2 Transportation and Equilibrium
Consider a free trade area formed by two countries named Home and Foreign that are
denoted by H and F, respectively. The rest of the world is denoted by the letter W. Extension
to an agreement formed by several countries is similar and will not be pursued here. Goods are
differentiated both by their characteristics and location. It is necessary, especially in international
trade, to distinguish goods by description and location of use. Feenstra (2004, pp. 192), for
example, suggests applying Arrow-Debreu-based methodology to study the welfare effects of the
formation of preferential agreements. According to Debreu “a good at a certain location and
the same good at another location are different economic objects, and the specification of the
location at which it will be available is essential.” (Debreu, pp. 29-30, emphasis in original.)
He notes that if location changes, “a different commodity results.” (Ibid., p. 30, emphasis in
original.)
Any good can be used for final consumption or as an intermediate good in production. A
good produced in one country and transported to another becomes a different good. We consider
economies that produce K types of goods, implying 9K goods in total (3 countries of origin and
3 countries of destination). Since goods are differentiated by their location and description, the
prices prevailing in the preferential trade agreement are described in a 9K × 1 vector. Note also
that trans-shipment technology is a form of production, and, therefore, a process of transforming
certain inputs into specific outputs. Moving a good from one location to another transforms
it and so the prices prevailing in a customs union or FTA represent the cost of transportation
between locations as well as preferences and production technology.
Since countries H and F form an FTA, we assume that they can implement different tarifs
and that internal free trade prevails between them. Thus, goods originating in the rest of the
world may have different prices in the FTA countries’ markets. Producers in the FTA desire to
sell their output in the member market with higher price. This may create an impediment to
member countries’ independent tarif setting. Potential conflict arises from the ability to import
a product from the rest of the world and trans-ship it to the member market with the higher
internal price. In this case, transportation would imply a relationship between the prices of goods
that is potentially inconsistent with the prices implied by the different tarifs of union members.
This issue must be treated in the proof of general equilibrium existence.
Let prices prevailing in the union be denoted by p. They differ from world prices pw by tarifs
t, p = pw + t. Thus,