Emission Permit Trading with Global Externality Problems · trading when the governments set their...

LiteratureThe model

Notraded permitsTraded permits

Conclusions

Emission Permit Trading withGlobal Externality Problems

Tapio Palokangas

University of Helsinki, HECER and IIASA

Paper to be presented in IIASA , July 26, 2017, Austria

Tapio Palokangas, Univ. of Helsinki Emission Permit Trading with Global Externality Problems

LiteratureThe model


Conclusions

Contents

1 Literature

2 The model

3 Notraded permits

4 Traded permits

5 Conclusions


LiteratureThe model


Conclusions

Abstract

A set of heterogeneous countries where firms producegoods from fixed resources and emitting inputs.Emissions cause global pollution (e.g. GHGs).An international benevolent regulator that determinesfirm-specific emission permits.Welfare decreases, if the firms are allowed to trade inemission permits.If the sellers of permits are on the average richer than thebuyers, then the regulator grants too much, and if poorer,too little permits from the welfare point of view.


LiteratureThe model


Conclusions

Motivation

The research question:Does emission permit trading cause inefficiency,when production causes simultaneous localizedand global externality problems (e.g. smog andglobal warming)?

I examine this in a simple framework where a benevolentinternational regulator determines emission permits.In Palokangas (2015), I derive the same results in anextended case where the regulator is self-interested,elected by the countries, and subject to lobbying by thecountries (cf. Dixit et al. 1997).


LiteratureThe model


Conclusions

Literature 1

Caplan 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, I assume a benevolentinternational regulator that issues emission permits.


LiteratureThe model


Conclusions

Literature 2

Montgomery (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.


LiteratureThe model


Conclusions

Production

A “continuum” of heterogeneous countries i ∈ [0,1] thatproduce the same numeraire good.Because all markets are competitive, it can be assumedthat the representative firm in country i (hereafter calledfirm i) produces the quantity fi of the good from emissionsmi and fixed local resources (e.g. land and labor):

fi(mi), f ′i > 0, f′′i < 0, fi(0) = 0.

A regulator grants emission permits Mi for firms i ∈ [0,1].Total emissions M .=

∫ 10 mkdk equal total permits

∫ 10 Midi :∫ 1

0mkdk =

∫ 10

Midi.

= M.


LiteratureThe model


Conclusions

Households

The representative household (hereafter household i)earns and consumes all income in country i ∈ [0,1].At each time t , it derives utility ui from consumption ci andglobal pollution n according to the strictly concave function

ui(ci ,M), uic.

=∂ui

∂ci> 0, uiM

.=∂ui

∂M< 0.


LiteratureThe model


Conclusions

The regulator

I assume that the regulator is benevolent.It maximizes a function of the utilities of countries i ∈ [0,1],

U .=∫ 1

0wiui(ci ,M)di ,

where wi is a positive constant that characterizes the sizeor influence of country i ∈ [0,1].This Paretian social welfare function is general enoughfor the comparison of different policies in the case ofheterogeneous countries.


LiteratureThe model


Conclusions

Setup

Nontraded emission permits Mi determine emissionsmi = Mi in all countries i ∈ [0,1].In that case, each country consumes what it produces,

ci = fi(mi) for i ∈ [0,1].Plugging this into the social welfare function yields

UN .=∫ 1

0wiui(fi(mi),M)di .

The regulator maximizes this by the emission permitsmi = Mi , ∈ [0,1]}, subject to the accumulation of GHGs.The maximization yields the Pareto optimum conditions

∂UN

∂Mi=∂UN

∂mi= wiuic f

′i +

∫ 10

wkukMdk = 0. i ∈ [0,1].Tapio Palokangas, Univ. of Helsinki Emission Permit Trading with Global Externality Problems

LiteratureThe model


Conclusions

Extensive game

With traded permits, there is an extensive form game with thefollowing stages:

(i) The regulator sets the emission permits{Mi}

.= {Mi | i ∈ [0,1]}.

(ii) The international market for emission permits clears.(iii) The local firms produce from emissions and fixed local

resources.This game is solved in reverse order.


LiteratureThe model


Conclusions

Firms

With emission permit trading, the representative firm incountry i ∈ [0,1] purchases emission permits mi at theprice p in the competitive market to produce fi(mi).The profit of that firm is

Πi.

= fi(mi)− pmi .

The firm maximizes this profit by emissions mi , given theprice p for emissions permits. This leads to the equilibriumprofit and the profit-maximization condition for the firm:

Πi = maxmi[fi(mi)− pmi ] and p = f ′i (mi) with

dpdmi

.= f ′′i < 0.


LiteratureThe model


Conclusions

The market for emission permits 1

Inverting the profit-maximization condition, I obtain countryi ’s emissions as a function of the emission permit price p:

mi = Ni(p) with N ′i.

= 1/f ′′i < 0.

Inserting the demand functions into the equilibriumcondition yields

∫ 10 Midi =

∫ 10 mkdk =

∫ 10 Nk (p)dk .

Differentiating this equation totally, one obtains the price foremission permits as a function of total emissions M:

p(M) with M .=∫ 1

0Midi and p′ =

(∫ 10

N ′kdk)−1

< 0.


LiteratureThe model


Conclusions

The market for emission permits 2

Plugging this into the first equation yields emissions mi ofcountry i ∈ [0,1] as a function of total emission permits M:

mi(M).

= Ni(p(M)) with m′i.

= N ′i p′ =

N ′i∫ 10 N

′kdk

∈ [0,1].

Household i ∈ [0,1] consumes the income of country i :profits Πi and the revenue for emission permits, pMi .Consumption in country i becomes a function of M and Mi :

ci = Πi + pMi = maxmi[fi(mi)− pmi ] + pMi

= maxmi

[fi(mi)− p(M)mi

]+ p(M)Mi

.= Ci(Mi ,M)

with∂Ci∂Mi

= p = f ′i and∂Ci∂M

= (Mi −mi)p′.


LiteratureThe model


Conclusions

The regulator 1

The regulator maximizes social welfare

UT =∫ 1

0wiui

(Ci(Mi ,M),M

)di .

This yields the first-order conditions

∂UT

∂Mi= wiuic

∂Ci∂Mi︸︷︷︸=f ′i

+

(∫ 10

wkukc∂Ck∂M︸︷︷︸

=(Mk−mk )p′

dk +∫ 1

0wkukMdk

)∂M∂Mi︸︷︷︸=1

= wiuic f′i +

∫ 10

wkukMdk + p′∫ 1

0(Mk −mk )wkukc dk = 0, i ∈ [0,1].


LiteratureThe model


Conclusions

The regulator 2

If the countries i ∈ [0,1] are heterogeneous, then thisviolates the Pareto optimality conditions by the last term.

PropositionIf the countries are heterogeneous, then emission permittrading decreases welfare.


LiteratureThe model


Conclusions

The role of asymmetry 1

In order to consider the effect of emission permit trading ontotal emissions, I introduce a parameter β so that

β = 0 holds true without trading (i.e. with mi = Mi )β = 1 with trading mi 6= Mi .

This combines the FOCs without and with trading as

∂H∂Mi

= (1− β) ∂UN

∂Mi

∣∣∣∣mi=Mi

+β∂UT

∂Mi

∣∣∣∣mi 6=Mi

= 0 for i ∈ [0,1].

The effect of β on emission permits Mi is first derived forcontinuous β ∈ [0,1], and the result is then extended forthe discrete choice β ∈ {0,1} by the mean value theorem.


LiteratureThe model


Conclusions


With continuous β ∈ [0,1], I obtain

dMidβ

= − ∂2H

∂Mi∂β

/∂2H∂M2i

> 0 ⇔∫Mk>mk

(Mk −mk )wkukc dk <∫

mk>Mk(mk −Mk )wkukc dk

for i ∈ [0,1], where wkukc is the marginal utility of income ukc incountry k , weighed by the size wk of that country,∫

Mk>mk(Mk −mk )wkukc dk the value of the net supplies

Mk −mk of emission permits throughout thecountries k with Mk > mk , and∫

mk>Mk(mk −Mk )wkukc dk the value of the net demands

mk −Mk for permits throughout k with mk > Mk .Tapio Palokangas, Univ. of Helsinki Emission Permit Trading with Global Externality Problems

LiteratureThe model


Conclusions


Then, by the mean value theorem, there is ξ ∈ (0,1) s.t.

Mi∣∣β=1−Mi

∣∣β=0=

dMidβ

∣∣∣∣β=ξ

β > 0 ⇔∫Mk>mk

(Mk −mk )wkukc dk

<

∫mk>Mk

(mk −Mk )wkukc dk for i ∈ [0,1].

This result can be rephrased as follows:


LiteratureThe model


Conclusions


Proposition(a) If the suppliers of emission permits (i.e. countries k with

Mk > mk ) are on the average “richer” (i.e. with a lowermarginal utility of income wkukc ) than the demanders ofemission permits (i.e. countries k with mk > Mk ), then theregulator provides more emission permits Mi to all countriesi ∈ [0,1], Mi

∣∣β=1> Mi

∣∣β=0, aggravating global pollution n.

(b) If the suppliers of emission permits are on the average“poorer” than the demanders of those , then the regulatorprovides less emission permits Mi to all countries i ∈ [0,1],Mi∣∣β=1< Mi

∣∣β=0, alleviating global pollution n.


LiteratureThe model


Conclusions

Conclusions 1

Environmental policy is at the international level (e.g. in theEU) commonly restricted to command-and-control ratherthan incentive-based instruments.Therefore, I consider the design of international emissionpolicy without fiscal instruments when the use of anemitting input causes global externality problems.The use of non-traded emission permits leads to Paretooptimum: the marginal product of emissions is equal to thedisutility of global warming in terms of consumption.


LiteratureThe model


Conclusions

Conclusions 2

Emission permit trading restricts the regulator’s policy setby equalizing the marginal product of emissions for allcountries. Then,

too much emission permits are granted to all countries,aggravating global pollution, if the suppliers of emissionpermits are on the average richer, having a lower marginalutility of income, than the demanders of those, andtoo little emission permits are granted, alleviating globalpollution, if the demanders of emission permits are on theaverage richer than the suppliers of those.

If it is impossible to use incentive-based instruments, thenattempts to improve the working of emission caps byemission permit trade may be counterproductive.


LiteratureThe modelNotraded permitsTraded permitsConclusions

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