Page 28 - DECO503_INTERNATIONAL_TRADE_AND_FINANCE_ENGLISH

International Trade and Finance

Notes comprehensive; but they are still closed, convex, bounded, and comprehensive. Proposition 2
still holds. Moreover, for each closed, convex, bounded, and comprehensive set we can find an
economy whose set of possible gains from trade and this set coincide.
• The domain of closed, convex, bounded, and comprehensive sets is the usual domain of problems
in bargaining theory. It is well-known that on this domain there is no maximal and monotonic
solution. We can weaken monotonicity to hold whenever the smaller of the two sets of gains
from trade is strictly comprehensive, and obtain a generalized version of the weighted-gains
family. A member of this generalized family measures gains from trade by the largest vector
proportional to a vector of weights, but, if this vector is not maximal, it drops some goods, and
continues measuring gains from trade proportional to a restricted vector of weights. We refer
to Thomson (2004) for a detailed treatment of this family in the context of bargaining theory.
• For the application to fair allocation, monotonicity of the metric was necessary for the proof of
Theorem 2. As stated in the text, we conjecture that an alternative proof can be obtained without
monotonicity if we require a welfare improving property.
• Finally, we discuss relaxing the requirement that metrics measure equal gains from trade in
economies with equal sets of possible gains from trade. Sets of possible gains from trade depend on
relatively little information about preferences. This property may be desirable when obtaining
information is costly, but we may lose too much information in the aggregation procedure.
Relaxing this property is an interesting an open question left for future research. For now, we
note that monotonicity of a metric implies this property.
2.6 Key-Words

1. Symmetric : Symmetry generally conveys two primary meanings. The first is an imprecise
sense of harmonious or aesthetically pleasing proportionality and balance; such
that it reflects beauty or perfection. The second meaning is a precise and well-
defined concept of balance or "patterned self-similarity" that can be demonstrated
or proved according to the rules of a formal system: by geometry, through physics
or otherwise. Although the meanings are distinguishable in some contexts, both
meanings of "symmetry" are related and discussed in parallel.
2. Maximality : Of relating to, or consisting of a maximum, being the greatest or highest possible
2.7 Review Questions

1. Write a short note on the gains from trade.
2. Discuss the measurement of gains from trade.
3. What are the concepts of trade? Discuss.
Answers: Self-Assessment
1. (i)(c) (ii)(b) (iii)(a) (iv)(d) (v)(d)
2.8 Further Readings

1. DEBREU, G. (1951) : “The coefficient of resource utilization,” Econometrica, 19,
273–292.
2. DOMINGUEZ, D. (2006) : “Lower bounds and recursive methods for the problem
of adjudicating conflicting claims,” mimeo.
3. FOLEY, D. (1967) : “Resource allocation and the public sector,” Yale Economic
Essays, 7, 45–98.
4. KALAI, E. (1977) : “Proportional solutions to bargaining situations : interpersonal
utility comparisons,” Econometrica, 45, 1623–1630.

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