Page 21 - DECO503_INTERNATIONAL_TRADE_AND_FINANCE_ENGLISH

Unit 2 : Measurement of Gains from Trade

2.2 How to Measure Gains from Trade Notes

Our proposal for measuring gains from trade in terms of quantities of goods can be interpreted as a
generalization, to a multi-agent setting, of some existing measures of welfare changes in single agent
decision making settings. The equivalent variation and compensating variation are measures of welfare
changes in terms of the difference in expenditure required to keep an agent’s welfare unchanged
after a change in prices. In our setting, change does not come from prices but from trading among
agents, and measuring gains in terms of quantities of goods seems natural in the absence of pre-
specified prices. In settings of choice under uncertainty, the risk premium measures how much an
agent is willing to forgo in order to obtain a constant consumption stream; the certainty equivalent
measures the level of constant consumption across states that leaves the agent’s welfare unchanged.
In our setting, we measure how much a set of agents can gain by redistributing risk among them.

Measuring gains from trade is equivalent to measuring the inefficiency of the endowment.
A measure the inefficiency of an allocation (or of the endowment profile) is its “coefficient
of resource utilization” (Debreu 1951). It assigns to each maximal vector in the set of
possible gains from trade a number equal to the dot product of the vector and its supporting

price.Then, it measures the inefficiency of the allocation by the maximal such value.
This way of measuring the inefficiency of an allocation is similar to ours. It also considers the set of
possible gains from trade of the economy. But, instead of measuring gains from trade by a vector of
commodities, it measures gains from trade by a scalar. Using a real-valued metric implies that we can
order the set of all economies according to their gains from trade. Using a vector-valued metric allows
for a partial order, which may be desirable if differences in goods require asymmetric treatment

across them. Moreover, this measure is not monotonic, an increase in the set of possible gains from
trade can lead to a decrease in the measurement of this gains.
Another advantage of using a vector-valued metric over a real-valued one, is that a vector-valued
metric leads to a natural allocation at which gains from trade are distributed fairly. The theory of fair
allocation can be categorized according to the nature of the problem under study : First, situations
where a social endowment has to be divided among a set of agents. Second, situations where agents
have private endowments and redistribution (trading) is possible. For the problem of allocating a
social endowment two notions of fairness are prominent. First is no-envy (Foley 1967) : no agent
should prefer another agent’s bundle over her own (see Kolm (1998) and Varian (1976)). Second is
egalitarian equivalence (Panzer and Schmeidler 1978) : there exists a reference bundle such that each
agent is indifferent between her bundle and the reference bundle. For the problem of redistributing
individual endowments these two notions can be adapted. No-envy in trades states that no agent
prefers another agent’s trade over her own. Egalitarian-equivalence from endowments states that
there exists a reference vector such that each agent is indifferent between her bundle and the bundle
obtained from the sum of her endowment and the reference vector.
Recently, a notion similar to egalitarian equivalence was proposed for economies with individual
endowments : an allocation is fair if it is welfare equivalent to an allocation obtained from summing
to the endowment profile a vector of fair “concessions” (Pérez-Castrillo and Wettstein 2006). This
notion generalizes egalitarian equivalence in two ways : first, it allows for differences in the reference
bundles according to differences in individual endowments; second, it allows for differences in
concessions.
Our notion of fairness is similar to Pérez-Castrillo and Wettstein (2006) but it differs in two ways.
First, our reference allocation is welfare equivalent to the endowment profile, and we sum to the
reference allocation the vector of contributions. Second, our vector of contributions differs from their
vector of concessions. Also, our results differ in form from theirs. They show existence of fair and
efficient allocations; we do not obtain a fair and efficient allocation immediately, but propose a recursive

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