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THE GAINS FROM INTERNATIONAL

TRADE AND INTERNATIONAL AID

IN THE PRESENCE OF PUBLIC GOODS

MURRAY C. KEMP

University of New South Wales, Sydney, NSW 2032

[email protected]

BINH TRAN-NAM

School of Taxation and Business Law,

University of New South Wales, Sydney, NSW 2032

[email protected]

It is well known that if the autarkic and free-trade equilibria are perfectly competitive withmarket distortions limited to non-negative taxes on imports and exports then free trade is

potentially (after country-specific lumpsum compensatory transfers) beneficial for each

trading country. It can now be shown that, even in a context of public goods of any kind,

free trade (after country-nonspecific lumpsum compensatory transfers) is potentially ben-

eficial for each trading country, whether or not the countries also extend aid in public goods

to each other.

Keywords: Gains from trade; gains from aid; public goods; public goods association.

JEL Classification: F11, F13, H41

1. Introduction

It was shown by Kemp and Wan (1972) that free trade is potentially (after country-

specific compensatory lumpsum transfers) beneficial for each trading country if the

autarkic and (post-compensation) free-trade equilibria are perfectly competitive

and if market distortions are limited to non-negative taxes on imports and exports.

However the KempWan conditions are merely sufficient; it has recently been

shown by Kemp and Shimomura (2001) that free trade is potentially beneficial foreach country in any CournotNash equilibrium in which the strategic variables of

*Paper presented at the 9th Biennial Pacific Rim Conference of the Western International Economic Association

hosted by the Queensland University of Technology, April 2629, 2011. An earlier version of Section 2 may be

found in Kemp (2011). The present paper offers a fairly complete analysis of finite normative trade theory in the

presence of public goods. We are grateful to Geoffrey Fishburn, Ngo Van Long and Henry Y Wan, Jr for their

helpful comments on earlier drafts.

Global Journal of Economics

Vol. 1, No. 1 (June 2012) 1250008 (9 pages)

World Scientific Publishing Company

DOI: 10.1142/S2251361212500085

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each household are elements of its consumption and output vectors and of its

vector of derived demands for factors of production, and from which variablereturns to scale are not excluded. The new proposition is quite general in scope. It

accommodates arbitrary numbers of industries, primary factors of production and

trading countries. Moreover, preferences, technologies and factor endowments may

differ arbitrarily among the households of the world; even returns to scale may

differ from household to household. Most important, the proposition does not

require that perfect competition prevails in each country: oligopolistic behaviour is

now the rule; indeed the proposition even accommodates trade-induced changes in

the strategies of individual households. In short, there is now available a substantialnew result in the normative theory of international trade. Our primary purpose in

writing the present paper is to show that a second new result, of vastly different

content, is also available. The additional result is concerned with competitive

economies that produce and/or consume public as well as private goods. It can now

be shown that, even in the context of public goods of any kind, free trade (after

country-nonspecific lumpsum compensatory transfers) is potentially beneficial for

each trading country, whether or not the countries also extend aid in public goods

to each other.1

Under autarky a country may consume public goods that are produced at home

or are produced abroad and on which the home country freely rides. Moreover it is

now generally accepted that if under autarky countries produce and/or consume

pure (non-excludable and non-rivalrous) public goods then only under special

circumstances is competitive free trade potentially (after compensation) beneficial

for all countries; and it is also known that this is true whether or not the voluntary-

financing mechanism of Lindahl (1919) is independently functioning in each

country.2

Indeed these statements are valid for public goods of any kind: they maybe consumption goods, intermediate goods or both; and they may be strictly local

1The normative trade theory of 1972 (produced by Kemp and Wan, and Grandmont and McFadden) was derived

from the WalrasArrowDebreuMcKenzie (closed-economy) model of general equilibrium. That model is based

on three dubious assumptions: each household is constrained by its preferences and a single (financial) budget;

each household is a price taker; and all commodities are private goods. The present paper is concerned only

with the last of these assumptions. The remaining assumptions are considered in a companion paper

(Kemp, 2012). Of the quartet (Walras, Arrow, Debreu, McKenzie) only Walras recognized explicitly that his

analysis was based on the complete neglect of public goods. This is clear from the definitive edition of the Cours,

translated by Jaff in 1954; see p. 257 of Jaffs translation. That Walras was explicit on this point in all editions

has been confirmed by Docks et al. (1988).2Lindahls analysis of 1919 was based on the earlier work of Wicksell (1896) and has been especially influential

in the closed-economy version of public economics. However, it has no role to play in normative trade theory.

Suga and Tawada (2007) have provided an example in which competitive free trade subject to the Wicksell

Lindahl mechanism is not potentially beneficial for all countries. Samuelson (1954) has emphasized that the

application of Lindahls mechanism requires more information than is generally available to governments. Suga

and Tawada have shown that the mechanism fails in open economies even with information of the type assumed

by Lindahl.

M. C. Kemp & B. Tran-Nam

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(appreciated only in countries the governments of which have provided them) or

partially cosmopolitan.However there are now available two alternative sufficient conditions for po-

tentially beneficial free trade for all perfectly competitive countries in a context of

public goods. Building on the earlier work of Wan (1972) on externalities and the

gains from trade, Kemp (2001:6162) has noted that free trade remains potentially

beneficial for all countries under.

Condition :

In each country, the aggregate net production vector of pure public goods under

free trade is maintained at its autarkic level.

Given condition , it follows that the consumption of public goods by any

country under free trade is the sum of that countrys aggregate net production of

public goods and any free riding by that country on the aggregate net production

vectors of other countries. The sufficiency of condition follows from the con-

vexity of each countrys set ofprivate production possibilities after allowing for the

constancy of each countrys net production vector of public goods.

The second sufficient condition is of a different kind and requires a longer

exposition. Building on the earlier findings of Kemp and Shimomura (2001),

Shimomura (2007) has shown that free trade remains potentially beneficial for all

countries under

Condition :

(a) all public goods are both pure and strictly local;

(b) benevolent governments play a CournotNash game with the public goods as

strategic variables; and

(c) the game has a solution, not necessarily unique.

However, it is difficult to take seriously the assumption that all public goods are

strictly local. In the modern world, non-local or cosmopolitan public goods are of

considerable importance: one thinks of the maintenance and improvement of a

common language and a common commercial law, of telecommunication facilities,

of medical facilities available in one country to citizens of all countries, of mea-

sures to improve public health and, in particular, to curb epidemics, of scientific

and artistic discoveries, of anti-pollution and anti-global-warming measures, of the

maintenance of infrastructure to support the production and transportation of other

goods and of expenditure on defence and anti-terrorist activities. Moreover, in each

country, local and non-local public goods are technologically and preferentially

The Gains from International Trade and International Aid

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inter-related. In such a world, free trade may fail to benefit trading countries, even

when the provision of public goods is the outcome of a Cournot

Nash gameplayed by benevolent but parochial governments.

On the other hand, not every non-local public good is fully cosmopolitan, that

is, appreciated in every trading country. This simple fact will play a significant role

in the formal analysis of Section 2, but at this stage it is noted only that while each

of the two sufficient conditions, taken by itself, is quite severe, nevertheless, taken

together, each in weakened form, they provide a simple but general sufficient

condition for potentially beneficial free trade in the context of pure public goods.

2. Analysis: The Gains from Trade

Throughout the present section, tradition is followed in that all public goods are

assumed to be pure; however, at the end of the analysis, it will be noted that the

assumption is not necessary. Moreover, it is assumed that each country contains

only representative households, that is, households that are identical in their pre-

ferences and endowments (including technological information and share hold-

ings). As Shimomura emphasized in his Remark 1, this assumption was not

necessary for his purposes; nor is it necessary here. Finally, it is assumed that in

each country the aggregate production set is closed and convex.

In view of Shimomuras recent finding, we depart from tradition in assuming

that all pure public goods are non-local or cosmopolitan. However, not all public

goods need be fully cosmopolitan. Without undue stretching of the imagination,

one may suppose that there exists a proper subset of pure and non-local public

goods, say G, and a subset of two or more trading countries, say C, such that

G contains the effective non-local public goods for each member of C but for no

non-members of C. Given a suitable system of Scitovszky (1941) lumpsum

transfers among the members of C, the latter will behave like a single country in

choosing a mixed vector of private and newly localized public goods. Equipped

with the Scitovszky transfers, the members of C will be referred to as a Public

Goods Association or PGA. With less confidence, one may suppose that several

PGAs co-exist, each with its own system of Scitovszky lumpsum transfers, each

choosing its own mixed vector of private and newly localized public goods and

accommodating all countries and all public goods. In this way, Shimomura

s modelin terms of individual countries and public goods localized by country is trans-

formed into an alternative model in terms of PGAs and public goods localized by

PGA; in short, the world economy is completely localized.3

3 In more conventional terminology, the public goods localized by a PGA have become club goods; see

Buchanan (1965) and, for a recent evaluation of the concept, Sandler and Tschirhart (1997).


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The collective governments of the PGAs play a CournotNash game in their

newly-localized public goods. Each government relies on lumpsum taxes andsubsidies to finance its purchases of public goods and to effect its Scitovszky

transfers. The game is played in two stages: in stage 1, the collective governments

choose the vectors of public goods to be provided and, in stage 2, the competitive

households and firms of all countries determine the prices both of private and of

public goods. Thus any solution to the game is a subgame-perfect equilibrium.

Proposition 1. If the world economy is completely localized, free trade is

potentially beneficial for each country.

Proof. After the substitution of individual PGAs (each with its own system of

Scitovszky transfers) for individual countries, the required proof can be seen to

follow that of Shimomura (2007).

Thus the restricted proposition provided by Shimomura can be extended to

accommodate non-local public goods. Indeed the extended proposition can be

further extended to accommodate impure public goods, the properties of which

depend on the number of households consuming them. Evidently the number of

public goods in each country then increases, as does the difficulty in forming aPGA. However, in principle, it is possible to further extend Shimomuras propo-

sition. Thus the above Proposition is valid whatever the world-wide mixture of

pure and impure, local and non-local public goods. In view of the lack of precise

information about the extent, distribution and composition of public goods, this is a

comforting thought.

Reliance has been placed on systems of Scitovszky transfers, one system for

each PGA, with no transfers from or to non-member countries. Given intra-PGA

transfers of this kind, each PGA will be prepared to play the CournotNash game

presupposed in the above Proposition. International transfers were not needed in

the derivation of earlier propositions concerning the gains from trade; see, for

example, Grandmont and McFadden (1972), Kemp and Wan (1972, 1993), Kemp

and Shimomura (1997, 2001) and Shimomura (2007). The transfers now intro-

duced are a measure of the international cooperation that suffices to ensure that

trade is always gainful even in a context of non-local public goods.4

4Towards the end of his paper, Shimomura (2007:953) remarked that conditions under which the GFT [Gains

from Trade] proposition survives international spillover effects is an important topic for future research. Earlier he

had proposed, as suitable conditions, (a) that all international spillovers positively affect each countrys pre-

ferences and technologies and (b) that in each country the vector of public goods consumed under free trade is not

smaller than the vector consumed under autarky. Evidently (a) and (b) make no allowance for international

cooperation but can be accepted as rather severe sufficient conditions. Condition (b) should not be confused with

condition .


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3. Analysis: The Gains from Trade and Aid

A large proportion of foreign aid takes the form of public goods, either publicconsumption goods (such as medical facilities) or public infrastructure (such as

educational facilities, highways and railroads, dockyards and reservoirs). Perhaps

for this reason, each donors choice of aid package is normally made after con-

sultation with potential recipient governments and with other potential donors. The

trend itself is understandable in view of the long-term needs of most less developed

countries.

While donor governments finance such projects, the actual provision of public

goods is usually left to private firms, which bid or tender for the privilege. Accessto the tendering process is often restricted by the donor government to firms that, in

some sense, are from the donor and/or recipient countries; the provision of aid is

tied in this sense. However, there is now a substantial measure of agreement

among leading donor governments that, without loss of control and with some gain

in world efficiency, firms from any country might be allowed to bid for any aid-

financed contract; see, for example, OECD (2001:2). Indeed this has been the

operating policy of the UK since 2001; and, more recently, the European Union

(EU) has moved in a similar direction by passing legislation unconditionallyuntying its aid to the least developed countries and by untying all its aid on a

reciprocal basis with other donor nations, whether or not they are members of the

EU: If you allow our firms to bid for your aid-financed contracts, we will allow

your firms to bid for our aid-financed contracts.5 Evidently, if all donor countries

accept this principle then each donor government will be freed of the need to

determine the home of a firm that has tendered for that governments aid-financed

contracts. It is noted also that Canada has untied all of its food aid since 2008 and

has announced that it plans to untie all remaining aid by 20122013; see

CIDA (2008).

The untying of aid has been welcomed both by aid recipients and by other

donor nations. For example, the untying of all aid has been described by an

Australian Government White Paper (Australian Government, 2006:23) as

international best practice. However, to determine whether the UK or the EU or

Canada has indeed adopted international best practice appeal must be made to a

model of the world economy which accommodates public goods in a suitably

restrictive manner. Such a model has been provided in Section 2. On the basis of

that model, it will be now shown that free trade in private goods combined

with foreign aid in public goods is potentially (after appropriate compensation)

5See Regulation (EC) No 2110/2005 of The European Parliament (2005) and the Council of the EU on access to

Community external assistance.


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beneficial to each country whether the aid is tied or untied and whether the

country is a donor or recipient.

6

As in Section 2, it is assumed that several PGAs coexist, each with its own

system of Scitovszky lumpsum transfers, each choosing its own mixed vector of

private and newly localized public goods and accommodating all countries and all

public goods. Thus, the world is again completely localized.7

Let us now recall the suggestion of Kemp and Shimomura (2002) that foreign

aid be recognized as a public good both by the donor and by the recipient. Without

this recognition, it is difficult to understand why countries should ever extend aid to

each other. Accepting their suggestion, then, aid from one country to anotherwithin the same PGA can be readily accommodated by the analysis of Section 2;

only the Scitovszky transfers within each PGA may need adjustment. Given that

each PGA has its own distinct set of public goods, each country will be left

potentially better off by its adjusted trade-cum-aid; moreover, each country is

potentially better off with reciprocally untied aid than with tied aid and potentially

better off with unconditionally untied aid than with reciprocally untied aid.

Proposition 2. Free trade in private goods combined with foreign aid in the form

of public goods ( from one country to another within the same PGA) is potentially

beneficial for each member country whether the aid is tied, reciprocally untied or

unconditionally untied. Moreover, each country is potentially better off with

reciprocally untied aid than with tied aid and potentially better off with

unconditionally untied aid than with reciprocally untied aid.

Like Proposition 1, Proposition 2 can be readily extended to accommodate

impure public goods.

4. Final Remarks

The reasoning of Sections 2 and 3 has been as brief as possible. However, to avoid

possible misunderstanding, several additional remarks are now added.

(a) In discussions of the gains from free trade, theorists usually assume that the

international distribution of technical skills or human capital is arbitrarily given,

perhaps by the earlier decisions of each countrys ministry of education. However

the decisions of governments concerning education, and therefore concerning the

international distribution of human capital, are ultimately controlled by the elec-

torates, at least in democratic countries. Education can be viewed as a public good

the consumption of which is compulsory up to the secondary level of schooling

6For earlier attempts to answer questions like those posed in the present section; see Kemp and Abe (1994) and

Kemp (1995, Chapter 29).7See footnote 3.


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and voluntary thereafter. Thus education is accommodated both in Proposition 1

and in Proposition 2.(b) The game played by the PGAs in Sections 2 and 3 is of the simplest

non-repetitive type, in keeping with the gains-from-trade propositions of 1972

and later. Thus no reliance has been placed on the so-called folk theorem

of repeated games.

(c) The reasoning employed in Sections 2 and 3 can be applied also to the

analysis of a closed economy with public goods that are effective only in a proper

subset of that countrys states or municipalities or only in a proper subset of its

industries. Those states, municipalities or industries that are members of the samenational PGA can free themselves of market distortions related to public goods by

jointly choosing an optimal vector of public goods, financed by lumpsum transfers

among members of that PGA. Evidently neighbouring states, municipalities and

technology- or preference-related industries are most likely to share membership in

a national PGA.

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