GAINS FROM TRADE

• Published date: 01 August 2017
• Author: Takashi Hayashi,Christopher P. Chambers
• DOI: http://doi.org/10.1111/iere.12240
• Date: 01 August 2017

INTERNATIONAL ECONOMIC REVIEW

Vol. 58, No. 3, August 2017

GAINS FROM TRADE∗

BYCHRISTOPHER P. CHAMBERS AND TAKASHI HAYASHI1

University of California, San Diego, U.S.A.; University of Glasgow, U.K.

In a social choice context, we ask whether there exists a rule in which nobody loses under trade liberalization.

We consider a resource allocation problem in which the traded commodities vary. We propose an axiom

stating that enlarging the set of tradable commodities hurts nobody. We show that if a rule satisfies this axiom,

together with an allocative efficiency axiom and an institutional constraint axiom stating that only preferences

over tradable commodities matter, gains from trade can be given to only one individual in the first step of

liberalization.

1. INTRODUCTION

A classical rationale for markets is that they allow gains from trade to be realized; at the very

least, no agent can be made worse off than her initial holding. However, this basic comparative

static only holds generally when starting from autarky. If a group of agents trade some goods

on the market, but others are untraded, opening markets in the untraded goods can potentially

hurt some of the agents. The intuition for this is simple: Opening trade in new goods can alter

the equilibrium price of already traded goods to accommodate the potential trade-offs for newly

traded goods.

In the international trade literature, this is known as a negative terms-of-trade effect (see

Krugman et al., 2012, for example). A related phenomenon occurs in the context of financially

incomplete markets. Hart (1975) offers an example establishing that opening a market in new

securities result in a Pareto loss. Elul (1995) and Cass and Citanna (1998) have shown that this

worsening is generic.

A very basic question remains. Although unregulated markets do not in general produce

gains from trade except in the special case of autarky, there may be room for transfers or

subsidies or regulations that allow such a result to be restored more generally. To this end,

our question does not take the competitive market solution in the Walrasian sense as given.

We ask: Is it possible to allocate resources, allowing redistribution of income or resources and

any other compensation or any price regulation so that that opening trade in new goods never

makes anybody worse off?

Somewhat surprisingly, we show that the answer is generally negative under certain domain

richness conditions. To qualify this statement, we first ask what our social choice function (SCF)

should or has to meet.

First, we ask that our SCF always respect weak Pareto efficiency, conditional on each given

trading opportunity. This corresponds to the idea of constrained efficiency in the literature of

general equilibrium theory.

∗Manuscript received December 2014; revised November 2015.

1We thank Marc Fleurbaey, Kohei Kawaguchi, Laurence Kranich, Akihiko Matsui, Hitoshi Matsushima, Herv´

e

Moulin, Koichi Tadenuma, Dan Sasaki, William Thomson, and Takashi Ui for helpful comments. We are also grate-

ful to two anonymous referees and an associate editor whose comments greatly improved the article. We thank

seminar participants at Hitotsubashi, Kobe, Kyoto, Osaka, Otaru, Tokyo, and participants of the SIRE microeco-

nomic theory workshop at Glasgow, and the SSCW meeting at Boston. Please address correspondence to: Takashi

Hayashi, Adam Smith Business School, University of Glasgow, Main Building, Glasgow, Scotland, U.K. E-mail:

Takashi.Hayashi@glasgow.ac.uk.

923

C

(2017) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

924 CHAMBERS AND HAYASHI

Second, we impose an informational/institutional constraint that SCF only take into account

preferences and endowments of traded commodities. We call this constraint (rather than a

normative postulate) Independence of Untraded Commodities.

In practical partial equilibrium mechanism design, the planner isolates the objects of allocation

from the rest of the economy and considers the agent’s preferences over those objects alone,

assuming that other things remain equal. Such an assumption is in general not compatible with

standard requirements, because preferences are generally not separable. Marginal preferences

over objects on the table alone are only part of the story.

Nevertheless, in many real-life situations we have to take this misspecification as a given

institutional constraint, in the sense that individuals are forced to behave as if their preferences

are separable, and partial equilibrium mechanism design is subject to such a constraint. Any SCF

going beyond this constraint would require extreme bureaucratic involvement on the part of a

social planner, requiring sophisticated knowledge of preferences over untraded commodities.

We do not claim that such constraints are normatively compelling. Rather, we simply point out

the constraint underlying the practical arguments. We believe this point has not received much

attention, so we would like to understand how restrictive it is.

More to the point, the revealed preference paradigm dictates that if commodities are not

tradeable, it is by definition impossible to infer preferences over these commodities from choice

behavior. Hence, if we interpret preference in the standard way as a representation device for

choice behavior, the condition is a necessary requirement for any mechanism in the environment

we study. Removing the condition would result in a framework involving elements, which cannot

be identified economically.

Now, the Walrasian solution, for example, satisfies these two properties. As our third and

final condition, we also ask that nobody be made worse off when opening markets to trade in

new goods. We call this No Loss from Trade.

We obtain two results. Imagine that we extend the SCF in two steps, first from autarky to

a class of smaller sets of commodities and second to the entire set of commodities, where the

preference domain satisfies certain Minimal Richness Conditions. Our first result is that as long

as we accept the Walrasian solution in the first step, it is impossible to extend the SCF in the

second step in a manner that does not hurt anybody, even when arbitrary compensation or

regulation is permitted.

The second result does not require acceptance of the Walrasian solution in the first step.

However, we establish that gains from trade require there to be a dominant individual who

reaps all of the gains; all other agents remain at the welfare level of their endowment.

1.1. Related Literature. Our result is related to several results in the literature in social

choice in exchange economies, for example, Moulin and Thomson (1988). A major theme of

this literature relates to whether everybody can benefit systematically when the set of available

objects increases somehow. The aforementioned result establishes that, in an exchange economy

environment without endowments, it is very hard for each agent to benefit when more of each

commodity is introduced. Our result follows this theme by considering the introduction of new

commodities, rather than introducing more of existing commodities.

In a setting of social evaluation of allocations when the set of commodities is variable,

Donaldson and Roemer (1987) propose an axiom stating that the social ranking over allocations

of any subset of commodities should be unchanged as far as individuals’ preferences over

consumptions of the subset remain the same, given any fixed allocation of the rest of the

commodities. Our independence axiom is weaker than theirs, in the sense that we do not take

arbitrary allocations of untraded commodities, since in our setting when commodities are not

tradable, individuals just consume their initial endowments of those.

Our independence axiom may resemble an independence axiom proposed by Fleurbaey and

Tadenuma (2007), stating that, in the setting of variable sets of physically present commodities,

only preferences over physically present commodities should matter. The difference here is

that we fix the set of physically present commodities and vary the sets of tradable commodities,