chance, Assumption Iwill be violated.14 Thus, our framework shows that the sequential enlarging
of free trade areas through implementation of hub-and-spoke free trade agreements fails to satisfy
the requirements for stepwise Pareto improvement.
Whether free trade areas ultimately constitute an aid to continuing freer trade, or, after initial
gains add to regional complacency of countries that view their trade to be free enough, may hinge
on other issues yet to be explored.
Appendix
Economics has expanded considerably in its ability to prove the existence of general equilibrium
under much more general conditions.15 Following Gale and Mas-Colell (1975), write the following
conditions for an economy:
E.l- The net production set Y is closed, convex, contains the negative orthant, and has a
bounded intersection with the positive orthant.
E.2- The consumption set for individual j, Xj, is closed, convex, non-empty and bounded
below.
E.3- The preference mappings Pj are irreflexive (that is, Xj ^ Pj(xj)), have an open graph
in Xj x Xj, and their values are non-empty, convex sets.
E.4- The functions αj∙ (p) are continuous and satisfy αj∙ (p) > p ■ x° > inf p ■ Xj for all p
where xθ is consumer j,s initial consumption bundle and αj∙(p) is the individual’s income.
Then the following proposition is immediate from Gale and Mas-Colell.
Proposition: There exists a competitive equilibrium for the economy. ■
14Deltas, Desmet, and Facchini (2007) present a thorough investigation of the effects of Hub-and-Spoke FTAs
on trade flows and welfare.
15Gale and Mas-Colell (1975), Shafer and Sonnenschein (1975), McKenzie (1981) and others, for example,
prove that competitive equilibria exist in economies with non-transitive, interdependent and price-dependent
preferences. Competitive equilibria also exist in the presence of production technologies where a finite amount
of output can be generated by zero input, and even in more abstract circumstances where the income of every
consumer is represented by any continuous function of prices. Hartwick, Variya, and Schweizer (1976) expand
existence results to the assumption that goods can be fixed (consumed in only one location) or mobile (transported
to all locations). Transportation technology is explicitly described by a linear function. The concern in their paper
is that certain fixed goods (e.g. housing) can not be consumed in more than one place and consumers need to
choose where to consume them (e.g. where to live). Then, they decided to divide goods into the two categories
as already described. In our paper, consumers that live in one country do not have the choice of where to live,
which is intuitive, and descreases the complexity of the model.
13