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International Trade and Finance Dilfraz Singh, Lovely Professional University

Notes
Unit 2 : Measurement of Gains from Trade

CONTENTS
Objectives
Introduction
2.1 Gains from Trade
2.2 How to Measure Gains from Trade
2.3 Measurements of Gain from International Trade
2.4 An Application to Fair Allocation
2.5 Summary
2.6 Key-Words
2.7 Review Questions
2.8 Further Readings

Objectives

After reading this Unit students will be able to:
• Describe how to measure Gains from Trade.
• Explain an Application to Fair Allocation.
Introduction

In the classical model of exchange gains from trade can be obtained if there exists a feasible allocation
which each agent prefers to her endowment. But, how can we measure the gains from trade in an
economy ? For interpersonal comparisons of welfare are typically not meaningful, we propose
measuring gains from trade in terms of quantities of goods, avoiding welfare comparisons. To do so,
we search for a “reference allocation”, composed of “reference bundles”, one for each agent, such
that : (i) each agent is indifferent between her endowment and her reference bundle, and (ii) the
reference allocation is feasible. Since no welfare gains are achieved, the difference between the
aggregate endowment and the resources at the reference allocation provides a measure of the gains
from trading from the endowment profile to the reference allocation.
In this manner, we obtain a measure of gains from trade in terms of quantities of goods. But, for most
economies, there is a continuum of reference allocations and the vectors of resources saved by trading
to each differ. The set of all such vectors defines the set of possible gains from trade of the economy.
We introduce the notion of a (vector-valued) “metric”, to select, for each economy, one representative
vector from its set of possible gains from trade.
Two economies may differ in preferences and endowment profiles but have equal sets of possible
gains from trade. Our premise is that, if two economies have equal sets of possible gains from trade,
a metric should not distinguish between them, and should select the same representative vector of
gains from trade in both economies. Thus, the notion of a metric is similar to the notion of a solution
for bargaining problems. A “bargaining problem” consists of a set of utility profiles and a disagreement
point; a “solution” maps each bargaining problem into a utility profile. In our setting, the set of utility
profiles corresponds to the set of possible gains from trade, and the disagreement point corresponds
to each agent consuming her endowment and no resources being saved. A metric maps each set of
possible gains from trade into a vector of gains from trade.
We follow an approach used in bargaining theory and look for metrics satisfying certain desirable
properties. Metrics should select a vector representative of the size of the set of possible gains from
trade. Thus, we look for metrics satisfying the following three properties that have strong intuitive

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