The name is absent

FTA is formed, import of a re-labeled good by F is counted as if it were an import of good WFk,
returning it to its true designation, both from the perspective of freezing world trade and applying
tariffs to imports.

^fT~       ^F^^"

Let y^,_l^l_lll and yF_F denote the production output (quantity) of goods that were relabeled
in the pre-FTA equilibrium by countries H and F, respectively. Enlarge the universe of goods
designations to ^^lικ by creating a place for relabeled goods at the end of the goods vector. Dehne
the closed convex set Aⁱ_k = {y e Yⁱ ∣ ⅛ = 0} ∩ {y e Yⁱ ∣ y∣^_fc = 0 }. Being in set Ak implies
no re-labeling. The following applies: The production set Yⁱ formed as the intersection ∩_k A^l_k
satisfies E.l and supports the same FTA equilibrium. Yⁱ, as an expository device, makes more
explicit the role of Assumption 2 rules of origin by preventing an initial inessential activity from
“coming on line” to become essential in the post FTA equilibrium.

The autarkic economy satisfies E.2 and E.3 by (ii) and (iii). Last, provide consumer j of
country i with income ɑ) ∖p] given by the fair sharing distribution rule used in Section 4. This
rule satisfies E.4, as would more general forms. Thus, the fictitious autarkic economy formed by
H and F with no trans-shipment and where the fictitious endowment of each country consists of
its usual endowments plus its pre-union external trade vector has an equilibrium 8. 8 is consistent
with Assumption 2 where firms maximize profits but are not allowed by rules of origin to choose
activities that involve duty-free trans-shipment of imported goods and where the pre-FTA external
trade of each country has been frozen by choice of external tarif. Thus, there exists an equilibrium
for the free trade area satisfying Assumptions l, 2 as was to be shown, where every household,
whether a member of the union or not, is not worse off than before the creation of the trade
area. This proves Proposition l.

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