The results can be applied to analyses of international oligopoly.
There is an extensive literature on the equivalence or non-equivalence
of tariffs and import volume quotas. For example, Bhagwati (1965,
1968) and Shibata (1968), Itoh and Ono (1982, 1984) are early seminal
works on this topic. Hwang and Mai (1988) and Fung (1989) show the
equivalence in a Cournot model with one domestic firm and one foreign
firm.8 We show the equivalence in a Cournot model with an arbitrary
number of domestic and foreign firms. Ono (1990) discusses a model
with a foreign firm and domestic firms and shows that there is a volume
quota level such that a reduction in the quota level always increases
national welfare. We show the result continues to hold even if there
are several foreign firms and domestic firms. Obviously, in the real
world, most countries import products from a large number of countries
and have several national firms. Moreover, we can find that production
efficiency often differs greatly among different countries. Contrary to
the models of previous papers, we can consider such differences in
our model, because there can be arbitrary many foreign firms whose
cost functions are different among them in our model. In addition, the
level of the quota of a foreign firm can be different from that of another
foreign firm. This generalization is also essential because there are
several important exceptions to the most favored nation principle of
GATT/WTO.9 Recently, many regional trading agreements, such as EU
and NAFTA, have been formed. That is, the countries signed some
regional trading agreements reduce or eliminate tariffs or non-tariff
barriers of the imports only from the members of the agreements.
Further, countries can provide developing countries special access to
their markets. In the models of previous studies, they cannot examine
such general policies. On the contrary, in our model, we can discuss
the effect of various policies. For example, we can examine the effect
of the establishment of a new FTA between two countries that eliminates
quotas between each other on market outcomes. In addition, we
can also consider the effect of allowing a developing country special
access. Finally, in our model, firms do not need to be bound by the
volume quotas assigned to them.