Taxation under oligopoly in a general equilibrium setting

DOIhttp://doi.org/10.1111/jpet.12373
Date01 August 2019
Published date01 August 2019
Received: 14 March 2018
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Revised: 4 March 2019
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Accepted: 16 April 2019
DOI: 10.1111/jpet.12373
ORIGINAL ARTICLE
Taxation under oligopoly in a general
equilibrium setting
David R. Collie
Cardiff Business School, Cardiff
University, Cardiff, U.K.
Correspondence
David Collie, Cardiff Business School,
Cardiff University, Aberconway Building,
Colum Drive, Cardiff CF10 3EU, U.K.
Email: Collie@cardiff.ac.uk
Taxation under oligopoly is analyzed in a general
equilibrium setting where the firms are large relative to
the size of the economy and maximize the utility of their
shareholders. Assuming that preferences are either
identical and homothetic or identical and quasilinear,
then the oligopoly model is an aggregative game, which
greatly simplifies the comparative statics for the effects of
taxation. This novel analysis of taxation leads to a
number of counterintuitive results that challenge con-
ventional wisdom in microeconomics. A lumpsum tax
may increase the price of the oligopolistic good and
decrease welfare whereas a profits tax may decrease the
price of the oligopolistic good and increase welfare. A
profits tax is shown to be superior to a lumpsum tax.
Furthermore, in line with conventional wisdom, total tax
revenue is always higher with an ad valorem tax than
with a specific tax that leads to the same price for the
oligopolistic good.
KEYWORDS
ad valorem taxes, aggregative games, general equilibrium, lumpsum
taxes, oligopoly, profits taxes, specific taxes
JEL CLASSIFICATION
C72, D21, D43, D51, H22, H25, L13, L21
1
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INTRODUCTION
The analysis of taxationunder oligopoly is usually undertaken in a partialequilibrium setting that
assumes the oligopolistic firms are small relative to the size of the economy and ignores the
income effect on demand. However, there is evidence that industries are becoming more
J Public Econ Theory. 2019;21:738753.wileyonlinelibrary.com/journal/jpet738
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© 2019 Wiley Periodicals, Inc.
concentrated and that firms are becoming more dominant with the rise of superstar firms.
1
In a
general equilibrium setting where firms are large relative to the size of the economy, a number of
additional effects of the decisions of oligopolistic firms have to be considered. First, the decisions
of an oligopolistic firm will affect the income of consumers through their effect on
the profits of the firm and through their effect on the profits of its competitors, which will
affect the demand facing the firm. Secondly, the decisions of an oligopolistic firm will affect the
prices paid for the firms output by its shareholders, which will affect the utility of the
shareholders. This article will show that if preferences are assumed to be either identical and
homothetic or identical and quasilinear then oligopoly in a general equilibrium setting can be
analyzed as an aggregative game allowing comparative statics for the effects of taxation to be
derived quite easily.
The modeling of oligopoly in a general equilibrium setting when oligopolistic firms are large
relative to the size of the economy has proved to be problematic for a number of reasons as
discussed by Bonanno (1990).
2
First, since the demand of consumers depends upon their income,
which includes the profits of the oligopolistic firms paid as dividends, there will be a feedback
effect into the objective of the oligopolistic firms that will be a function of their own profits and
the profits of their competitors, which complicates the optimization problem facing the firms. To
avoid this complication, the optimization problem has been solved by assuming that there is no
income effect asin Hart (1982) or that profits are taxedat 100% as in Guesnerie and Laffont(1978)
or that firms take the profits of competitors as given as in Myles (1989). Secondly, if the
oligopolistic firms are assumed to maximize profits then the choice of the numeraire good can
have a real effect on the equilibrium outcome as shown by Gabszewicz and Vial (1972).Finally, it
has been argued that profit maximization may not be a valid objective for the firms. As explained
by Dierker and Grodal (1998, 1999), profit maximizationis only a valid assumption if the firms are
pricetakers or if the shareholders of the firm do not consume the firms product. A view
supported by Kreps (2013, pp. 200201):
it is worth noting that the assertion that owners prefer profit maximization is very
bound up in the assumption that the firm has no impact on prices. When firms affect
prices, and when owners of the firm consume (or are endowed with) the goods whose
prices the firm affects, it is no longer clear that the owners either should or do prefer
profitmaximizing choices by firms.
Similarly, Hart (1985, pp. 106107) argues for owner utility maximization as the objective:
The reason is that the owners of a firm are interested not in monetary profits per se,
but rather in what this profit can buy. This argument suggests that we should
substitute owner utility maximization for profit maximization as the firms goal.
When shareholders consume the product of the oligopolistic firm, Dierker and Grodal (1998,
1999) also argue that the objective of the firm should be the maximization of the real wealth of
1
See Autor, Dorn, Katz, Patterson, and Van Reenen (2017) and the report by Tim Harford, Undercover Economist (Harford, 2017). Also, according to The Nokia
Effect, The Economist, August 25, 2012, some firms have revenues that are substantial in comparison with the GDP of their country of domicile.
2
An alternative approach to the modeling of oligopoly in a general equilibrium setting has been to assume that firms are large in their industry, but that the
industries are infinitesimally small in the economy as in Neary (2003). Then, the output decisions of an oligopolistic firm have an infinitesimally small effect on
prices facing shareholders.
COLLIE
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