Palokangas, T.

International Institute for Applied Systems Analysis (IIASA)

LiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryEmission Permit Management withSimultaneous Localized and Global ExternalityProblemsTapio PalokangasUniversity of Helsinki, HECER and IIASAPaper to be presented in Jekaterinburg, October 2-7, 2016,RussiaTapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryContents1 Literature2 The model3 Nontraded permits4 Traded permits5 The role of asymmetryTapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryMotivationThe research question:Does emission permit trading cause inefficiency,when production causes simultaneous localizedand global externality problems (e.g. smog andglobal warming)?I examine this question in a simple framework where abenevolent international common agency determinesemission permits.In Palokangas (2015), I derive the same results in anextended case where the common agency isself-interested, elected by the countries, and subject tolobbying by the countries (cf. Dixit et al. 1997).Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryLiterature 1Caplan and Silva (2005) examine joint tradable permitswhen pollutants cause regional and global externalities.They find that joint domestic and commonly internationalpermit markets are Pareto efficient.Holtsmark and Sommervoll (2012) consider emissiontrading when the governments set their national emissiontargets individually and grant emission permits for thedomestic firms. They find that emission permit tradingincreases emissions and decreases efficiency.In contrast to these articles, however, I assume that thereis a benevolent international common agency that issuesemission permits.Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryLiterature 2Montgomery (1972), Shiell (2003) and MacKenzie et al.(2008) consider the redistributive effects of the initialallocation of emission permits. I use the representativehousehold framework to ignore all such redistributiveeffects.I ignore the effects of market imperfections (cf. Hintermann2011 and Meunier 2011), and assume that there is acompetitive market for emission permits.Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryThe economyThe economy consists of a large number (“continuum") ofcountries j ∈ [0,1] that produce the same good from asingle source of emissions (called hereafter energy, forconvenience) and fixed local resources (e.g. land andlabor).The extraction costs of energy are ignored, for simplicity.The international common agency grants emission permits.Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryEnergy and pollutionThe use of energy causes both global (called globalwarming) and localized externality (called smog).Global externality is represented by a single index M,which is called global pollution, for convenience.I define the energy inputs mj and emission permits Mj forcountries j ∈ [0,1] in terms of global pollution. Then, totalemissions∫ 10 mkdk are equal total emission permits:∫ 10mkdk = M =∫ 10Mjdj .Because the use of energy mj causes locally smog nj , theformer can be used as a proxy of the latter as follows:nj = mj .Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryProductionThe representative firm in country j produces the quantityfj of the final good from energy mj and fixed factors:fj(mj), f ′j > 0, f′′j < 0, fj(0) = 0.At the same time, in country j , smog nj causes abatementcosts gj according to an increasing and convex functiongj(nj), g′j > 0, g′′j > 0, gj(0) = 0.Total consumption c is equal to aggregate output∑j fjminus abatement costs∑j gj throughout all countries:c .=∫ 10fj(mj)dj −∫ 10gj(nj)dj =∫ 10[fj(mj)− gj(nj)]dj .Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryHouseholdsTo avoid distributional considerations, I consider therepresentative household of the whole economy.Consumption c increases and global pollution Mdecreases household utility u according to the functionu(c,M), uc.=∂u∂c> 0, uM.=∂u∂M< 0, u strictly concave.Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryWelfare maximizationNontraded emission permits determine energy inputsmj = Mj .The international common agency maximizes householdwelfare u(c,M) by emission permits mj = Mj subject toglobal emissions M =∫ 10 Mjdjsmog nj = mj for j ∈ [0,1]total consumption c =∫ 10 [fj (mj )− gj (nj )]dj .Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryPareto optimumThe welfare maximization leads to the the Pareto optimumMp, cp and mpj for j ∈ [0,1]:Mp =∫ 10mpj dj , cp =∫ 10[fj(mpj )− gj(mpj )]dj ,f ′j (mpj ) = g′j (mpj )−um(cp,Mp)uc(cp,Mp)for j ∈ [0,1],wheref ′j the marginal product of energyg′ the marginal costs of smog−um/uc the marginal disutility of global warming, interms of consumption.Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryEmission permit tradingWith emission permit trading, the representative firm incountry j ∈ [0,1] can sell its excess supply of permits,Mj −mj , or buy its excess demand for permits, mj −Mj , inthe competitive market at the price p.The profit of that firm isΠj.= fj(mj) + (Mj −mj)p,wherefj(mj) income from productionMj −mj the net supply of emission permitsp the international price for emission permits(Mj −mj)p net revenue from emission permits.Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryTotal consumptionNoting abatement costs g(nj), the revenue of country j ispij = Πj − g(nj) = fj(mj)− g(nj) + (Mj −mj)p.Given this, total consumption is equal to total revenue:c =∫ 10[fk (mk )− gk (nk )]dk =∫ 10pikdk .Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryThe extensive form gameThere is an extensive form game with the following stages:(i) The common agency sets emission permits Mj for countriesj ∈ [0,1] to maximize the household welfare u(c,M) byemission permits mj = Mj subject toglobal emissions M =∫ 10 Mjdjsmog nj = mj for j ∈ [0, 1]total consumption c =∫ 10 pik (Mk ,M)dk .(ii) The international price p for emission permits adjusts toclear the market for these.(iii) Firm j uses energy mj to maximize its profitΠj.= fj (mj ) + (Mj −mj )p.This game is solved in reverse order.Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryStage (iii): the behavior of firmsThe firm in country j maximizes its profitΠj.= fj(mj) + (Mj −mj)pby energy input mj , given the emission permits Mj and theprice p for those.This yields the equilibrium profit and the inverse demandfunction for energy as follows:Πj = maxmj[fj(mj) + (Mj −mj)p],p = f ′j (mj) withdpdmj.= f ′′j < 0.Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryStage (ii): the market for emission permitsDifferentiating the inverse demand function, and noting thesmog nj = mj , one obtains pollution nj and energy input mjas a function of the price:nj = mj = Nj(p) with N ′j.= 1/f ′′j < 0.Total emissions then becomeM =∫ 10nkdk =∫ 10Nk (p)dk .Differentiating this equation totally yields the price as afunction of total emissions:p(M), p′ =(∫ 10N ′kdk)−1< 0.Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryStage (ii): the market for emission permits; 1Plugging this price function into the demands for energynj = mj = Nj(p) yields smog nj as a function of totalemissions M in all countries j ∈ [0,1]:nj(M).= Nj(p(M)) withn′j.= N ′j p′ =(∫ 10N ′kdk)−1N ′j ∈ [0,1].Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryStage (ii): the market for emission permits; 2Given the price and energy-demand functions, the revenueof country j is a function of total emissions M and theemission permits for that country, Mj :pij(Mj ,M).= maxmj[fj(mj)− gj(nj(M))+ (Mj −mj)p(M)]with∂pij∂Mj= p and∂pij∂M= −g′j n′j + (Mj −mj)p′.Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryStage (i): the behavior of the common agencyThe common agency maximizes household utility u(c,M)subject toglobal emissions M =∫ 10 Mjdjsmog nj (M) for j ∈ [0,1]total consumption c =∫ 10 pik (Mk ,M)dk .This leads to the first-order conditions:0 =1uc(c,M)du(c,M)dMj=∂c∂Mj+umuc=1︷︸︸︷∂M∂Mj= −∫ 10g′kn′kdk + f′j +umucfor j ∈ [0,1].This implies that terms f ′j (mj) are equal for all j ∈ [0,1],which violates the first of the Pareto optimality conditions.Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryThe first resultPropositionEmission permit trading decreases welfare by equalizing themarginal product of energy, f ′j (mj), throughout all countriesj ∈ [0,1].Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryThe case of identical countriesIf the countries are fully identical,mj = nj = m, fj(m) = f (m) and gj(n) = g(n) for j ∈ [0,1].then it follows that Nj(p) = N(p) and n′j = 1 for j ∈ [0,1].This leads to the Pareto optimum:0 = −∫ 10g′(m)n′kdk + f′ +umuc= −g′(m) + f ′(m) + umuc.Thus, the inefficiency of emission permit trading is due tothe heterogeneity of the countries.Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryThe effect of emission permit tradingNext, to consider the effect of emission permit trading ontotal emissions, I introduce a parameter β so that β = 0holds true without mj = Mj and β = 1 with emission permittrading mj 6= Mj .By this variable, I can combine the equilibrium conditionswithout and with trading as follows:0 = −β∫ 10g′kn′kdk + f′j − (1− β)g′j +umucfor j ∈ [0,1].The effect of β on emission permits Mj is first derived onthe assumption that β is continuous in the limit [0,1]. Then,by the mean value theorem, the result is extended for thediscrete choice β ∈ {0,1}.Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetrySome definitionsThe damage of smog in country j – i.e. the decrease ofincome in that country due to smog nj – is g′j .The localized technology in country j is called relativelyclean, if the damage in country j , g′j , is smaller than the theweighed average of the damages of all countries,g′j <∫ 10g′kn′kdk ,and relatively dirty, if the damage g′j is greater than thataverage,g′j >∫ 10g′kn′kdk .Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryThe second resultAssuming the equilibrium unique and differentiating thecombined equilibrium condition totally yields the resultdMjdβ< 0 ⇔ g′j <∫ 10g′kn′kdk .This can be rephrased as follows:PropositionWith the introduction of emission permit trading, the commonagency provides less permits to countries with relatively cleanlocalized technology (i.e. g′j <∫ 10 g′kn′kdk holds), and morepermits to countries with relatively dirty localized technology(i.e. g′j >∫ 10 g′kn′kdk holds).Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality ProblemsLiteratureThe modelNontraded permitsTraded permitsThe role of asymmetryInterpretationThe use of non-traded emission permits lead to Paretooptimum: the marginal product of energy is equal to themarginal cost of smog plus the disutility of global warmingin terms of consumption.Emission permit trading restricts the common agency’spolicy set by equalizing the marginal product of energy forall countries.Welfare decreases in that case, because the commonagency provides less permits to countries with relativelyclean and more permits to those with relatively dirtylocalized technology.Tapio Palokangas, Univ. of Helsinki Emission Permit Management with Simultaneous Localized and Global Externality Problems

Emission Permit Management with Simultaneous Localized and Global Externality Problems

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