Prices versus quantities in the presence of a second, unpriced, externality

• Author: Guy Meunier
• Date: 01 April 2018
• DOI: http://doi.org/10.1111/jpet.12250
• Published date: 01 April 2018

Received: 1 June 2016 Accepted: 29 March 2017

DOI: 10.1111/jpet.12250

ARTICLE

Prices versus quantities in the presence

of a second, unpriced, externality

Guy Meunier

INRAand École Polytechnique

GuyMeunier, INRA–UR1303 ALISS &

EcolePolytechnique, Ivry-sur-seine, France

(guy.meunier@ivry.inra.fr).

Financialsupport from the Ecole Polytechnique

chairEDF-Sustainable Development and the

BusinessSustainability Initiative at Europlace

Instituteof Finance is gratefully acknowledged.

This paper analyzes whether the presence of a second unregulated

externality influences the choice between a price and a quantity

instrument to address an externality.The author studies a situation

in which two goods jointly generate an externality but only one of

them is regulated. The two instruments differ because of the pres-

ence of uncertainty regarding the private value of the two goods. To

ignore the unregulated good and apply Weitzman’s classical result

on the comparison of the slopes of marginal benefit and cost could

be misleading because of the randomness of the unregulated good’s

quantity. Beside the relative slope of the marginal damage, the sub-

stitutability and the distribution of shocks play a role in the com-

parison. If there is a “cocktail effect” and the regulated and unreg-

ulated goods’ quantities are negatively correlated, which occurs if

they are substitutes, this reinforces the appeal of a price instrument.

Furthermore, if the two goods are weak substitutes with correlated

demands, the variance of the quantity of the unregulated good is

larger under a quota than a tax, which further reinforces the appeal

of the tax instrument.

1INTRODUCTION

When correcting for an externality (e.g., climate change),policymakers have to choose both the instrument to be used

and its level. There are two broad categories of instruments: price-based (e.g., taxes) and quantity-based (e.g., quo-

tas, which are possibly tradable). Furthermore, the regulatory scope is usually incomplete, namely,some unregulated

goods (e.g., foreign emissions) also generate externalitiesand interact with the regulated good. A question is whether

the presence of these unregulated externality-generating goods influences the choice between a price and a quantity

instrument.

Without uncertainty, it is equivalent to choose the optimal price or optimal quantity of the regulated good. With

uncertainty,or asymmetric information, Weitzman (1974) shows that the two instruments differ and establishes a sim-

ple rule to choose between them. The difference relies on the use of information; with a tax instrument, the quantity

produced depends on the information available to economic agents, which is beneficial but implies that the total quan-

tity produced is random.A quota is less flexible, in the sense that some information is left unexploited, but it guarantees

a certain external cost. In a quadratic specification, Weitzman (1974) shows that if the slope of the marginal external

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2017 Wiley Periodicals,Inc. wileyonlinelibrary.com/journal/jpet Journal of Public Economic Theory.2018;20:218–238.

GUYMEUNIER 219

cost is larger than that of the marginal economic benefit, the quantity instrument should be preferred. Uncertainty

over the external cost does not influence the comparison, and uncertainty overthe private benefit does not influence

the sign of the comparison but only its magnitude.1

In the present work, the analysis of Weitzman (1974) is extended to a model with two goods; these goods jointly

create a private economic benefit and an external cost. The goods are either substitutes or complements in the eco-

nomic benefit function and can interact positivelyor negatively in the external damage function; thus, there might be a

“cocktaileffect.” The framework is quadratic, and there is an additive uncertainty regarding the marginal private value

created by each good.

One of the goods is regulated by either a tax or a quota, while the other good is not regulated. The presence of an

uncorrected externality does not by itself introduce a distinction between the two instruments. Without uncertainty,

both instruments are still equivalent and the optimal tax should be modified to encompass the influence of the regu-

lated good on the unregulated good.2

The introduction of a second externality modifies the comparison of instruments in severalrespects. The main find-

ing is that imposing a quota on the regulated good does not ensure the stability of the external cost because of the

uncertainty overthe quantity of the unregulated good. In addition to the expected benefit and external cost associated

with the regulated good, two additional expected external costs are addressed in the comparison. These two costs

relate to the variance of the quantity of the unregulated good and the correlation between the two goods’ quantities

with a tax. A positive correlation is costly if there is a cocktail effect. And the variance of the unregulated good is higher

with a quota than a tax, if goods are weak substitutes with correlated demands. Because of these two additional costs,

the tax instrument is preferred for severalinteresting parameter specifications.

If the two goods are perfect substitutes in the external costs (e.g., home country and foreign CO2emissions), at

an intermediate degree of economic substitution and given substantial uncertainty surrounding the demand for the

unregulated good, the tax instrument is preferred regardless of the slope of the marginal external cost because the

changes in the quantity of the unregulated good are compensated by the changes in the quantity of the regulated good

using a tax.

This work is related to severalstrands of the literature—most notably, the comparison of instruments under uncer-

tainty and multipollutant regulation.

The analysis of Weitzman(1974) has been extended in various directions.3Notably, Stavins (1996) introduces a cor-

relation between the randommarginal external cost and the private benefit in a single-good framework. The ranking of

instruments is then modified and a positive (respectively,negative) correlation is favorable (respectively, detrimental)

to the quantity instrument. Indeed, with a positive correlation, the external cost is likelyto be high precisely when the

quantity produced under a tax is large, which increases the expected externalcost due to the randomness of quantity

in the presence of a tax. This phenomenon arises endogenously in the present work, from the interaction of the regu-

lated good with the unregulated good in both the private benefit and the external cost functions. Interestingly,Stavins

(1996) cites the existence of a complementary pollutant as a possible explanation for a positive correlation, but his

analysis does not incorporate the full external cost associated with this second pollutant that is done in the present

work.

Several authors compare instruments in a second-best setting in which, in addition to uncertainty,there is another

uncorrected market failure. The second marketfailure in itself does not justify discriminating among instruments, but

1Notethat in Weitzman (1974) and most subsequent articles, the analysis is framed in terms of abatement cost and external benefits (often environmental). In

thispaper, we consider private benefits and external costs. The two frameworks are equivalent; abatement costs correspond to the foregone private benefit,

andthe external benefit corresponds to the avoided external costs.

2Asa general property of second-best analysis, first-best optimality conditions (e.g., a Pigouvian tax) are no longer necessary for optimality (Lipsey & Lancaste r,

1956).In our case, the second-best tax on the regulated good is equal to the marginal external cost (Pigouvian component) plus a corrective term equal to the

marginalexternal costs of the unregulated good times the sensitivity of this good’s quantity to the regulated good’s quantity.

3Some notable contributions that are not closely related to the present work include Roberts and Spence (1976) and Weitzman (1978), who consider the

use of hybrid instruments: a system of cap-and-trade permits with a price floor and a price ceiling. Hoel and Karp (2002) and Newell and Pizer (2003) com-

pare instruments in the case of a stock pollutant in a dynamic framework.Krysiak (2008) and Weber and Neuhoff (2010) introduce innovation in abatement

technologies.