International Factor-Price Equalisation Once Again
Author(s): Paul A. Samuelson
Source: The Economic Journal, Vol. 59, No. 234 (Jun., 1949), pp. 181-197
Published by: Wiley on behalf of the Royal Economic Society
Stable URL: http://www.jstor.org/stable/2226683
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INTERNATIONAL FACTOR-PRICE EQUALISATION
ONCE AGAIN
1. INTRODUCTION
My recent paper I attempting to show that free commodity
trade will, under certain specified conditions, inevitably lead to
complete factor-price equalisation appears to be in need of further
amplification. I propose therefore (1) to restate the principal
theorem, (2) to expand upon its intuitive demonstration, (3) to
settle the matter definitively by a brief but rigorous mathematical
demonstration, (4) to make a few extensions to the case of many
commodities and factors, and finally (5) to comment briefly upon
some realistic qualifications to its simplified assumptions.
I cannot pretend to present a balanced appraisal of the bearing
of this analysis upon interpreting the actual world, because my
own mind is not made up on this question: on the one hand, I
think it would be folly to come to any startling conclusions on
the basis of so simplified a model and such abstract reasoning;
but on the other hand, strong simple cases often point the way to
an element of truth present in a comnplex situation. Still, at the
least, we ought to be clear in our deductive reasoning; and the
elucidation of this side of the problem plus the qualifying discussion
may contribute towards an ultimate appraisal of the
theorem's realism and relevance.
2. STATEMENT OF THE THEOREM
My hypotheses are as follows:-
1. There are but two countries, America and Europe.
2. They produce but two commodities, food and clothing.
3. Each commodity is produced with two factors of
production, land and labour. The production functions of
each commodity show " constant returns to scale," in the
sense that changing all inputs in the same proportion changes
output in that same proportion, leaving all " productivities "
1 "International Trade and the Equalisation of Factor Prices," EcoNoMIc
JoURNAL, Vol. LVIII, June, 1948, pp. 163-184. I learn from Professor Lionel
Robbins that A. P. Lerner, while a student at L.S.E., dealt with this problem. I
have had a chance to look over Lerner's mimeographed report, dated December
1933, and it is a masterly, definitive treatment of the question, difficulties and all.
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182 THE ECONOMIC JOURNAL [JUNE
essentially unchanged. In short, all production functions
are mathematically " homogeneous of the first order " and
subject to Euler's theorem.
4. The law of diminishing marginal productivity holds:
as any one input is increased relative to other inputs, its
marginal productivity diminishes.
The commodities differ in their " labour and land
intensities." Thus, food is relatively " land using " or
" land-intensive," while clothing is relatively " labourintensive."
This means that whatever the prevailing ratio
of wages to rents, the optimal proportion of labour to land
is greater in clothing than in food.
6. Land and labour are assumed to be qualitatively
identical inputs in the two countries and the technological
production functions are assumed to be the same in the two
countries.
7. All commodities move perfectly freely in international
trade, without encountering tariffs or transport costs, and
with competition effectively equalising the market priceratio
of food and clothing. No factors of production can
move between the countries.
8. Something is being produced in both countries of both
commodities with both factors of production. Each country
may have moved in the direction of specialising on the commodity
for which it has a comparative advantage, but it has
not moved so far as to be specialising completely on one
commodity.'
All of this constitutes the hypothesis of the theorem. The
conclusion states:
Under these conditions, real factor prices must be exactly
the same in both countries (and indeed the proportion of
inputs used in food production in America must equal that
in Europe, and similarly for clothing production).
Our problem is from now on a purely logical one. Is " If H,
then inevitably C " a correct statement? The issue is not whether
C (factor-price equalisation) will actually hold; nor even whether
H (the hypothesis) is a valid empirical generalisation. It is
whether C can fail to be true when H is assumed true. Being a
1 Actually we may admit the limiting case of "incipient specialisation,"
where nothing is being produced of one of the commodities, but where it is a
matter of indifference whether an infinitesimal amount is or is not being produced,
so that price and marginal costs are equal.
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1949] INTERNATIONAL FACTOR-PRICE EQUALISATION 183
logical question, it admits of only one answer: either the theorem
is true or it is false.
One may wonder why such a definite problem could have
given rise to misunderstanding. The answer perhaps lies in the
fact that even so simple a set-up as this one involves more than
a dozen economic variables: at least four inputs for each country,
four marginal productivities for each country (marginal productivity
of American labour in food, of American land in food . . .),
two outputs for each country, the prices of the two commodities,
the price in each country of the two inputs, the proportions of the
inputs in different lines of production, and so forth. It is not
always easy for the intellect to move purposefully in a hyperspace
of many dimensions.
And the problem is made worse by the fact, insufficiently
realised, that constant returns to scale is a very serious limitation
on the production functions. A soon as one knows a single
" curve " on such a surface, all other magnitudes are frozen into
exact quantitative shapes and cannot be chosen at will. Thus,
if one knows the returns of total product to labour working on
one acre of land, then one already knows everything: the marginal
productivity schedule of land, all the iso-product curves, the
marginal-rate-of-substitution schedules, etc. This means one
must use a carefully graduated ruler in drawing the different
economic functions, making sure that they are numerically
consistent in addition to their having plausible qualitative
shapes.
3. INTUITIVE PROOF
In each country there is assumed to be given totals of labour
and land. If all resources are devoted to clothing, we get a
certain maximum amount of clothing. If all are devoted to
food production, we get a certain maximum amount of food.
But what will happen if we are willing to devote only part of
all land and part of total labour to the production of food, the
rest being used in clothing production? Obviously, then we are
in effect sacrificing some food in order to get some clothing. The
iron law of scarcity tells us that we cannot have all we want of
both goods, but must ultimately give up something of one good
in getting some of another.
In short there is a best " production-possibility," or " transformation
" curve showing us the maximum obtainable amount
of one commodity for each amount of the other. Such a production-possibility
schedule was drawn up for each country in Figure 1
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184 THE ECONOMIC JOURNAL [JUNE
of my earlier article. And in each case it was made to be a
curve convex from above, so that the more you want of any good
the greater is the cost, at the margin, in terms of the other good.
This convexity property is very important and is related to the
law of diminishing marginal productivity. Few readers had any
qualms about accepting convexity, but perhaps some did not
realise its far-reaching implications in showing why the factorprice
equalisation theorem had to be true. I propose, therefore,
to show why the production-possibility curve must obviously
be convex (looked at from above).'
To show that convexity, or increasing relative marginal costs
must hold, it is sufficient for the present purpose to show that
concavity, or decreasing marginal costs, involves an impossible
contradiction. Now at the very worst, it is easily shown we
can move along a straight-line opportunity cost line between the
CLOTHING
A
\ \s ,,Op~~0timat
. _ \ s O %,>Possible, but
\ R s not optimal
Impossible
z
two axes. For suppose we agree to give up half of the maximum
obtainable amount of food. How much clothing can we be sure
of getting? If we send out the crudest type of order: " Half of all
labour and half of all land is to be shifted to clothing production,"
we will (because of the assumption of constant returns to scale)
exactly halve food production; and we will acquire exactly half of
the maximum amount of clothing produceable with all resources.
Therefore, we end up at a point, R, exactly half-way between
the limiting points A and Z. Similarly, if we decide to give up
10, 20, 30 or 90% of the maximum amount of food produceable,
we can give out crude orders to transfer exactly 10, 20, 30 or
90% of both inputs from food to clothing. Because of constant
returns to scale, it follows that we can be sure of getting 90, 80,
70 or 10% of maximum clothing.
1 I am indebted for this line of reasoning to my colleague at M.I.T., Professor
Robert L. Bishop, who for some years has been using it on beginning students in
economics, with no noticeable disastrous effects. This proof is suggestive only,
but it could easily be made rigorous.
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1949] INTERNATIONAL FACTOR-PRICE EQUATISATION 185
In short, by giving such crude down-the-line orders that
transfer both resources always in the same proportion, we can at
worst travel along a straight line between the two limiting
intercepts. Any concave curve would necessarily lie inside such
a constant-cost straight line and can therefore be ruled out: hence
decreasing (marginal, opportunity) costs are incompatible with
the assumption of constant returns to scale.
But of course we can usually do even better than the straightline
case. A neophyte bureaucrat might be satisfied to give
crude down-the-line orders, but there exist more efficient ways of
giving up food for clothing. This is where social-economist (or
"welfare economist ") can supplement the talents of the mere
technician who knows how best to use inputs in the production
of any one good and nothing else. There are an infinity of ways
of giving up, say, 50% of food: we may simply give up labour,
or simply give up land, or give up constant percentages of labour
and land, or still other proportions. But there will be only one
best way to do so, only one best combination of labour and land
that is to be transferred. Best in what sense? Best in the sense
of getting for us the maximum obtainable amount of clothing,
compatible with our pre-assigned decision to sacrifice a given
amount of food.
Intuition tells us that, qualitatively, we should transfer a
larger proportion of labour than of land to clothing production.
This is because clothing is the labour-intensive commodity, by
our original hypothesis. This means that the proportion of
labour to land is actually declining in the food line as its production
declines. What about the proportion of labour to land in
clothing production? At first we were able to be generous in
sparing labour, which after all was not " too well adapted " for
food production. But now, when we come to give up still more
food, there is less labour left in food production relative to land;
hence, we cannot contrive to be quite so generous in transferring
further labour to clothing production. As we expand clothing
production further, the proportion of labour to land must also
be falling in that line; but the labour-land ratio never falls
to as low as the level appropriate for food, the land-intensive
commodity.'
1 Some readers may find it paradoxical that-with a fixed ratio of total labour
to total land-we nevertheless lower the ratio of labour to land in both industries
as a result of producing more of the labour-intensive good and less of the other.
Such readers find it hard to believe that men's wages and women's wages can
both go up at the same time that average wages are going down. They forget
that there is an inevitable shift in the industries' weights used to compute the
No. 234-vOL. LIX. 0
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186 THE ECONOMIC JOURNAL [JUNE
Intuition tells us that by following an optimal pattern which
recognises the difference in factor intensities of the two goods,
we can end up on a production possibility curve that is bloated
out beyond a constant-cost straight line: in short, on a production
possibility curve that is convex, obeying the law of increasing
marginal costs of one good as it is expanded at the expense of the
other good. Or to put the same thing in the language of the
market-place: as the production of clothing expands, upward
pressure is put on the price of the factor it uses most intensively,
on wages relative to land rent. An increase in the ratio of wages
to rent must in a competitive market press up the price of
the labour-intensive commodity relative to the land-intensive
commodity.
This one-directional relationship between relative factor
prices and relative commodity prices is an absolute necessity,
and it is vital for the recognition of the truth in the main
theorem. Let me elaborate therefore upon the market mechanism
bringing it about. Under perfect competition, everywhere
within a domestic market there will be set up a uniform ratio of
wages to rents. In the food industry, there will be one, and
only one, optimal proportion of labour to land; any attempt to
combine productive factors in proportions that deviate from the
optimum will be penalised by losses, and there will be set up a
process of corrective adaptation. The same competitive forces
will force an adaptation of the input proportion in clothing
production, with equilibrium being attained only when the input
proportions are such as to equate exactly the ratio of the physical
marginal productivities of the factors (the " marginal rate of
substitution " of labour for land in clothing production) to the
ratio of factor prices prevailing in the market. The price
mechanism has an unconscious wisdom. As if led by an invisible
hand, it causes the economic system to move out to the optimal
production-possibility curve. Through the intermediary of a
common market factor-price ratio, the marginal rates of substitution
of the factors become the same in both industries. And it
is this marginal condition which intuition (as well as geometry
and mathematics) tells us prescribes the optimal allocation of
resources so as to yield maximum output. Not only does
expanding clothing production result in the earlier described
average-factor ratio. Really to understand all this the reader must be referred
to the Edgeworth box-diagram depicted in W. F. Stolper and P. A. Samuelson,
" Protection and Real Wages," Review of Economic Studies, Vol. IX (1941), pp.
58-73.
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1949] INTERNATIONAL FACTOR-PRICE EQUALISATION 187
qualitative pattern of dilution of the ratio of labour to land in
both occupations; more than that, a price system is one way of
achieving the exactly optimal quantitative degree of change in
proportions.
I have established unequivocally the following facts:
Within any country: (a) a high ratio of wages to rents will
cause a definite decrease in the proportion of labour to land in
both industries; (b) to each determinate state of factor proportion
in the two industries there will correspond one, and only
one, commodity price ratio and a unique configuration of wages
and rent; and finally, (c) .that the change in factor proportions
incident to an increase tn wages must be followed by a one-rents
directional increase in clothing prices relative to food prices.
An acute reader may try to run ahead of the argument and
may be tempted to assert: " But all this holds for one country,
as of a given total factor endowment. Your established chain of
causation is only from factor prices (and factor proportions) to
commodity prices. Are you entitled to reverse the causation and
to argue that the same commodity-price ratio must-even in
countries of quite different total factor endowments-lead back
to a common unique factor-price ratio, a common unique way of
combining the inputs in the food and clothing industries, and a
common set of absolute factor prices and marginal productivities
? "
My answer is yes. This line of reasoning is absolutely
rigorous. It is only proportions that matter, not scale. In such
a perfectly competitive market each small association of factors
(or firm, if one prefers that word) feels free to hire as many or as
few extra factors as it likes. It neither knows nor cares anything
about the totals for society. It is like a group of molecules in a
perfect gas which is everywhere in thermal equilibrium. The
molecules in any one small region behave in the same way regardless
of the size of the room around them. A sample observed in
the middle of a huge spherical room would act in the same way
as a similar sample observed within a small rectangular room.
Similarly, if we observe the behaviour of a representative firm 1
in one country it will be exactly the same in all essentials as a
representative firm taken from some other country-regardless of
1 The representative firm concept is in the case of homogeneous production
functions not subject to the usual difficulties associated with the Marshallian
concept; in this case, it should be added, the " scale " of the firm is indeterminate
and, fortunately, irrelevant.
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188 THE ECONOMIC JOURNAL [JUNE
the difference in total factor amounts and relative industrial
concentration-provided only that factor-price ratios are really
the same in the two markets.
All this follows from the italicised conclusion reached just
above, especially from (c) taken in conjunction with (a) and (b).
This really completes the intuitive demonstration of the
theorem. The same international commodity-price ratio, must
so long as both commodities are being produced and priced at
marginal costs-enable us to infer backwards a unique factorprice
ratio, a unique set of factor proportions, and even a unique
set of absolute wages and rents.
W/R W/R
C
F
M N
C
pf /Pc E L/T
L
All this is summarised in the accompanying chart. On the
right-hand side I have simply duplicated Figure 2 of my earlier
paper. On the left-hand side I have added a chart sliowing the
one-directional relation of commodity prices to factor prices.' As
1 The left-hand curve is drawn in a qualitatively correct fashion. Actually
its exact quantitative shape is determined by the two right-hand curves; but
the chart is not exact in its quantitative details.
We may easily illustrate the importance of point (5) of our hypothesis, which
insists on differences in factor intensities. Consider the depicted pathological
W/R W/R
Pf /PF C L/T
case which does not meet the requirements of our hypothesis, and in which factor
intensities are for a range identical, and in still other regions food becomes the
labour-intensive good. The resulting pattern of commodity prices does not neces.
sarily result in factor-price equalisation. Cf. p. 175, n. 1 of my earlier article.
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1949] INTERNATIONAL FACTOR-PRICE EQUALISATION 189
wages fall relative to rents the price of food is shown to rise
relative to clothing in a monotonic fashion. The accompanying
chart applies to either country and-so long as neither country is
specialising completely-its validity is independent of their
differing factor endowments. It follows that when we specify
a common price ratio (say at L), we can move backward unambiguously
(from M to N, etc.) to a common factor-price ratio
and to a common factor proportion set-up in the two countries.
4. MATHEMATICAL PROOF
Now that the theorem has been demonstrated by commonsense
reasoning, let me confirm it by more rigorous mathematical
proof. The condition of equilibrium can be written in a variety
of ways, and can be framed so as to involve more than a dozen
equations. For example, let me call America's four marginal
physical productivities-of labour in food, of land in food, of
labour in clothing, of land in clothing-a, b, c and d. I use
Greek letters-oc, fi, y, 8-to designate the corresponding
productivities in Europe. Then we can end up with a number of
equilibrium expressions of the form
a c, a. y a =oc. ec
b _ ' 8CC_ y. et
A number of economists have tortured themselves trying to
manipulate these expressions so as to result in a = a, etc., or at
least ina = a etc. No proof of this kind is possible. T
essential thing is that these numerous marginal productivities are
by no means independent. Because proportions rather than scale
are important, knowledge of the behaviour of the marginal
productivity of labour tells us exactly what to expect of the
marginal-productivity schedule of land. This is because increasing
the amount of labour with land held constant is equivalent to
reducing land with labour held constant.'
1 J. B. Clark recognised in his Distribution of Wealth that the " -upper triangle"
of his labour-marginal-productivity diagram must correspond to the " rectangle"
of his other-factors diagram. But his draughtsman did not draw the curve
accordingly! This is a mistake that Philip Wicksteed in his Co-ordination of the
Laws of Distribution (London School of Economics Reprint) could not have made.
Clark, a believer in Providence, was unaware of the blessing-in the form of
Euler's theorem on homogeneous functions-that made his theory possible.
Wicksteed, a man of the cloth, appreciated and interpreted the generosity of
Nature. Cf. also F. H. Knight, Risk, Uncertainty and Profit, ch. IV, for a partial
treatment of these reciprocal relations. G. J. Stigler, Production and Distribution
Theories: the Formative Period, gives a valuable treatment of Wicksteed's theory
as exposited by Flux and others.
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190 THE ECONOMIC JOURNAL [JUNE
Mathematically, instead of writing food production, F, as any
joint function of labour devoted to it, Lf, and of land, Tf, we can
write it as
F _ F(Lp Tf) Tff(L) . . . (1)
where the function f can be thought of as the returns of food on
one unit of land, and where the number of units of land enters
as a scale factor. The form of this function is the same for both
countries; and there is, of course, a similar type of function
holding for cloth production, C, in terms of LC and TC namely
C = C(Lc TC) = T, . . . (2)
It is easy to show mathematically, by simple partial differentiation
of (1), the following relations among marginal physical
productivities
aF , L
M.P.P. labour in food
where f' represents the derivative of f and depicts the schedule
of marginal product of labour (working on one unit of land).
This must be a declining schedule according to our hypothesis of
diminishing returns, so that we must have
ftf< 0.
By direct differentiation of (1), or by use of Euler's theorem, or
by use of the fact that the marginal product of land can also be
identified as a rent residual, we easily find that
M.P.P. land in food = - f (Lf\ Lff(Lf) -(Lf'
Tf Tf) Tf\Tf/ Tf/
where g is the namne for the rent residual. It
Lf (Tf =- f(By
similar reasoning, we may write the marginal productivity
of land in clothing production in its proper relation to that of
labour
M.P.P. labour in clothing c
M.P.P. land in clothing' - _ '(i =h(7)aTc (c) TC TC TC
h, LmC = CI ,csLch
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1949] INTERNATIONAL FACTOR-PRICE EQUALISATION 191
The art of analysis in these problems is to select out the
essential variables so as to reduce our equilibrium equations to
the simplest form. Without specifying which country we are
talking about, we certainly can infer from the fact that something
of both goods is being produced with both factors the following
conditions:Real
wages (or labour marginal " value " productivities)
must be the same in food and clothing production when
expressed in terms of a common measure, such as clothing;
the same is true of real rents (or land marginal " value"
productivities). Or
(food price) (M.P.P. labour in food)
= (clothing price) (M.P.P. labour in clothing)
(food price) (M.P.P. land in food)
= (clothing price) (M.P.P. land in clothing)
which can be written in terms of previous notation I as
(PC) Tf) (T )
(Pf ) L(f ) f I (f Le L L6(c T)] ?
Now these are two equations in the three variables
and !X If we take the latter price ratio as given to us by
national-demand conditions, we are left with two equations to
determine the two unknown factor proportions. This is a solvent
situation, and we should normally expect the result to be
determinate.
But a purist might still have doubts: " How do you know
that these two equations or schedules might not twist around and
intersect in multiple equilibria? " Fortunately, the answer is
simple and definite. On our hypothesis, any equilibrium configuration
turns out to be absolutely unique. We may leave to
a technical footnote the detailed mathematical proof of this
fact.2
In terms of our earlier a, b, . . ., oc, , . . ., these equations are of the
p.ta =-c, Pb =d, etc.?a?
2 The Implicit Function Theorem tells us that two suitably continuous
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192 THE ECONOMIC JOURNAL [JUN3E
5. MULTIPLE COMMODITIES AND FACTORS
Adding a third or further commodities does not alter our
analysis much. If anything, it increases the likelihood of complete
factor-price equalisation. For all that we require is that at
least two commodities are simultaneously being produced in both
countries and then our previous conclusion follows. If we add a
third commodity which is very much like either of our present
commodities, we are not changing the situation materially. But
if we add new commodities which are more extreme in their
labour-land intensities, then we greatly increase the chance that
two regions with very different factor endowments can still come
into complete factor-price equalisation. A " queer " region is not
penalised for being queer if there is queer work that needs doing.
I do not wish at this time to go into the technical mathematics
of the n commodity, and r factor case. But it can be said
that: (1) so long as the two regions are sufficiently close together
in factor proportions, (2) so long as the goods differ in factor
intensities, and (3) so long as the number of goods, n, is greater
than the number of factors, r, we can hope to experience complete
factor-price equalisation. On the other hand, if complete
specialisation takes place it will do so for a whole collection of
goods, the dividing line between exports and imports being a
variable one depending upon reciprocal international demand
(acting on factor prices) as in the classical theory of comparative
advantage with multiple commodities.'
equations of the form W1(Y1, Y2) = 0 = W2(y1, Y2), possessing a solution (Yi0, Y2?)
cannot have any other solution provided
Cw1 CwY
AYi aY2
aW2 OW2
5YI OY2
In this case, where Y, = Lf/Tf, etc., it is easy to show that
-c" L, Lf]
|- f! + L, P0 T0 T1
By hypothesis of diminishing returns f" and c" are negative, and the term in
brackets (representing the respective labour intensities in food and clothing)
cannot be equal to zero. Hence, the equilibrium is unique. As developed
earlier, if the factor intensities become equal, or reverse themselves, the one-to-one
relation between commodity and factor prices must be ruptured.
1 The real wage of every resource must be the same in every place that it is
used, when expressed in a common denominator. This gives us r (n - 1)
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1949] INTERNATONAL FACTOR-PRICE EQUALISATION 193
When we add a third productive factor and retain but two
commodities, then the whole presumption towards factor-price
equalisation disappears. Suppose American labour and American
land have more capital to work with than does European labour
and land. It is then quite possible that the marginal physical
productivities of labour and land might be double that of Europe
in both commodities. Obviously, commodity-price ratios would
still be equal, production of both commodities will be taking
place, but nonetheless absolute factor prices (or relative for that
matter) need not be moved towards equality. This is our general
expectation wherever the number of factors exceeds the number of
commodities.
6. THE CONDITIONS OF COMPLETE SPECIALISATION
If complete specialisation takes place in one country, then
our hypothesis is not fulfilled and the conclusion does not follow.
How important is this empirically, and when can we expect
complete specialisation to take place ? As discussed earlier, the
answer depends upon how disparate are the initial factor endowments
of the two regions-how disparate in comparison with the
differences in factor intensities of the two commodities.'
Unless the two commodities differ extraordinarily in factor
intensities, the production-possibility curve will be by no means
so convex as it is usually drawn in the neo-classical literature of
international trade, where it usually resembles a quarter circle
whose slope ranges the spectrum from zero to infinity. It should
rather have the crescent-like shape of the new moon. Opportunity
costs tend to be more nearly constant than I had previously
realised. This is a step in the direction of the older classical
theory of comparative advantage. But with this important
difference: the same causes that tend to produce constant costs
also tend to produce uniform cost ratios between nations, which
independent equations involving the (n - 1) commodity-price ratios and the
n(r- 1) factor proportions. If n r, we have a determinate system once the
goods price ratios are given. If n > r, we have the same result, but now the
international price ratios cannot be presented arbitrarily as there are constantcost
paths on the production-possibility locus, with one blade of Marshall's
scissors doing most of the cutting, so to speak. If n < , it is quit6 possible for
free commodity trade to exist alongside continuing factor-price differentials. It
is never enough simply, to count equations and unknowns. In addition we
must make sure that there are not multiple solutions: that factor intensities in
the different commodities and the laws of returns are such as to lead to a one-toone
relationship between commodity prices and factor prices.
1 The reader may be referred to the earlier paper's discussion of Figures 1
and 2, with respect to " step-like formations " and overlap.
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194 THE ECONOMIC JOURNAL [JUNE
is not at all in the spirit of classical theory. (Undoubtedly much
of the specialisation observed in the real world is due to something
different from all this, namely decreasing-cost indivisibilities,
tempered and counteracted by the existence of localised resources
specifically adapted to particular lines of production.)
A parable may serve the double purpose of showing the range
of factor endowment incompatible with complete specialisation
and of removing any lingering element of paradox surrounding
the view that commodity mobility may be a perfect substitute for
factor mobility.
Let us suppose that in the beginning all factors were perfectly
mobile, and nationalism had not yet reared its ugly head. Spatial
transport costs being of no importance, there would be one
world price of food and clothing, one real wage, one real rent,
and the world's land and labour would be divided between food
and clothing production in a determinate way, with uniform proportions
of labour to land being used everywhere in clothing
production, and with a much smaller-but uniform-proportion
of labour to land being used in production of food.
Now suppose that an angel came down from heaven and
notified some fraction of all the labour and land units producing
clothing that they were to be called Americans, the rest to be
called Europeans; and some different fraction of the food industry
that henceforth they were to carry American passports.
Obviously, just giving people and areas national labels does not
alter anything: it does not change commodity or factor prices or
production patterns.
But now turn a recording geographer loose, and what will he
report ? Two countries with quite different factor proportions,
but with identical real wages and rents and identical modes of
commodity production (but with different relative importances
of food and clothing industries). Depending upon whether the
angel makes up America by concentrating primarily on clothing
units or on food units, the geographer will report a very high or
a very low ratio of labour to land in the newly synthesised
" country." But this he will never find: that the ratio of
labour to land should ever exceed the proportions characteristic
of the most labour-intensive industry (clothing) or ever fall short
of the proportions of the least labour-intensive industry. Both
countries must have factor proportions intermediate between the
proportions in the two industries.
The angel can create a country with proportions not interThis
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1949] INTERNATIONAL FACTOR-PRICE EQUALISATION 195
mediate between the factor intensities of food and clothing. But
he cannot do so by following the above-described procedure, which
was calculated to leave prices and production unchanged. If he
wrests some labour in food production away from the land it has
been working with, " sending " this labour to Europe and keeping
it from working with the American land, then a substantive
change in production and prices will have been introduced.
Unless there are abnormal repercussions on the pattern of effective
demand, we can expect one or both of the countries to speciallse
completely and real wages to fall in Europe relative to America in
one or both commodities, with European real rents behaving in
an opposite fashion. The extension of this parable to the manycommodities
case may be left to the interested reader.
7. SOME QUALIFICATIONS
A number of qualifications to this theoretical argument are
in order. In the first place, goods do not move without transport
costs, and to the extent that commodity prices are not equalised
it of course follows that factor prices will not tend to be fully
equalised. Also, as I indicated in my earlier article, there are
many reasons to doubt the usefulness of assuming identical
production functions and categories of inputs in the two countries;
and consequently, it is dangerous to draw sweeping practical
conclusions concerning factor-price equallsation.
What about the propriety of assuming constant returns to
scale? In justice to Ohlln, it should be pointed out that he,
more than almost any other writer, has followed up the lead of
Adam Smith and made increasing returns an important cause for
trade. It is true that increasing returns may at the same time
create difficulties for the survival of perfect competition, difficulties
which cannot always be sidestepped by pretending that
the increasing returns are due primarily to external rather than
internal economies. But these difficulties do not give us the
right to deny or neglect the importance of scale factors.1 Where
1 Statical increasing returns is related to, but analytically distinct from, these
irreversible cost economies induced by expansion and experimentation and which
provide the justification for " infant industry " protection. Statical increasing
returns might justify permanent judicious protection but not protection all
around, since our purpose in bringing about large-scale production is to achieve
profitable trade and consumption.
One other point needs stressing. For very small outputs, increasing returns to
scale may take place without affecting the above analysis provided that total
demand is large enough to carry production into the realm of constant returns to
scale. Increasing the " extent of the market " not only increases specialisation,
it also increases the possiblity of viable pure competition.
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196 THE EiCONOMIC JOURNAL [JUNE
scale is important it is obviously possible for real wages to differ
greatly between large free-trade areas and small ones, even with
the same relative endowments of productive factors. And while
it may have been rash of me to draw a moral concerning the
worth of emigration from Europe out of an abstract simplified
model, I must still record the view that the more realistic deviations
from constant returns to scale and the actual production
functions encountered in practice are likely to reinforce rather
than oppose the view that high standards of life are possible in
densely populated areas such as the island of Manhattan or the
United Kingdom.
There is no iron-clad a priori necessity for the law of diminishing
marginal productivity to be valid for either or both commodities.1
In such cases the usual marginal conditions of
equilibrium are replaced by inequalities, and we have a boundary
maximum in which we go the limit and use zero of one of the
inputs in one industry. If it still could be shown that one
commodity is always more labour intensive than the other, then
the main theorem would probably still be true. But it is precisely
in these pathological cases that factor intensities may become
alike or reverse themselves, giving rise to the difficulties discussed
in my earlier footnote on p. 188.
In conclusion, some of these qualifications help us to reconcile
results of abstract analysis with the obvious facts of life concerning
the extreme diversity of productivity and factor prices in different
regions of the world. Men receive lower wages in some countries
than in others for a variety of reasons: because they are different
by birth or training; because their effective know-how is limited
and the manner of their being combined with other productive
factors is not optimal; because they are confined to areas too small
to develop the full economies of scale; because some goods and
materials cannot be brought to them freely from other parts of the
world, as a result of natural or man-made obstacles; and finally
because the technological diversity of commodities with respect to
factor intensities is not so great in comparison with the diversity
1 A " Pythagorean " production function of the form P = VL2 + T2 is an
example of such a homogeneous function with increasing marginal productivity.
So long as neither factor is to have a negative marginal productivity, average
product must not be rising; but this is quite another thing. Surprisingly enough,
the production possibility curve may still be convex with increasing marginal
productivity. I have been asked whether any essential difference would be
introduced by the assumption that one of the commodities, such as clothing, uses
no land at all, or negligible land. Diminishing returns would still affect food as
more of the transferable factor is added to the now specific factor of land; but
no essential modifications in our conclusions are introduced.
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1949] INTERNATIONAL FACTOR-PRICE EQUALISATION 197
of regional factor endowments to emancipate labourers from the
penalty of being confined to regions lacking in natural resources.
In the face of these hard facts it would be rash to consider the
existing distribution of population to be optimal in any sense,
or to regard free trade as a panacea for the present geographical
inequalities.
PAUL A. SAMUELSON
Massachusetts Institute of Technology.
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