The Gains from International Trade Once Again
Author(s): P. A. Samuelson
Source: The Economic Journal, Vol. 72, No. 288 (Dec., 1962), pp. 820-829
Published by: Wiley on behalf of the Royal Economic Society
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THE GAINS FROM INTERNATIONAL TRADE
ONCE AGAIN1
I. INTRODUCTION
IN 1939 I wrote a paper that showed how some international trade
makes a society potentially better off than it would be if restricted to
autarky.2 Although this paper has received a flattering amount of notice,
I had always regarded it as somewhat incomplete and had long planned to
follow it with a more definite companion piece. For it was written with
two purposes in mind other than to say all that can be said about the gains
from international trade.
First, it was an attempt to show how the new theories of revealed preference
could be used to demonstrate important theorems in welfare economics.
And second, it was intended to mediate the dispute between two of my
famous teachers, Jacob Viner (then of Chicago) and Gottfreid Haberler
(Harvard), over the doctrine of opportunity cost in international trade and
value theory: my 1939 article was shaped to show how the eclectic doctrine
of general equilibrium could take changes in factor supplies in its stride
and by the index-number methods of revealed preference illustrate how the
Haberlerian transformation curve could be generalised.
Even after the passage of twenty years, the final chapter seemed still
to be lacking in the literature. And an interesting 1958 Danish criticism
of my earlier paper's treatment of income distribution by Mr. Erling Olsen 3
led me to defend the argument and at long last take up the thorough completion.
This time there was no need to worry about the obsolete doctrine
of opportunity cost; nor to use index numbers of revealed preference, since
for better or worse this approach had already won its place in the literature
of economic theory. Good fortune, however, brought Dr. Murray Kemp
to M.I.T. as a visiting professor in 1959-61 on his way from Canada to a
chair at the University of New South Wales. For, in discussing the present
paper, Professor Kemp showed that my alternative approach of 1939 could
indeed be carried through all the way to achieve the same final goals.4
In a real sense, therefore, our two papers are complementary and benefit
from simultaneous publication.
Grateful acknowledgement is made to the Ford Foundation for research assistance.
2 P. A. Samuelson, " The Gains from International Trade," Canadian Journal of Economics and
Political Science, Vol. V (May 1939), pp. 195-205. Reprinted in the Readings in the Theory of International
Trade of the American Economic Association.
8 Erling Olsen, " Udenrigshandelns Gevinst," Nationalokonomisk Tideskrift, Haefte 1-2 (Argana,
1958), pp. 76-9. I am grateful to Mr. Olsen for sending me an English translation of his
interesting paper.
4 Murray C. Kemp, " The Gain From International Trade," pp. 803-19 above.
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DEC. 1962] THE GAINS FROM INTERNATIONAL TRADE ONCE AGAIN 821
II. THE SMALL COUNTRY CASE
On the special assumption that our country under consideration is to
small to affect its terms of trade, and on the assumption that the price rati
abroad differ from those that would prevail at home under autarky, Fig. 1
heavy line EUF represents, our " consumption possibility frontier " wi
V
y \\
D
Q F X
FIG. 1. With no trade, we
at V, with UV the vector of algebraic imports.
some trade. With autarky the consumption possibility frontier is given by
the production locus PDUQ. Since the trade frontier lies everywhere 1
north-east of the autarky frontier, our society can have more of all goods
(and less of all irksome inputs) with some trade. It is in this sense that trade
makes us potentially better off.
III. AN IMPORTANT ENVELOPE
I wish to increase the generality of my 1939 argument by now dropping
the assumption that our country is small. Let us be large enough to affect
our terms of trade as we move along Fig. 2's Marshallian offer curve of the
rest of the world for our two-goods.
1 At U itself the frontiers coincide. Thus, if there were some distribution of income which
brought us under autarky to U rather than D, opening up trade would at that point (1) in fact
be followed by no international transactions taking place, and hence would (2) represent the
limiting case where trade neither helps nor hurts us. (If individuals' tastes and endowments
happen to be much alike at home there might be no redistribution of income that would, unde
autarky, get us to U. In such a case we would know that the cum-trade utility frontier of Fig. 4
does lie uniformly outside the autarky utility frontier. On the other hand, if U is a possibl
autarky point the cum-trade frontier will touch the autarky utility frontier at one or more points;
but it must always lie north-east of the autarky point corresponding to D-as we shall see.)
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822 THE ECONOMIC JOURNAL [DEC.
A y imports
- E x imports
B
FIG. 2. AOB is the familiar Marshallian offer curve of the rest of the world, but plotted in terms
of our algebraic imports.
Y E W
Q F x
FIG. 3. The important Baldwin envelope EF is generated by sliding AOB along PQ in such a way
as to trace out the frontier of consumable product. The slopes at W are necessarily equal to
the slope at 0'.
Now draw up the envelope frontier 1 of Fig. 3 by sliding the origin of
the AOB offer curve along the domestic production possibility locus PQ in
such a way as to trace out the maximal amount of each good that is available
1 See R. E. Baldwin, " Equilibrium in International Trade: A Diagrammatic Analysis,"
Quarterly Journal of Economics, Vol. LXII (1948), pp. 748-62; " The New Welfare Economics and
Gains in International Trade," Quarterly Journal of Economics, Vol. LXV (1952), pp. 91-101. See
also the valuable paper by Peter B. Kenen, " On the Geometry of Welfare Economics," Quarterly
Journal of Economics, Vol. LXXI (1957), pp. 426-4-7. Given more than two goods, we need modify
the exposition only trivially.
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1962] THE GAINS FROM INTERNATIONAL TRADE ONCE AGAIN '823
for given amounts consumed of the other good.' The resulting envelope
may be called society's cum-trade consumption possibility frontier. Like
Fig. l's EUF, of which it is a generalisation, the new consumption frontier
lies uniformly (save 2 for one point like U) outside the autarky consumption
frontier. Hence our society is potentially better off in the sense that there is a way
of reallocating the enlarged totals of goods so as to make every person better off.
It may be noted that the envelope frontier could be attained by an
optimal Mill-Bickerdike tariff or by more direct means. The Kahn-Graaff
paradox,3 that the size of the optimal tariff depends only on foreigners'
demand elasticity and not on home consumers' demand, is easily resolved
as follows: the envelope's slope at any point like W is related to the slope
of O'W as determined by the AOB curve alone; but never forget that home
demand must tell us which W will be the equilibrium one.
IV. THE UTILITY POSSIBILITY FRONTIER
Practical men and economic theorists have always known that trade
may help some people and hurt others. Our problem is to show that trade
lovers are theoretically able to compensate trade haters for the harm done
them, thereby making everyone better off. The ordinal utility diagram of
Fig. 4 is the natural tool to use for this purpose.4
The horizontal axis represents ordinal utility of one of our citizens. The
vertical axis represents ordinal utility of a second citizen. And for simplicity
I suppose there are only two citizens, or two classes of identical
citizens in our country. A point represents the simultaneous position of
both men: because utility need not be numerically measurable, only north
and south and east and west relationships count.
The point d corresponds to point D of Fig. 1. The broken locus
d'dd" represents the utility possibility frontier if the fixed goods to
are allocated in favour of man 1 or man 2 by ideal-sum transfers so that
1 It may help the reader to imagine the offer curve as being cut out from Fig. 2 with scissors
and then being carefully transposed over to Fig. 3 so as to trace out the envelope of its outlying
tangents. At a point like W not only is the offer curve tangential to the envelope but in addition
if we go back to the corresponding pivot point O' the slope of the production possibility schedule
there will also necessarily be the same. This follows from the geometrical properties of an envelope
and has the important economic interpretation that at an optimal point production substitution
ratios must be equal to trading substitution ratios (as well as to consumption substitution ratios).
2 If the autarky point D will in fact become outmoded by the opening of trade, then D and U
cannot coincide and we know that-by going north-east from D-everyone can be made better
off than they were under autarky.
3 See J. deV. Graaff, Theoretical Welfare Economics (Cambridge, 1957), Chapter IX.
4 Pareto's economics would have been better understood had he explicitly used the utility
frontier concept. I may refer the reader to my Foundations of Economic Analysis, Chapter 8; to
" Evaluation of Real National Income," Oxford Economic Papers (New Series), 2, pp. 1-29, particularly
p. 6; to " Social Indifference Curves," Quarterly Journal of Economics, Vol. LXX (February
1956), pp. 1-22. As Graaff points out in Chapter IV of his just-cited book, Professor M. Allais of
Paris also developed this social-utility-frontier concept.
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824 THE ECONOMIC JOURNAL [DEC.
there is no " inefficiency " or deadweight loss involved in the transfers.
On the other hand, the envelope pq is generated by treating every point o
PQ the way we have treated D and then drawing in the north-east frontier.
What is the envelope ef? It is the frontier traced out by all the points
on EF. Thus, it is tangential at v to the broken locus v'w" representing the
U," P e
XV
q U'
f
FIG. 4. The ef social utility frontier lies outside the autarky frontier pq. But the vv' frontier
corresponding to reallocation of the actual post-trade totals may well loop inside the autarky
point. (Utilities being ordinal not cardinal, the curvatures of the loci are of no definite signs.)
ideal reallocation of the goods at the post-trade point V. Since EF lies
north-east of PQ, ef must obviously lie north-east of pq.1
Now let us carefully compare the pre-trade point d with a post-trade
point v. Since v is south-east of d, it would be dangerous to say that trade
has made the world better off: man 1 is better off, man 2 is worse off. But
let us ideally reallocate the goods of v, moving north-west on vv' to compensate
man 2. Can we in this way make both men better off? Mr.
Olsen's reply would be: Not necessarily. If I may translate his analysis
into my terminology, he argues: The v'v locus of reallocation may pass
north-east of the autarky point d, or it may pass south-west of that point.
1 As mentioned in footnote 1 on p. 821, ef might touch pq at one or more points (indeed in the
limiting case where trade is always indifferent, at all points). It would be wrong, though, to
think that ef must somewhere touch pq: as already indicated, the point u corresponding to U might
never touch the pq frontier; and in that case ef would lie everywhere north-east of pq. If ef refers
to a country large enough to affect its terms of trade, we can define a new frontier midway, so to
speak, between the autarky frontier pq and the optimum-tariff frontier ef. I refer to the free-trade
frontier that results from zero tariffs but with different lump-sum redistributions of income. This
new frontier can never loop inside pq or outside ef. It corresponds to a free-trade locus that could
be pencilled into Fig. 3 midway between PQ and EF.
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1962] THE GAINS FROM INTERNATIONAL TRADE ONCE AGAIN 825
I have no dispute with this last possibility. In fact, Fig. 4 is drawn wit
Vv' passing below d so that the gainers from trade cannot (by realloca
the given totals) bribe the losers into acquiescing to trade.
But nothing in my 19391 or present argument required that the co
pensation or bribing be possible out of fixed totals. What I was concer
to argue was that the cum-trade utility envelope frontier ef-not vv'outside
the autarky frontier pq. And this is true despite the Ols
contention.
As a matter of fact, imagine compensation beginning to take place
v and V. This will automatically change the pattern of imports, moving v nor
westward on ef and moving V north-westward on EF. Where will th
process end? If the losers are fully compensated-and my argument pro
conclusively that they can be-the points v and V will be moved so far nor
westward as to cause the Olsen effect to disappear necessarily. Thus, w
end up north-east of d.
I hope no one will think that I advocate: (1) compensation, or (2) no
compensation. We need a Bergson social-welfare function to answer th
questions, and I have always pointed out the illogic of those new welf
economists who used to try to reach normative conclusions on the basi
insufficient norms.
V. SCITOVSKY COLLECTIVE INDIFFERENCE CURVES
In 1939, two years before Professor Tibor Scitovsky 2 introduced h
collective indifference curves, I, of course,) did not use them in my expositio
Nor have I yet used them here. But in that Olsen has used them, I oug
to mention them briefly.
Through D in Fig. 1 (or as well in Fig. 3), Olsen would draw a Scitovs
indifference curve: this gives the minimum required totals of the goo
needed to keep all men as well off as they actually were under autarky
Olsen then argues that the after-trade point V could conceivably lie und
this Scitovsky curve, not above it. This I freely admit (as in my Fig. 4
passing of vv' below d).
But what do I need for my argument that some trade makes a societ
potentially better off in the sense of making it possible for all men to
made better off, the gainers being able to more than compensate the losers
Not that V lie above the D Scitovsky indifference curve. But rather th
weaker, and inevitable, condition that the EF envelope frontier somewhere
1 See Robert E. Baldwin, " A Comparison of Welfare Criteria," Review of Economic Studies, Vol.
XXI (1953-54), p. 160, for a defence of my 1939 argument against an Olsen-like criticism.
2 T. Scitovsky, " A Reconstruction of the Theory of Tariffs," Review of Economic Studies, Vol. IX
(1941-42), pp. 89-110, reprinted in Readings in the Theory of International Trade. See, too, my cite
Quarterly Journal article for a discussion of how these concepts all fit together.
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826 THE ECONOMIC JOURNAL [DEC.
pass above the Scitovsky indifference curve. Fig. 5 shows how inevitable
this is, and how irrelevant the crossing of the V and D Scitovsky curves is.
y
E
Pre-trade Scitovsky curve
Post-trade Scitovsky curve
Q F x
FIG. 5. The Scitovsky community indifference curve of the actual post-trade configuration V may
well pass above the community indifference curve of the actual autarky configuration D.
But for the winners to be able ideally to compensate the losers requires only that UE cut
somewhere above the autarky community indifference curve-as is always the case. The
fact that the post-trade community indifference curve always passes above the autarky point
means that trade satisfies the 1941 Scitovsky test for an improvement-namely, the losers from
trade can never afford to bribe the trade gainers into unanimously repealing all trade.
VI. INDEX NUMBER COMPARISONS
Finally, let me review and extend the index-number type of argument
used in my 1939 paper. For simplicity, I shall revert back to Fig. l's case
where the country is too small to affect its terms of trade.' In Figs. 1 and 5
the tangent line of the equilibrium point V contains U inside of it, and
afortiori because of the strong curvature of PQ it must contain D inside of
in terms of index number comparisons,2 this means
4.VQV > IPVQD
If only a single individual or a " representative man " standing for
identical citizens were involved we could, from the familiar economic
theory of index numbers,3 deduce that the post-trade point was 'better
1 Since convexity of PQ makes the EF envelope convex too, I believe the argument could be
extended to the general case.
2 I have changed my 1939 notation and am neglecting changes in factor supplies.
3 See Foundations, Chapter VI, for the conclusions of the Pigou, K6nus, Staehle, Frisch, Haberl
Leontief, R. G. D. Allen, Lerner, Samuelson, Hicks line of reasoning.
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1962] THE GAINS FROM INTERNATIONAL TRADE ONCE AGAIN 827
than " the autarky point. Most of my 1939 paper dealt with this oneperson
case; and the remainder, to which Mr. Olsen's remarks all apply,
was well advised not to use the index-number method.
What does the above index-number comparison mean when there are
different men in our economy so that it must be written
PV(qV' + q V + * . .) > IPV(qD' + qD" +
and when we observe only the totals in parentheses?
Professor Hicks stated in 1940 a beautiful theorem I that gives a partial
answer. By it, the index-number comparison alone will tell us that the
post-trade point v in Fig. 4 necessarily lies outside the autarky loci pq or
dd". Thus, Mr. Olsen's conclusion-which he derived in his last paragraph
by perceiving that the Scitovsky collective indifference curve through V
would have to lie outside the point D (and indeed outside all autarky points
of PQ)-follows: Those hurt by trade are never able to bribe the trade
winners into going back to autarky.
In terms of welfare economics, Mr. Olsen has proved that the post-trade
situation satisfies the 1941 test 2 added by Scitovsky to supplement the
Kaldor-Hicks 1939 test that the gainers from trade-or any improvementbe
capable of bribing the losers. Though Mr. Olsen has proved that the
Scitovsky test holds, I believe he has not thereby shown that my proof of
the Kaldor-Hicks tests' holding is faulty. Actually, my proof I deem
satisfactory, and by it I establish something stronger-that an infinity of
tests or comparisons between the pre-trade and post-trade utility frontiers
show the latter to be the frontier farther out. (All this is specified at a
glance in Fig. 4.)
In this sense trade makes a country potentially better off.
VII. A WARNING ABOUT FEASIBILITY
What in the way of policy can we conclude from the fact that trade is a
potential boon? As I pointed out in my 1950 paper, we can actually conclude
very little.
To see this turn to Fig. 6, which is much like Fig. 4. Suppose the social
welfare function, if we knew it, " favoured " the man hurt by trade, man 2
-as shown by the Bergson contours of welfare indifference. And suppose,
as is the simple truth, that ideal lump-sum redistributions are never really
available to us. Instead the only feasible redistributions must cause harmful
substitution and other effects. Then the feasibility locus upon which we
1 J. R. Hicks, " The Valuation of Social Income," Economica, New Series, Vol. VII (1940),
pp. 105-24. See my cited Oxford 1950 paper, pp. 7-10, for a reformulation and proof of the Hicks
theorem on group index-number comparison.
2 T. Scitovsky, " A Note on Welfare Propositions in Economics," Review of Economic Studies,
Vol. VIII (1941), pp. 77-88.
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828 THE ECONOMIC JOURNAL [DEC.
are free to move looks like the dotted curve in Fig. 6, vg, looping inside the
ef frontier. Now it is quite possible that this feasibility locus might even
loop inside the autarky point d. It evidently follows that, with the given
Bergson contours, autarky is preferable to the post-trade situation-showing
how difficult must be any rigorous interpretation of " potential"
improvement.'
Social
welfare
contours
wil
Feasibility locus7(\Wl
WI
F
\ ~~~~ul
f
FIG. 6. If lump-sum transfers are not feasible, so that vg rather than ef is the feasibility frontier,
the highest social-welfare contour obtainable from free trade might be lower than that
obtainable under autarky.
VIII. CONCLUSIONS
Rather than summarise what has been a lengthy argument, I shall
simply stand by my earlier position and jot down some truths that are
perhaps better understood to-day than twenty years ago.2
1 Perhaps some situation very near to autarky, but involving a little trade, could be proved to
give points north-east of d. This is suggested by the fact that small redistributions will usually
involve small deadweight distortions of a higher order of infinitesimals. For the theory of
feasibility-sometimes called the theory of the second best-and still in its infancy, see F. P.
Ramsey, " A Contribution to the Theory of Taxation," ECONOMICJOURNAL, VOl. XXXVII (1927),
pp. 47-61; M. Boiteux, " Sur la question des Monopoles Publics astreints l'a quilibre budg6taire, "
Econometrica, Vol. 24 (1956), pp. 22-40; R. G. Lipsey and R. K. Lancaster, " The General Theory
of the Second Best," Review of Economic Studies, Vol. XXIV (1956-57), pp. 11-32; I. M. D. Little,
A Critique of Welfare Economics (Oxford, 1957), 2nd edition, Appendix IV; J. de V. Graaff, loc. cit.,
Chapter V; P. A. Samuelson, Oxford Economic Papers, loc. ci., pp. 18-19.
2 See P. A. Samuelson, " Welfare Economics and International Trade," American Economic
Review, Vol XXVIII (1938), pp. 261-68, for a discussion of these issues and for what appears to
be the first of the modern rediscoveries of the Mill-Bickerdike theorem that some tariff is optimal.
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1962] THE GAINS FROM INTERNATIONAL TRADE ONCE AGAIN 829
1. If the laws of returns were appropriate for perfect competition (no
external effects, indivisibilities, monopolies, dynamic uncertainties, learning
processes, etc.), free trade 1 and ideal transfers could be used to give maximal
world production in the sense of a farthest out world production possibility
frontier.
2. Free trade and ideal transfers could give a similar maximal world
utility frontier for all individuals.
3. Free trade will not necessarily maximise the real income or consumption
and utility possibilities of any one country-even though by ideal bribes
the international winning countries could bribe the losers into a unanimous
vote for free trade.
4. Free trade will not necessarily maximise the income, consumption
and utility possibilities of a subset of persons or factors within a country.
5. If all but one country will always trade freely it (almost) always pays
that one country to behave monopolistically, imposing optimum MillBickerdike
tariffs or other interferences to take advantage of less-thaninfinitely-elastic
international demand.
6. Whatever the fixed pattern of tariffs abroad, it usually pays one
country to introduce an optimum duty unilaterally. Some countries may
then end up better off than under free trade; or perhaps none will end up
better off. But never can all countries end up better off; and indeed, the
losers from the tariff pattern can always theoretically offer the winners large
enough ideal bribes to get rid of all tariffs and interferences with free trade.
7. Only at a point reachable by free trade would an international
individualistic social welfare function be at its maximum maximorum.
8. For a given country, autarky cannot be optimal if ideal transfers are
possible. Some trade is better than no trade in the sense of making the
nation better off, with a farther out consumption-possibility frontier an
farther out utility-possibility frontier.
If ideal lump-sum reallocations of income are not feasible the above conclusions
need serious modification and qualification. The same is true
when we introduce imperfections of competition, uncertainties, induced
changes of an irreversible type and game-theoretic struggles for power and
welfare.
P. A. SAMUELSON
Massachusetts Institute of Technology.
1 Other devices, such as perfect planning or perfect discrimination, might accomplish the same
result.
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