faces a tax on its emissions in the home country, under time consistent and precommitment environmental policies.we show that the monopolist will delocate more often under time consistent emission taxes. A government, which cannot commit to an environmental policy, is unable to adjust the emission tax downwards in order to prevent the monopolist's delocation. Total domestic welfare is higher when the government can precommit to an emission tax, but only for the parameter values under which the monopolist decides to delocate in the time consistent policy regime. Otherwise, total welfare is higher under time consistent emission taxes. Keywords: Monopoly, Delocation, Time Consistent Policies, Precommitment, Emission Tax, Abatement E ort. JEL Classi cation: L12, Q25, Q28. Department of Economics, University of Crete, University Campus, 74100 Rethymno, Crete. Fax: 30-831-77406, e-mail: xepapad@econ.soc.uoc.gr, petrakis@econ.soc.uoc.gr. We would like to thank Massimo Motta for his helpful comments and suggestions.of course, the authors are responsible for all remaining errors.
1 Introduction The response of rms to environmental policy has always been an issue of central importance in environmental economics. One aspect of this issue relates to the e ects that environmental policy has on the location decisions of the rms. Arguments have been put forward suggesting that tough environmental policies may cause rms' delocation so that in the long run rms move to countries with lax environmental regulations, or conversely, environmental dumping can be used in an attempt to attract foreign investment. Most of the delocation analysis is set up in a two-country, or two-region context, with countries using environmental taxation as the policy instrument, either cooperatively or non-cooperatively. 1 When a policy instrument such as emission taxes is used, which can a ect both short-term decisions of the rm such as output decisions and long-term decisions such as environmental innovation or abatement e ort, then issues of time consistency associated with the temporal structure of the policy problem arise. In the traditional approach the government precommits to an emission tax, and then the selects its abatement e ort and output. If, however, the government is unable to commit to an emission tax in the rst stage, rms will rationally anticipate that the government will adjust its emission tax in response to their own environmental innovation e orts. Thus in this case rms can strategically select their abatement e orts in order to in uence the emission tax the government will eventually set. A time consistent emission tax arises in the absence of government commitment when the rm chooses its abatement e ort rst, then the government sets an emission tax, and nally the sets decides its output. The second scenario emerges whenever the government's policy is non-credible. 2 This paper analyzes and compares delocation decisions of a monopolist who faces a tax on its emissions in the home country. The emission tax can be determined either through government precommitment or as a time consistent tax as described above. We show that the monopolist will delocate more often 1 See for example Carraro and Soubeyran (1998); Hoel (1994); Markusen, Morey and Olewiler (1993, 1995); Motta and Thisse (1994); Rauscher (1995). 2 There is a growing interest in issues related to the credibility of government policies, which has mainly been analyzed in the context of macroeconomic policies. See for example the survey by Persson and Tabellini (1997). However more recently credibility issues related to microeconomic policies have come under consideration (e.g. Maskin and Newbery (1990); Leahy and Neary (1995, 1996, 1997); Koujianou Goldberg (1995); Herguera et al. (1997)). A basic question raised in the policy context is whether the ability of the government to precommit to a speci c policy measure has bene cial e ects on various aspects of economic activity, such as the innovation rate, economic growth, or welfare. Despite the importance that the credibility of government policies may have for environmental innovation and hence pollution control, this issue has been relatively neglected in the analysis of environmental policy. A few exceptions include La ont and Tirole (1996a, 1996b), Kennedy and Laplante (1999), Petrakis and Xepapadeas (1999).
2 under time consistent emission taxes. A government which cannot commit to an environmental policy, is unable to adjust the emission tax downwards in order to prevent the monopolist's delocation. Comparing welfare under precommitment and time consistent policies, we show that total domestic welfare is higher when the government can precommit to an emission tax, but only for the parameter values under which the monopolist decides to delocate in the time consistent policy regime. Otherwise, total welfare is higher under time consistent emission taxes. 2 The Model We consider a monopolist producing and selling a homogeneous good in the home market. The monopolist faces a linear market demand, P (q) =a q: Pollution is a by-product of its production process. The monopolist, faced with a tax on its emissions t; can undertake an abatement e ort (environmental innovation) w to reduce its emissions level, and thus reduce its tax burden. Environmental innovation increases costs but reduces emissions. The cost function for the monopolist is assumed to be additively separable in production costs and environmental innovation costs, i.e. c(q;w) =cq + w2 : That is, there are constant returns to scale 2 in production, i.e. the marginal production cost c is constant. On the other hand, innovation costs are quadratic in innovation e ort w; i.e. the marginal innovation cost is increasing in w. Further, its emission function is, s(q; w) = q w. The monopolist, by investing the amount of w2 in environmental R&D, can reduce its 2 emissions by w: The monopolist can also delocate its production plant to a foreign country where the environmental policy is more favorable. Without loss of generality, we assume that there is no active environmental policy in the foreign country. The cost of delocation, F; is a xed cost. After its delocation, the monopolist exports its good and, as previously, sells in the home market alone. This could be for example the case of a plant of a multinational company that serves the home market and keeps serving the home market after its delocation. We assume, for simplicity, that exporting the good does not involve any additional costs. We shall assume that delocation costs are small enough that the monopolist may, under some circumstances, have incentive to delocate, that is, F A2 12 : Finally, the damage function for the home country is assumed to be quadratic in aggregate emissions, i.e. D(q; w) = 1 2 d(q w)2 ; where d is the slope of the marginal damage function. We shall assume that d 1; i.e. the marginal damage coe±cient is large enough that environmental policy should be in place. We compare two alternative scenarios: The traditional scenario, where the government precommits to an emission tax and then the monopolist, taking this tax as given, chooses to delocate or not, and also selects its abatement e ort and output. However, due to both the investment characteristics of abatement
3 expenses, which imply that abatement represents a long-term decision as compared to the short-term output decision, and also the ability of the government to change the emission tax following normal legislative procedures, the tax structure determined in this scenario cannot be credible unless the government possesses a speci c commitment mechanism. Once the abatement e ort has been chosen by the monopolist, the emission tax determined through precommitment is not ex post optimal and therefore is not time consistent. The monopolist rationally anticipates a change in the emission tax once its abatement expenses are already sunk. Therefore, when the government cannot credibly commit to a policy and is expected to change the emission tax after abatement expenses have been chosen, then a time consistent emission tax implies that the tax is ex post optimal, given abatement expenses and the rm's future output response to the emission tax. To determine this time consistent tax, we consider the following scenario. The monopolist rst selects whether to delocate or not, and also chooses its abatement e ort. If the monopolist decides to produce in the home country, then the government sets its emission tax, and nally the monopolist chooses its output. We begin our analysis with this second scenario. In section 3.1 we analyze delocation decisions in the case of time consistent emission taxes, while in section 3.2 the precommitment case is treated. Finally, section 3.3 compares the results when the government can, or cannot, precommit to an emission tax. 2.1 Delocation Decisions under Time Consistent Policies In the last stage, if the monopolist has decided to produce in the home country, it will choose its output to maximize pro ts: max[(a q)q cq 1 q 2 w2 t(q w)] where t is the tax per unit of emissions in the home country. From the rst-order condition we obtain the monopolist's optimal output and pro ts: q m = 1 2 (A t) and ¼m =(q m ) 2 + tw 1 2 w2 (1) where A = a c; is a measure of the market size. Note that the monopolist's output decreases with the emission tax, t: On the other hand, if the monopolist has decided to delocate its plant and export the good to the home market, it faces no environmental policy in the foreign country, and thus makes no abatement e ort, i.e.w D =0: The monopolist will select its output to maximize pro ts, (a c q)q F: Thus, qd m = A and 2 ¼D m = A2 F: Since the monopolist sells in the home market without causing any 4 environmental damages, total domestic welfare equals A2 8.
4 In the second stage, if the monopolist has decided to produce in the home country, the government chooses the emission tax to maximize total domestic welfare, taking into account the monopolist's reaction in the subsequent output selection stage. The total welfare is de ned as the (unweighted) sum of consumer surplus, monopolist's pro ts and environmental damages due to the monopolist's emissions. Given that the monopolist selects output according to (1), the government solves: max t Z q m which is equivalent to: 0 (a c x)dx 1 2 d(qm w) 2 1 2 w2 max[aq m 1 t 2 (qm ) 2 1 2 d(qm w) 2 1 2 w2 ] (2) The rst-order condition is: [A q m d(q m w)] dqm =0 (3) dt where dqm = 1 < 0: Then, from (1), we get the optimal tax on the monopolist's dt 2 emissions, t (d 1)A 2dw = (4) 1+d Note that the optimal emission tax increases with the marginal damage, d: More interestingly, it decreases with the monopolist's abatement e ort, w. Therefore, the monopolist, by increasing its environmental innovation expenditures, can strategically induce a lower tax on its emissions. Now, substituting (4) into (1) and (2), we get the monopolist's output and pro ts and the total domestic welfare: q m = A + dw 1+d ¼ m = (A +2dw + d2 w)(a w) (1 + d) 2 1 2 w2 (5) TW = A2 +2Adw d 2 w 2(1 + d) 1 2 w2 (6) In the rst stage, the monopolist decides to delocate or not, and if the decision is to stay in the home country, it also selects its abatement e ort to maximize its pro ts, taking into account that its decision will a ect the government's optimal policy in the subsequent stage. If the monopolist decides not to delocate, then it chooses w to maximize ¼ m (see (5)). From the rst-order condition, we obtain the optimal abatement e ort for the monopolist when the government cannot credibly commit to an emissions tax, w m = (1 + d)2 2 1+6d +3d 2 A (7)
5 Since d 1, w m > 0: Then: t = d2 2d 1 1+6d +3d 2 A (8) q m = ¼ m = 1+4d + d2 1+6d +3d 2 A (9) 3+2d + d2 2(1 + 6d +3d 2 ) A2 > 0 (10) TW = 2d(1 + d)2 (3 + d) (1 + 6d +3d 2 ) 2 A2 > 0 (11) Clearly, q m w m > 0. Note that t < 0 whenever d<2:4142; i.e. the time consistent emission tax is negative whenever the marginal damage coe±cient is small enough. As the monopolist has decreased its emissions substantially by overinvesting in abatement technology, the government, through emission subsidies, partially corrects for the ine±ciency provoked by the monopolist's market power. On the other hand, if the monopolist decides to delocate, its pro ts are equal to: ¼D m = A2 4 F The monopolist delocates if ¼D m >¼ m : Let f = F : Comparing ¼ m A 2 D with ¼ m we obtain the following results. Proposition 1 If the government cannot precommit to an emission tax, then the monopolist will delocate if, for any given f; d> 1+12f + p (6 80f +96f 2 ) 1 12f d # (f) Note that d # is increasing in f; d # (0) = 1:45 and d # ( 1 )=1: Thus for 12 su±ciently steep marginal damage function the monopolist will relocate. This is the result of the e ects of the steepness of marginal damages on the emission tax and the monopolist's pro ts. From 8 and 10 we have: @t @d @¼ m @d = 4A 2z +3z2 +1 (1 + 6z +3z 2 ) 2 > 0 = 8(1+d) A 2 (1 + 6d +3d 2 ) 2 < 0
6 Thus the steeper the marginal damage function, the higher the emission tax and the lower the monopolist's pro ts. Since ¼ m is monotonously decreasing in d for asu±cientlyhighd; ¼ m <¼D m and the monopolist delocates. Comparing the total welfare when the monopolist produces in the home country (11) with the total welfare when it delocates, 2 ; it can be seen that the A 8 delocation of the monopolist will decrease total domestic welfare for all d: As thegovernmentcannotcrediblycommittoanemissiontax,itisunabletouse its environmental policy to alter the decision of the monopolist to delocate its production plant to a foreign country. 2.2 Delocation Decisions under Government Precommitment The output selection stage is the same as above. In the environmental innovation selection stage, the monopolist chooses its abatement e ort to maximize pro ts: max w [(qm ) 2 + tw 1 2 w2 ] Since dqm dw thus, = 0, from the rst-order condition we get, ewm = t: Then eq m = A t 2 ; ~¼ m (A t)2 = + t2 (12) 4 2 The monopolist will delocate its production plant whenever its pro ts abroad, A 2 4 F; are larger than ~¼m (t): That is, it will delocate whenever the emission tax, t; is higher than t c ; where t c solves: ~¼ m (t c )= A2 F: Hence, the critical value of 4 the emission tax is, t c = 1 p (1 12f) A (13) 3 In the rst stage, the government chooses the emission tax that maximizes total welfare, taking into account how the monopolist will react to its environmental policy. Substituting output and innovation e ort into (2) we obtain the total welfare as a function of t ( A(A t) gtw (A t)2 = t2 2 8 2 d (A 3t)2 if t t 8 c (14) A 2 if t>t 8 c From the rst-order condition of the unconstrained problem we get: et = 3d 1 9d +5 A = ewm > 0 (15)
7 Then: eq m = 3(d +1) 9d +5 A e¼m = 27d2 +30d +19 2(9d +5) 2 A 2 and g TW = 2(d +1) 9d +5 A2 (16) Note that eq m ew m > 0: Total domestic welfare is higher if the monopolist does not delocate its production plant, because TW g > A2 for all values of d: Hence, if t e t 8 c ; the government will choose the optimal emission tax and the monopolist will not delocate. From (13) and (15), it can be checked that if f < 0:056 then t>t e c. However, for 0:056 <f 1 ; t e t 12 c if and only if the damage function is not too convex, i.e. d 8 5p (1 12f) 9 p ed(f) (1 12f) where d e is increasing in f and d( e 1 )=1: 12 On the other hand, if t>t e c ; the government has the option to set the emission tax equal to t c in order to keep the monopolist's production in the home country. Of course, the government will use this option only if TW(t g c ) A2 : From (14) 8 this occurs if, for given f, the damage function is not too convex, i.e. d 2[1 + 30f +8p (1 12f)] bd(f) 9(1 12f) where d b is increasing in f; d(0) b = 2; and d( b 1 )=1: Also, it can be checked that 12 max[1; d(f)] e < d(f) b forallf: The following Proposition summarizes the results. Proposition 2 If f>0:056 and d< e d(f) then the government selects the optimal emission tax e t and the monopolist does not delocate. Moreover, for any given f; if max[1; e d(f)] <d< b d(f); the government selects the minimum emission tax, t c ; such that the monopolist has no incentive to delocate. Finally, for any given f; if d> b d(f) the monopolist will always delocate, as the government has no incentive to prevent its delocation. 2.3 Delocation Decisions and Welfare under Alternative Policy Regimes Let us now compare the delocation decisions of the monopolist under the two alternative policy regimes. Note rst that d(f) b >d # (f) > max[1; d(f)] e for all f: This can been easily seen by plotting these functions in the same gure. In Figure 1, the parameter space (d; f); d 1; 0 f 1 ; has been divided in four regions. 12 Under government precommitment to an emission tax, the monopolist delocates only in the North-West region IV, while under time consistent emission taxes,
8 the monopolist delocates in regions III and IV. The intuition is simple. When the government can precommit to an emission tax, it has the ability to commit to the lowest possible emission tax such that the monopolist has no incentive to delocate its production plant. This is not possible under time consistent policies, because the government selects the emission tax only after the monopolist has decided upon its abatement e ort. Thus, if the monopolist expects a relatively high emission tax after its innovation costs are already sunk, it would rather choose to delocate its plant instead of producing in the home country and spending on abatement to reduce its tax burden. The following Proposition summarizes. Proposition 3 If the government cannot precommit to an emission tax, the monopolist will delocate its production plant under a broader range of parameter constellations. We now turn to the welfare comparison. In region IV, where the monopolist delocates under both policy regimes, total welfare equals A2 : In region III, the 8 monopolist delocates only if the government cannot precommit to an emission tax. In this region, the government which is able to precommit will set the emission tax equal to t c to prevent the monopolist's delocation because total welfare is higher when the monopolist produces in the home country. Hence, in region III, total welfare is higher under government precommitment. In regions I and II, the monopolist does not delocate its production plant. Note rst that as t c is not optimal in the unconstrained problem, total welfare in region III when the government precommits is lower than TW g (see (16)). Moreover, from (11), we have, gtw TW = 2(1 + d)(5d3 +5d 2 +3d 1) A 2 < 0 (5 + 9d)(1 + 6d +3d 2 ) 2 Therefore, in regions I and II total welfare is higher whenever the government cannot credibly commit to an emission tax. If, under time consistent emission taxes, the monopolist decides not to delocate, then it will spend more on abatement in order to strategically reduce the tax on its emissions. As the government moves second, the optimal emission tax will depend on the abatement e ort that the monopolist has already made. As we have seen, the optimal tax decreases with the monopolist's abatement e ort (see (4)). Therefore, under time consistent policy, the monopolist spends more on abatement, the optimal emission tax is lower and the total welfare is higher. The following Proposition summarizes. Proposition 4 If the government can precommit to an emission tax, total welfare is higher for the range of parameter values where the monopolist decides to delocate under time consistent emission taxes (regions III and IV). Otherwise, total welfare is lower (regions I and II).
9 3 Conclusions The paper examines the location decisions of a monopolist which faces emission taxes that could be implemented in two di erent regimes. The rst is the traditional one where government precommits to the emission tax and then the monopolist chooses environmental innovation and output. The second regime consists of a time consistent emission tax which is determined after the monopolist has chosen its innovation e ort. This time consistent emission tax can be implemented by a contract between the government and the monopolist. The contract will specify the tax rate for any given innovation e ort. We show that under a time consistent emission tax the government cannot a ect the monopolist's location decisions. Location decisions can be a ected if the government can credibly commit to an emission tax. Of course there are always parameter combinations under which the rm will delocate irrespective of the policy regime. The range of delocation parameters is however broader under time consistent policies. If the government can precommit to the emission tax in a case where under a time consistent tax the rm would have delocated, then welfare under precommitment is higher relative to time consistent policy that eventually would have lead to delocation. When however the parameter values are such that the monopolist will not delocate under any regime, then time consistent policies will lead to higher welfare. This result indicates that, contrary to results obtained previously where government precommitment led to relatively higher welfare, 3 welfare gains can also be obtained under time consistent emission policies. A policy implication of these results is that in cases where the government wants to prevent capital ight while keeping emission taxes in place, commitment to an emission tax which is adjusted in an appropriate manner relative to the critical tax rate might prevent delocation, while a time consistent policy regime will not do so. 3 See Leahy and Neary (1996), Herguera et al. (1997).
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11 Markusen, J.R., E.R. Morey and N. Olewiler (1995), "Competition in Regional Environmental Policies when Plant Locations are Endogenous", Journal of Public Economics, 56, 55-77. Maskin, E., and D. Newbery (1990): "Disadvantageous Oil Tari s and Dynamic Consistency", American Economic Review, Vol. 80, 143-56. Motta, M. and J-F Thisse (1994), "Does Environmental Dumping Lead to Delocation?", European Economic Review, 38, 563-576. Petrakis, E., and A. Xepapadeas (1999), "Does Government Precommitment Promote Environmental Innovation?" in E. Petrakis, E Sartzetakis and A. Xepapadeas, (Eds), Environmental Regulation and Market Power, Edward Elgar, forthcoming. Persson T. and G. Tabellini (1997): "Political Economics and Macroeconomic Policy', CEPR Discussion paper No 1759. Rauscher, M. (1995), "Environmental Regulation and the Location of Polluting Industries", International Tax and Public Finance, 2, 229-244.
d I II III IV ã Figure 1: Delocation of the monopolist under government precommitment and under time consistent emission taxes: A comparison.