We apply this theorem to Proposition 1 as follows: Assume that i = H, F are two economies
engaged in world trade where (i) the production set of each economy is closed, convex, con-
tains the negative orthant, and is such that positive output requires at least one positive input
(impossibility of free production), (ii) the consumption set of each individual is closed, convex,
non-empty and bounded below, (iii) the preference mappings of each individual satisfy E.3, and
(iv) the income of each individual satisfies E.4. Assume that the two economies form a free trade
area satisfying Assumptions 1 and 2.
To prove that equilibrium exists for the free trade area, follow the Kemp-Wan strategy of
creating an artificial autarkic economy by adding the pre-union external trade vector of each
member to the member country’s endowment. In addition, because we are considering a free
trade area, impose the operation of rules of origin (Kemp and Wan did not need this step). Then
show that assumptions E.1-E.4 hold for the artificial economy consisting of the H, F pair, hence
it has an equilibrium. The final step is to observe that the equilibrium for the artificial economy
is an equilibrium for the original H, F free trade area.
By (i) and standard results, the autarkic economy satisfies E.1.1δ Firms in H are free to
select yεYhto maximize profits subject to prices p in (1). No inconsistency arises between the
independence of prices in (1) except possibly for goods of type yHFk because firms could trans-
ship to F such goods imported from W. This potential conflict is prevented, however, because
the production∕trans-shipment of imported goods between H and F is proscribed. Such a good
would bear the same description к as one of its inputs and be prohibited from duty free re-export
to F. A similar observation applies to yF production.
The key is how rules of origin affect trans-shipment and re-labeling. From country H’s per-
spective, consider the process of re-labeling a good imported from the rest of the world, WHk,
as domestic production, HHk (one unit of WHk becomes one unit of HHk with no physical al-
teration). Re-labeling is characterized by input of —ywHk units of input (e.g. 5 Persian rugs
imported from the rest of the world) and output of yHHk of numerically equal size (5 units of
identical Persian rugs labeled as if they were a product of country H). By definition, the re-labeled
good is a perfect substitute with its original form. Thus, the presence or absence of re-labeling
affects nothing real and is inconsequential from the point of view of prices, consumption, or
market clearing.
Rules of origin prevent re-labeling and trans-shipment from becoming consequential in the
post-FTA equilibrium. Since what they limit was originally non-binding or inessential, however,
they do not have production consequences with respect to the FTA. In particular, when the
16Arrow and Hahn (1975), pp. 62-65, Debreu (1959), p. 41.
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