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1 econstor Make Your Publication Visible A Service of Wirtschaft Centre zbwleibniz-informationszentrum Economics Eichner, Thomas; Pethig, Rüdiger Working Paper Incidence of unilateral consumption taxes on world carbon emissions Volkswirtschaftliche Diskussionsbeiträge, Universität Siegen, Fakultät III: Wirtschaftswissenschaften, Wirtschaftsinformatik und Wirtschaftsrecht, No. 49- Provided in Cooperation with: Fakultät III: Wirtschaftswissenschaften, Wirtschaftsinformatik und Wirtschaftsrecht, Universität Siegen Suggested Citation: Eichner, Thomas; Pethig, Rüdiger 20) : Incidence of unilateral consumption taxes on world carbon emissions, Volkswirtschaftliche Diskussionsbeiträge, Universität Siegen, Fakultät III: Wirtschaftswissenschaften, Wirtschaftsinformatik und Wirtschaftsrecht, No. 49- This Version is available at: Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence.

2 Fakultät III Wirtschaftswissenschaften, Wirtschaftsinformatik und Wirtschaftsrecht Volkswirtschaftliche Diskussionsbeiträge Discussion Papers in Economics No. 49- November 20 Thomas Eichner Rüdiger Pethig Incidence of unilateral consumption taxes on world carbon emissions

3 Universität Siegen Fakultät III Wirtschaftswissenschaften, Wirtschaftsinformatik und Wirtschaftsrecht Fachgebiet Volkswirtschaftslehre Hölderlinstraße 3 D Siegen Germany ISSN Available for free from the University of Siegen website at Discussion Papers in Economics of the University of Siegen are indexed in RePEc and can be downloaded free of charge from the following website:

4 Incidence of unilateral consumption taxes on world carbon emissions Thomas Eichner Department of Economics, University of Hagen Rüdiger Pethig Department of Economics, University of Siegen Abstract This note investigates the suitability of unilateral consumption taxes for alleviating climate change in a two-period two-country general equilibrium model with a finite stock of fossil fuel. We analyze the incidence of a unilateral consumption tax in the first period on world carbon emissions. If countries are identical or if the taxing country imports both fossil fuel and consumption goods in the second period, increases in the tax rate lower first-period carbon emissions in both countries implying a negative rate of carbon leakage. JEL classification: Key words: H22, Q38, Q58 unilateral consumption tax, world emissions, leakage Eichner: Department of Economics, University of Hagen, Universitätsstr. 4, Hagen, Germany, thomas.eichner@fernuni-hagen.de; Pethig: Department of Economics Fakultät III), University of Siegen, Hölderlinstr. 3, Siegen, Germany, pethig@vwl.wiwi.uni-siegen.de

5 Introduction In the Kyoto Protocol a number of countries have committed to reduce unilaterally their emissions of greenhouse gases. The effort of the abating countries may be offset to some extent by carbon leakage Felder and Rutherford 993), that is, by increasing carbon emissions in non-abating countries. Even worse, demand-reducing measures of abating countries may increase rather than decrease aggregate world emissions, which has been labelled green paradox Sinn 2008). taxes. The literature so far has analyzed leakage rates resulting from unilateral emission Eichner and Pethig 20) find that positive leakage rates are unavoidable and identify the intertemporal substitution elasticity of consumption and the demand elasticity for fossil fuel as the main determinants of a green paradox. Empirical estimates of carbon leakage based on large-scale simulation models range from low levels Burniaux and Martins 200) to leakage rates implying a green paradox Babiker 2005). Essentially, carbon leakage and the green paradox, a fortiori, compromize the use of unilateral emission taxes as climate policy instruments. The present paper sets up a two-period two-country general equilibrium with a nonrenewable fossil energy resource and examines the incidence of a unilateral first-period consumption tax on first-period world carbon emissions. That incidence appears to be straightforward, at first glance. Consumption and production is shifted from the first to the second period decreasing the demand for fossil fuel and the discharge of emissions in the first period. At second glance, we observe countervailing price effects in the general equilibrium model. Nonetheless, informative results can be obtained if either both countries are identical or if the taxing country imports fossil fuel and consumer goods in the second period. In those cases which appear to be relevant scenarios the consumption tax turns out to reduce total first-period emissions and not only avoids leakage rates exceeding 00% green paradox) but, on the contrary, implies a negative leakage rate, because both countries reduce their production and with it their consumption of fossil fuel in the first period. 2 Cap and trade systems are equivalent to emission taxes in most abstract analytical models. 2 Negative leakage rates may also result from unilateral emission taxes in one-period models as pointed out by Copeland and Taylor 2005), Karp 200) or Fullerton et al. 20).

6 2 The model Using essentially the analytical framework of Eichner and Pethig 20), we consider a twoperiod model with two countries A and B. 3 In each period t =, 2 each country i produces the output x s it of the consumption good X with the input of fossil fuel, e it, according to the strictly increasing and concave production function x s it = X i e it ) i = A, B ) The representative consumer of country i derives utility from consumption x it in period t =, 2 according to the intertemporal CES utility function 4 u i = U i x i, x i2 ) = γ x σ i σ i i + γ 2 x σ i ) hσ i σ i σ i i2 i = A, B, 2) with γ, γ 2, h > 0 and σ A = σ B σ > 0, σ. In each period, good X and fossil fuel are traded on perfectly competitive world markets at prices p xt and p et, respectively. For t =, 2 the market equilibrium conditions are x s At + x s Bt = x At + x Bt, 3) e t = e At + e Bt, 4) where e t is the fossil fuel supply in period t. The intertemporal constraint for fossil fuel is then given by ē = e + e 2. 5) In 5), ē is a finite stock of fossil fuel. Country i owns the share α i [0, ] of that stock, where α A + α B =. Carbon emissions are generated in strict proportion to the amount of fossil fuel consumed. Hence with suitable definitions of units, e it denotes fuel consumption as well as carbon emissions. The government of country A levies a unit tax at rate τ on 3 The only difference to Eichner and Pethig 20) is that their model features a third country which owns the resource fossil fuel whereas in the present paper the countries A and B are the owners of the fossil fuel stock. However, it can be shown that this modification leaves the results of Eichner and Pethig 20) unaltered. 4 The results derived in the sequel are also obtained for isoelastic utility functions of the form µx η i U i η x i, x i2 ) = + +ρ µx η i2 η for µ > 0, η, ln x i + +ρ ln x i2 for η =, where ρ 0. It is worth noting that both for CES and for isoelastic functions the intertemporal substitution elasticity is constant. 2

7 the domestic first-period consumption of good X. 5 In the regulated) competitive market economy an aggregate resource firm extracts the entire stock of fossil fuel, ē, over both periods. In addition, in each country i an aggregate firm produces the consumption good X. With the discount rate being zero the profits are, respectively, Π i := t Π F := t [p xt X i e it ) p et e it ] i = A, B, p et e t, where the extraction costs of the resource firm F are assumed to be zero. profits yields the first-order conditions Maximizing p xt Xe i it = p et i = A, B and t =, 2, 6) p e = p e2. 7) Equation 7) is a simplyfied Hotelling rule. The representative consumer in country A and B, respectively, maximizes utility subject to her budget constraint p x + τ)x A + p x2 x A2 = Π A + α A Π F + τx A, 8) p x x B + p x2 x B2 = Π B + α B Π F, 9) where Π i is the maximum profit of the firm in country i = A, B and Π F is the maximum profit of the fossil fuel extracting firm. Utility maximization yields U xa2 U xa = p x2 p x + τ and U x B2 U xb = p x2 p x. 0) For convenience of exposition we take good X in period as numéraire p x = ), and write p x2 p x and p e = p e2 p e. 3 Incidence of the consumption tax In this section we consider the competitive equilibrium in the two-country model ) - 0) and explore the comparative static effects of increasing the tax rate τ in country A. We wish to determine, in particular, the sign of de = de A + de B, where de A/ and de B / may take on any sign. If de / > 0 the tax steepens rather than flattens the carbon 5 For the benefit of a clear focus on the consumption tax incidence we refrain from adding emissions taxes or cap and trade systems to the model. 3

8 emission path and thus exacerbates climate change. 6 The consumption tax qualifies as an instrument of unilateral climate policy under the following constellations of tax incidence: > leakage rate positive, but < 00%, de < 0 and de B = < 0 = no leakage, The comparative statics in the Appendix) reveal that sign de A = sign de B negative leakage. = sign dp e = signdp x. ) The first equality sign in ) means that the consumption tax either exacerbates climate change de A / > 0) or is a promising climate policy instrument that even reduces country B s first-period emissions negative leakage) although countr is politically inactive. It is interesting to compare that observation with the scenario studied by Eichner and Pethig 20) where country A increases the rate π of a tax on its first-period emissions. They show that de A /dπ < 0 holds unconditionally 7 but that the leakage rate is always positive, possibly larger than 00% green paradox). Now the crucial question is how restrictive the conditions are for de A / < 0 or, equivalently, for de / < 0. We derive in the Appendix that de = ρτ) ψτ) e A θτ) x A2 2) where e A := α A ē e A e A2, x A2 := x s A2 x A2 and where ρτ), ξτ) and θτ) are parameters defined in the Appendix that satisfy ρτ) > 0 for τ 0, ξτ) = θτ) = 0 for τ = 0, and ξτ) > 0, θτ) > 0 for τ > 0. Proposition. An increase in the consumption tax rate flattens the carbon extraction path and implies negative leakage, if the following conditions i) or ii) hold: i) The countries differ with respect to production functions and energy resource endowments α A 2), and the initial competitive equilibrium is characterized a) either by τ = 0 b) or by τ > 0 and by imports of fossil fuel e A 0) and second-period consumption good x A2 0) on the part of country A. 6 The case of de / > 0 where the direct effect de A / is negative could be called a green paradox because it implies a carbon leakage rate exceeding 00%. 7 What is needed is the textbook assumption that the firm s demand for fossil fuel is strictly decreasing in the fuel price. 4

9 ii) The countries are identical same production functions and α A = ) and the initial 2 competitive equilibrium is characterized by τ 0. 8 Proposition i) is straightforward from 2). In order to assess the conditions b) in Proposition i) observe that e A < 0 is the more likely the smaller is the energy resource endowment of country A α A small). Moreover, if production capacities do not differ too much in both countries, x A2 < 0 is also plausible because the reduction in the relative consumer price of the second-period consumption good is lower in country A than in country B. 9 Thus the conditions b) appear to approximate the characteristics of the group of countries that have committed to emission reduction in the Kyoto Protocol. worth mentioning that the conditions b) are sufficient but not necessary. It is also Unfortunately, reversals in the sign of e A and x A2 cannot be excluded when the tax rate is successively raised or lowered. Such reversals may, in turn, switch the sign of de / in 2). It is therefore not quite clear how restrictive the conditions b) in Proposition i) are or, to put it differently, how attractive the consumption tax is as an instrument for fighting climate change. Proposition ii) provides additional support for a role of the consumption tax in climate policy by establishing for the case of symmetry that e is monotone decreasing in τ. The proof in the Appendix shows that under the condition of identical countries e A = 0 and x A2 < 0 holds for all τ 0 such that in 2) de / < 0 for all τ 0. It is interesting to compare the price effects of an increase in the consumption tax τ with those of an increase in the unilateral first-period emission tax π under the condition that in both cases total first-period emissions are curbed de / < 0 and de /dπ < 0). We infer dp e / > 0 and dp x / > 0 from ), whereas Eichner and Pethig 20) find dp e /dπ < 0 and dp x /dπ < 0. Obviously, the emission tax reduces the world demand for fossil fuel at any given price and thus lowers the equilibrium fuel price. Consumption in period becomes relatively more expensive and thus induces the necessary shift of consumption from the first into the second period. In sharp contrast, p e needs to rise in case of an increase of the consumption tax rate because otherwise producers would not reduce their first-period demand for fossil fuel. > 0 discourages first-period consumption in country A such that the increase in countr s first-period consumption due to dp x > 0) is overcompensated. 8 The proof of Proposition ii) is provided in the Appendix. 9 Observe that the budget constraints 8) and 9) can be rearranged to the intertemporal trade balances x i + p x x i2 + p e e i = 0 for i = A, B. Then e A < 0 and x A2 < 0 implies that country A exports consumption goods in the first period x A > 0). 5

10 4 Concluding remarks In general, those tax instruments are best suited to reduce pollution-generating emissions whose tax base are emissions rather than non-polluting) consumer goods. Accordingly, in the climate-change context the perfect tax for reducing total first-period carbon emissions is a uniform emission tax on all first-period emissions. However, unilateral emission taxes inevitably create distortions and excess costs as do unilateral consumption taxes. This note suggests that the unilateral consumption tax has the potential of an instrument for fighting climate change, if full cooperation cannot be attained. It might thus be a promising alternative or supplement to unilateral emission taxes or other unilateral conventional emission-reducing environmental policy instruments. References Babiker, M. H. 2005): Climate change policy, market structure, and carbon leakage, Journal of International Economics 65, Burniaux, J.-M. and J.O. Martins 200): Carbon leakages: a general equilibrium view, Economic Theory, in press. Copland, B.R. and M.S. Taylor 2005): Free trade and global warming: A trade theory view of the Kyoto Protocol, Journal of Environmental Economics and Management 49, Eichner, T. and R. Pethig 20): Carbon leakage, the green paradox and perfect future markets, International Economic Review, in press. Felder, S. and T. Rutherford 993): Unilateral CO 2 reductions and carbon leakage: the consequences of international trade in oil and basic materials, Journal of Environmental Economics and Management 25, Fullerton, D., Karney, D. and K. Baylis 20): Negative leakage, working paper, University of Illinois. Karp, L. 200): Reflections on carbon leakage, working paper, University of Berkeley. Sinn, H.-W. 2008): Public policies against global warming: a supply side approach, International Tax and Public Finance 5,

11 Appendix Derivation of ): When first-period consumption is taxed in country A the competitive equilibrium is characterized by the equations X A e A p e = 0, A) X B e B p e = 0, A2) p x X A e A2 p e = 0, A3) p x X B e B2 p e = 0, A4) e e A e B = 0, A5) ē e e A2 e B2 = 0, A6) X A e A ) x A + p x [X A e A2 ) x A2 ] + p e e A = 0, A7) X B e B ) x B + p x [X B e B2 ) x B2 ] + p e e B = 0, A8) X A e A2 ) + X B e B2 ) x A2 x B2 = 0, A9) U xa2 p x U xa + τ = 0, A0) U xb2 p x U xb = 0, A) where e i := α i ē e i e i2 for i = A, B. The endogenous variables determinded by the equations A) - A) are e A, e A2, e B, e B2, e, x A, x A2, x B, x B2, p e and p x. The tax rate τ is treated here as exogenous parameter. Total differentation of A) - A) yields, after some rearrangement of terms, ê A ˆp e η A = 0, A2) ê B ˆp e η B = 0, A3) ˆp x + ê A2 ˆp e η A2 = 0, A4) ˆp x + ê B2 ˆp e η B2 = 0, A5) e ê e A ê A e B ê B = 0, A6) e ê e A2 ê A2 e B2 ê B2 = 0, A7) x Aˆx A p x x A2ˆx A2 + e A p eˆp e + x A2 p xˆp x = 0, A8) x Bˆx B p x x B2ˆx B2 + e B p eˆp e + x B2 p xˆp x = 0, A9) p e e A2 ê A2 + p e e B2 ê B2 p x x A2ˆx A2 p x x B2ˆx B2 = 0, A20) ˆx A2 ˆx A + σˆp x στ ˆτ + τ = 0, A2) ˆx B2 ˆx B + σˆp x = 0, A22) 7

12 where x it := x s it x it and η it := X i e it /e it X i e it e it ) < 0 for t =, 2 and i = A, B. We insert A2) in A8) and A22) in A20) to obtain ˆx A2 = e Ap e y A ˆx B2 = e Bp e Using A2), A3) in A6) we find ˆp e = ˆp e + p x x A2 σx A y A ˆp x + στx A + τ)y A ˆτ, A23) ˆp e + p x x B2 σx B ˆp x. A24) i=a,b e iη i e ê, A25) Inserting A3), A4) in A7) and taking advantage of A24) we get after rearrangement of terms ˆp x = i=a,b e iη i + A2), A3) A25) and A26) establish ). i=a,b e i2η i2 ) e ê. A26) Derivation of 2): Inserting A7) in A20) yields p e e ê = p x x i2ˆx i2. i=a,b A27) Making use of A23) and A24) in A27) we obtain p x x A2 x A σ px x A2 = p e e ê p xx B2 + τ)y A y A y B px x A2 p ) xx B2 px x A x A2 p x x A2ˆp x + σ y A y A ) e A p eˆp e + p xx B x B2 ) ˆp x. A28) With the help of A25) and A26) equation A28) can be rearranged to p x x A2 x A σ px x A2 = p e p ) xx B2 p e e A + τ)y A de y A ) p x x A2 px x A2 y A p xx B2 px x A x A2 +σ + p xx B x B2 y A A29) can be rewritten in the form i=a,b e + iη i ) i=a,b e iη i + i=a,b e iη i i=a,b e i2η i2 i=a,b e i2η i2 ) ). A29) de =, ρτ) ξτ) e A θτ) x A2 A30) 8

13 where ρτ) := + τ)y A p x x A2 x A ξτ) := + τ)y A p x x A2 x A θτ) := + τ)y A x A2 x A [ p e σ i=a,b e + iη i [ [ p e i=a,b e iη i px x A2 i=a,b e iη i + The properties of ρτ), ξτ) and θτ) are specified in y A i=a,b e i2η i2 y A ) px x A x A2 + p )] xx B x B2, A3) p xx B2 i=a,b e i2η i2 Lemma. { } { } p x x A2 > p x x B2 > i) τ 0. x A + p x x A2 = x B + p x x B2 = ii) ρτ) > 0, ξτ) = θτ) = 0 for τ = 0. iii) ρτ) > 0, ξτ) > 0, θτ) > 0 for τ > 0. ) ], A32) ) px x A2 y A p ) ] xx B2.A33) γ Proof: i) Observe that CES utility functions imply x A = x A2 p σ, x γ 2 +τ)) xb = x B2 ) σ and hence γ p x γ 2 p x x A2 x A + p x x A2 = p x + p x γ p x γ 2 +τ) ) σ p x + p x γ p x γ 2 ) σ = p x x B2 x B + p x x B2, A34) where the equality in the sign in A34) holds if and only if τ = 0. The Lemmas ii) and iii) follow from Lemma i), η i < 0 for i =, 2 and + τ) > 0. Proof of Proposition ii): An equilibrium with identical production functions is characterized by e A = e B and e A2 = e B2. Differentiation of these equalities yields de A = de B and de A2 = de B2. A35) Next we differentiate e A = α A ē e A e A2 and e B = α A ) e B e B2 to obtain d e A ) d e B ) de = α A de A de A2, = α A ) de de B de B2. Substracting A37) from A36) and accounting for A35) yields A36) A37) d e A ) d e B) = 2α A ) de. 9 A38)

14 Since e A = e B and hence d e A ) = d e B ) we infer from A38) α A = 2 = d e A) Next, we use A39), A22) in A9) to get = d e B) = 0. A39) dx B = x B2σ + x B2 )x B dp x. A40) In addition, from A3) and differentiating x s B = Xe B) we get dx s B d x B ) = e B η B dp e, = dxs B dx B dp e = e B η B x B2σ + x B2 )x B dp x. A4) A42) Consider an unregulated equilibrium τ = 0) which is characterized by e A = x A = x A2 = 0 for identical production functions and α A =. Suppose next that this initial 2 equilibrium is disturbed by a tax increase > 0. Applying Proposition i)a) we know that de < 0, τ=0 dp x Accounting for A43) in A42) we get d x B) equilibrium for τ = > 0) has the properties > 0 and dp e τ=0 > 0. A43) τ=0 < 0. Due to A39) the new regulated τ=0 x A = x B > 0, x A2 = x B2 < 0, e A = e B = 0. A44) Hence the presuppositions of Proposition i)b) are satisfied. Using the same arguments as before it is straightforward to show that further increases of τ result in equilibria at which A44) holds. 0