OPTIMUM‐WELFARE AND MAXIMUM‐REVENUE TARIFFS UNDER BERTRAND DUOPOLY
| Published date | 01 July 2006 |
| Author | Roger Clarke,David R. Collie |
| Date | 01 July 2006 |
| DOI | http://doi.org/10.1111/j.1467-9485.2006.00386.x |
OPTIMUM-WELFARE AND
MAXIMUM-REVENUE TARIFFS
UNDER BERTRAND DUOPOLY
Roger Clarke and David R. Collie
n
Abstract
This article derives the maximum-revenue tariff and the optimum-welfare tariff
under Bertrand duopoly with differentiated products. It is shown that both tariffs
are lower under Bertrand duopoly than under Cournot duopoly. Also, the optimum-
welfare tariff may exceed the maximum-revenue tariff under both Bertrand
duopoly and Cournot duopoly. This result is more likely the lower the costs of the
home firm relative to the costs of the foreign firm, and the greater the degree of
product substitutability. Also, it is shown that the optimum-welfare tariff is less
likely to exceed the maximum-revenue tariff under Bertrand duopoly than under
Cournot duopoly.
I Intro ductio n
In conventional trade theory, where a large country can use a tariff to improve
its terms of trade, Johnson (1951–1952) derived the well-known proposition that
the maximum-revenue tariff exceeds the optimum-welfare tariff. When the tariff
is set to maximise welfare, the marginal gain in tariff revenue equals the
marginal loss of consumer surplus from the tariff. Therefore, tariff revenue must
be increasing when welfare is maximised so the optimum-welfare tariff must be
lower than the maximum-revenue tariff. In the new trade theory, with imperfect
competition, Brander and Spencer (1984) have shown that a tariff has a profit-
shifting effect in addition to its effect on consumer surplus and tariff revenue,
and Collie (1991) has shown that the optimum-welfare tariff may exceed the
maximum-revenue tariff in a Cournot duopoly. With homogeneous products
and linear demand, he shows that this will be the case unless the costs of the
home firm relative to the costs of the foreign firm are sufficiently high. A similar
result has been obtained by Larue and Gervais (2002) in a model where the
domestic industry is a Cournot oligopoly competing with price-taking foreign
firms.
The comparison of the optimum-welfare tariff and the maximum-revenue
tariff may be relevant for a couple of reasons. First, tariff revenue may be an
n
Cardiff University
Scottish Journal of Political Economy, Vol. 53, No. 3, July 2006
rScottish Economic Society 2006, Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK
and 350 Main Street, Malden, MA 02148, USA
398
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