Mixed Duopoly and Environment

• Author: BIBHAS SAHA,RUPAYAN PAL
• Published date: 01 February 2014
• Date: 01 February 2014
• DOI: http://doi.org/10.1111/jpet.12056

MIXED DUOPOLY AND ENVIRONMENT

RUPAYAN PAL

Indira Gandhi Institute of Development Research (IGIDR)

BIBHAS SAHA

University of East Anglia

Abstract

We show under general demand and cost conditions that

in a mixed duopoly with pollution the government can im-

plement the socially optimal outputs and abatements by a

tax-subsidy scheme and keeping the public firm fully public.

The scheme requires taxing outputs and subsidizing abate-

ments at different rates, unlike a pollution tax. Our result

improves on the shortcoming of a pollution tax to imple-

ment the social optimum. We also show that when the pri-

vate firm is partly foreign-owned, the government will adopt

some privatization and will not implement the social opti-

mum, though the social optimum is implementable.

1. Introduction

Generally it is argued that a publicly owned firm tends to pollute more than a

privately owned firm because it produces more than a private firm. So an im-

portant question is whether the firm ownership matters for the performance

of environmental policies. A number of papers have studied the effects of

a pollution tax in the presence of a public firm (Barcena-Ruiz and Garzon

2006; Beladi and Chao 2006;Cato2008; Naito and Ogawa 2009;Wangand

Wang 2009; Wang, Wang, and Zhao 2009;Saha2012). In a mixed duopoly,

which involves one public firm and one private firm, a pollution tax curbs

the private firm’s output and pollution, but encourages the public firm to

produce more (via strategic effects) and in turn pollute more. Therefore,

Rupayan Pal, Indira Gandhi Institute of Development Research (IGIDR), Film City Road,

Gen. A. K. Vaidya Marg, Goregaon (East), Mumbai 400065, India (rupayan@igidr.ac.in).

Bibhas Saha, School of Economics, University of East Anglia, Norwich NR4 7TJ, United

Kingdom (b.saha@uea.ac.uk).

We gratefully acknowledge helpful comments from two anonymousreferees. Remaining

errors, if any, are our responsibility.

Received January 27, 2011; Accepted February 16, 2012.

C2013 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 16 (1), 2014, pp. 96–118.

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Mixed Duopoly and Environment 97

when the government can choose the degree of public ownership along with

the pollution tax, it would partially privatize the public firm to restrain its

incentive to pollute. Moreover, it is known that the optimal pollution tax will

not bring the pollution down to the socially optimal level if pollution abate-

ment is technologically feasible (Barcena-Ruiz and Garzon 2006;Wangand

Wang 2009).

By and large, this body of work has strengthened a negative perception

of public ownership that has been a feature of this literature since deFraja

and Delbono (1989) and Matsumura (1998). One might wonder why public

ownership can be an impediment to social optimality, especially in a model

of externality. Perhaps one should examine what policies can implement the

social optimum, rather than examining what a given policy can do. We try to

take this approach and also overcome some of the limitations of the existing

literature.

We allow the demand and cost functions to be fairly general and permit

asymmetry between firms, unlike most of the previous work. At the same time

we make the policy space slightly larger; to be more specific, we allow the tax

on the output and the subsidy on the abatement to be two independent

instruments. This is a more general approach than relying on a pollution

tax, which penalizes outputs and rewards abatements at the same rate.

Abatement in this literature is assumed to be a clean-up operation per-

formed alongside production. An example would be a paper mill that re-

leases effluents which need to be treated to minimize adverse environmental

impacts (such as eutrophication of water). See Collins and Harris (2002)for

abatement in the UK metal manufacturing industry and Schneider, Lazarus,

and Kollmuss (2010) for nitrous oxide abatements in adipic acid plants glob-

ally. However, in certain industries, such as oil extraction or chemical pesti-

cides, accidents can cause large damages.1Clean-up of such accidental pol-

lution is not the subject matter of our study, though we comment on it later;

see Shavell (2010) and van ’t Veld and Hutchinson (2009) for legal reme-

dies and policy options for such problems. We should stress that the envi-

ronmental economics literature have studied a wider set of policies ranging

from taxes and pollution standards to tradeable emission permits in various

market settings, but not in the context of mixed oligopoly; see Lehmann

(2012) for a survey of policies and also Silva and Zhu (2009), Bhattacharya

and Pal (2010), and Colla, Germain, and Van-Steenberghe (2012).

The social optimum in our setup must be realized in two dimensions—

output and abatement. Each firm’s output should equate the price with

the social marginal cost of production and its abatement should equate the

marginal abatement cost with the marginal damage to the environment. Our

key result is that the social optimum is achievable by a combination of full

1Examples are the 1984 Union Carbide explosion in Bhopal, India resulting in the loss of

25,000 lives and the 2010 British Petroleum (BP) disaster at its Deep-water Horizon oil rig,

theGulfofMexico.