Ohlin Was Right Author(s): Paul A. Samuelson Source: The Swedish Journal of Economics, Vol. 73, No. 4 (Dec., 1971), pp. 365-384 Published by: Wiley on behalf of The Scandinavian Journal of Economics Stable URL: http://www.jstor.org/stable/3439219 Accessed: 21-06-2017 11:22 UTC REFERENCES Linked references are available on JSTOR for this article: http://www.jstor.org/stable/3439219?seq=1&cid=pdf-reference#references_tab_contents You may need to log in to JSTOR to access the linked references. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://about.jstor.org/terms The Scandinavian Journal of Economics, Wiley are collaborating with JSTOR to digitize, preserve and extend access to The Swedish Journal of Economics This content downloaded from 147.251.185.127 on Wed, 21 Jun 2017 11:22:30 UTC All use subject to http://about.jstor.org/terms OHLIN WAS RIGHT* Paul A. Samuelson Massachusetts Institute of Technology, Cambridge, Mass., USA I was originally led to study the problem of complete factor-price e tion by the need to explain to a class in international trade Bertil O seminal proposition that, although free mobility of factor inputs in national trade will equalise factor returns all the way, free mobility o can serve only to move factor-prices toward (but not all the way to) price equalisation. As has been discussed elsewhere,' I found I could n prove the last part of the Ohlin proposition, that factor-price equa by trade would have to be necessarily partial and incomplete. Indeed, case where there are zero transport costs, no complete specialization in country, and where two goods are strongly relative factor-intensive i respective inputs of the two inputs available to society, with the sam of knowledge operative everywhere, I ended up proving that Ohlin was w in the Pickwickian sense of being less than right: namely I proved later learned Abba Lerner had done more than a decade earlier in an unpublished paper at the London School of Economics) that there would to be more than partial factor-price equalisation--there would have t full factor-price equalisation.2 I. Vindication Recently in another connection I presented a simple, but rigorous, mo general equilibrium in international trade that could be expressed in ter the two-dimensional diagrams of Marshall's partial equilibrium suppl * Thanks go to the National Science Foundation for financial aid and to Mary T for editorial assistance. My score of indebtedness, mounting over the years, to B. Ohlin, Interregional and International Trade (Harvard University Press, Cambridge, Mass., 1933) will be self-evident. Forty years have not aged this classic which sprang full-blown from the brow of its youthful author. 1 P. A. Samuelson, "International Trade and the Equalisation of Factor Prices", Economic Journal, Vol. 58 (1948), pp. 163-184. The vast literature on this topic is surveyed in P. A. Samuelson, "Summary on Factor-Price Equalisation", International Economic Review, Vol. 58 (1967), pp. 286-295, where reference is made to the contributions of Lerner, Tinbergen, Meade, Pearce, McKenzie, Nikaido-Gale, and many others. a To my knowledge only one support for the necessarily-incomplete equalisation thesis appeared in the literature. H. Uzawa, "Prices of the Factors of Production in International Trade", Econometrica, Vol. 27 (1959), pp. 448-468, sets forthin Section 6 alineardemand model in which necessarily-incomplete-equalisation was deduced: unfortunately, the Uzawa functions were assumed to have single-valuedness properties which contradict the constant-returns-to-scale technologies presupposed in the discussions; hence the argument is not germane. Uzawa does quote Haberler's approval of the Ohlin thesis, but that approval may well have had reference to realistic transport costs for goods which, all are agreed, will present complete equalisation of either goods' prices or factors' prices. Swed. J. of Economics 1971 This content downloaded from 147.251.185.127 on Wed, 21 Jun 2017 11:22:30 UTC All use subject to http://about.jstor.org/terms 366 P. A. Samuelson demand. The supply conditions of that model are of interest for the sake since they portray what might be called the Ricardo-Viner case rent.2 They provide what this intricate subject can use to advantage, ternative simple model that can free the discussion from the straigh of the box-diagram analysis which Stolper and I imposed on the trad ture decades ago.3 My old classmate from Chicago days, Martin Bronfenbrenner, recently to complain that I had not explained the implications of the new mo factor-price equalisation. Always game to try to fill any pointed-out I proceeded to provide that analysis. The conclusion of the effort wa After all, Bertil Ohlin's contention for partial but not total factor equalisation is essentially vindicated in this technological model. It is the purpose of the present paper to describe these findings. II. Graphical Resum6 Before turning to the new model, I show in Fig. 1 a self-contained su of how free mobility in goods must compensate completely in the Le muelson model for immobility of factors in equalising factor returns, pr two regions differ by not too much in geographical endowments. The post-trade situation, the heavy SPEP'S' locus, is contrasted with the n light NT locus and with the Ohlin-thesis broken line OH locus. The horizontal axis portrays the labour/land endowment in Regio ratio to that in Region B. Equality is at 1, the intersection of the ax vertical axis portrays the wage/rent outcome in Region A relative to B. The reader might, for simplicity, think of Region B as vastly greater Region A; then he can imagine the relative endowment of Region A d by more and more from unity in either direction. (If the goods come to 1 P. A. Samuelson, "An Exact Hume-Ricardo-Marshall Model of Internationa Journal of International Economics, Vol. 1 (1971), pp. 1-18. There is also my con to the Kindleberger Festschrift (ed. J. Bhagwadi et al.), Trade, Balance of Paym Growth (North Holland Publishing Co, Amsterdam, 1971), Part 6, Chapter 15 the Trail of Conventional Beliefs About the Transfer Problem". Although the pr per adopts the industry-supply relations of these papers, it abandons their Ma partial-equilibrium demand relations. SViner's famous 1931 article, "Cost Curves and Supply Curves", in which the dra Wong will not draw the envelope of costs incorrectly despite Viner's insistence, the case. The original reference is to the 1931 Zeitschrift fiTr Nationalekconomie, article has been reproduced in many anthologies and the reader is best advised t a version which includes a new appendix written a decade later. Cf. K. E. Bo G. J. Stigler, Readings in Price Theory (Richard D. Irwin, Inc., Chicago, 1952), 1, pp. 198-232. 9 W. A. Stolper & P. A. Samuelson, "Protection and Real Wages", Review of E Studies, Vol. 9 (1941), pp. 58-73. Swed. J. of Economics 1971 This content downloaded from 147.251.185.127 on Wed, 21 Jun 2017 11:22:30 UTC All use subject to http://about.jstor.org/terms Ohlin was Right 367 Relative Factor Prices 0 N E PRelative P 1 Factor Endowments S' Fig. 1. As Region A's relative factor endowments diverge in ratio to Region B's from equality or unity, the No-Trade locus, NT, shows that inequality of relative factor prices can be expected under autarky. With trade serving to raise the demands for the cheap factor in each region, Ohlin claimed that the OH locus of partial but incomplete factorprice equalisation would result. However, the Lerner-Samuelson model is seen to have complete factor-price equalisation on the PEP' horizontal branch of SPEP'S'. Once complete regional specialization on a single commodity is induced, the SP branch shows that the wage-rent ratios are only partially equalised in the Ohlin manner, even for the Lerner-Samuelson model; and partial transport costs would produce a similar effect. change factor intensities at distant factor prices, the S'P' branch could encounter another horizontal branch below the horizontal axis.)' As Ohlin was the foremost to emphasize, difference in regional tastes can offset difference in regional factor endowments. Therefore, if both countries are of a comparable size, we can sidestep, or isolate, taste-difference complications by assuming the same tastes for all consumers all over the world no matter what their incomes ("uniform, homothetic preferences").2 III. The Ricardo-Viner case This model assumes labour to be the only input transferable between indus tries. If labour worked alone at constant returns, this would give us the con stant-cost case of classical comparative advantage. If, in addition, the laws 1 Positive transport costs for the goods, of a constant percentage of price per unit, would cause the horizontal branches through P and P' to lie, respectively, above and below the horizontal axis, each terminating in the no-trade locus (which will, in the close neighborhood of E, be alone relevant). 2 For derivation of the concept of social product in the simplifying case of homethetic, uniform tastes, see my contribution to the Hicks Festschrift (ed. J. N. Wolfe), Value, Capital and Growth (Edinburgh University Press, 1968), Ch. 19, "Two Generalizations of the Elasticity of Substitution", pp. 467-80, particularly Part II on homothetic genera equilibrium and equation (20). Swed. J. of Economics 1971 This content downloaded from 147.251.185.127 on Wed, 21 Jun 2017 11:22:30 UTC All use subject to http://about.jstor.org/terms 368 P. A. Samuelson w M.P.P. Li P_1 total rent product labour cost Li Qi 2 Labour Output Clothing (a) (b) (c) Fig. 2. For a typi in (a) and (b) resp L,, half and half concave (from be working in each the case where b labour costs only of knowledge w functions were tion costs (no occur. The kiss of Ohlin's analysis of increasing returns wo sleeping beauty of international trade even in a one f in this paper we turn our backs on this aspect of Oh and stay with the constant returns-to-scale assumption. We go on to assume that there typically works with lab a non-transferable "land" specialized to that industry land).' Figs. 2a and 2b show the familiar marginal product and marginal cost curves. Fig. 2c shows the resulting regional bowed-out production-probability frontier. It looks like the similar frontiers of the Stolper-Samuelson model but now it could be a quarter circle with absolute slope running the gamut from 0 to infinity or 00 to 900. IV. One Region-Analysis Within a single isolated region, the relative prices of goods (food and clothing) and relative factor prices (wages, food-land, clothing-land rents) will depend on the relative scarcity of the factors (labour, food-land, clothing- 1 There could be more than one kind of specialized land, as we shall analyze. Swed. J. of Economics 1971 This content downloaded from 147.251.185.127 on Wed, 21 Jun 2017 11:22:30 UTC All use subject to http://about.jstor.org/terms Ohlin was Right 369 land). The emerging general equilibrium will, of course, depend also on demand-tastes; but in the simplifying case where all tastes are uniform at all income levels, the system is in effect producing social product-i.e. food-clothing units whose constituent components depend only on the relative goods, prices once tastes are specified. Labour abundance. Within a single region it is easy to see that an increasing abundance of any one factor-say, labour, first-will lower the real wage. Under our homothetic assumption, it must raise the output of both food and clothing, and hence by the law of diminishing returns to variable labour applied to fixed lands, the real wage will have to fall in terms of both goods and a fortiori in terms of social real product. By the same law, real rent of foodland must rise in terms of food; real rent of clothing-land must rise in terms of clothing. But we have no way of knowing what increased labour abundance will do to the relative price of food and clothing. This could remain unchanged. Or, if food production happened to be more expandable by variable labour than is clothing production-as in the Cobb-Douglas case where labour's share in food costs exceeds its share in clothing costs-increased labour abundance must raise the ratio of clothing price to food price; hence the real foodland rent in terms of clothing need not necessarily be raised by labour abund- ance. What about the effect of labour abundance on the r land in terms of social product itself? No invariable r There is perhaps a presumption that labour abundanc any land's real rent-certainly all lands' rents togethe it is possible that the deterioration of food-land's real wa ing could be so great as to make it drop in terms of so Summary. Labour abundance raises the real rents of each l products. Relative prices can move in either direction strongly labour encounters diminishing returns in various lar good's relative price is much raised, the other land m real rents relative to it (and even relative to social product A balanced increase in both lands is just like a reduct rents together are lowered in terms of social product as terms rises (along a reversible two-variable "factor-price f Fig. 3a summarizes the effect of labour abundance possibility frontier. The new equilibrium must involve otherwise there are no restrictions on the possibilities.2 1 If labour and food-land are infinitely great substitutes and la infinitely-strong complements, the "perverse" result will follow 2 To prove this, suppose the contrary that one good, say fo price would then rise relative to that of clothing. But how th of clothing have been coaxed out? Thus we are led to the pr must increase. Swed. J. of Economics 1971 This content downloaded from 147.251.185.127 on Wed, 21 Jun 2017 11:22:30 UTC All use subject to http://about.jstor.org/terms 370 P. A. Samuelson Q1 01 EE Q2 2 clothing clothing la) (b) F ig. 3. (a) Labour ab goods and affecting diminishing returns of social product; t land pivots the prod ing intercept at Z. The price of food w fall in terms of all tion, the real rent wage. If the food-c here), the real rent food. Food-land-abundance. We may briefly describe the increase, in a closed economy with Ricardo-Viner technology and homothetic demand, of an increase in one land alone, say food-land. As Fig 2a shows, this tilts the production-possibility frontier vertically around the unchanged intercept of maximum clothing production. Hence food must be cheapened relative to clothing. The legend to Fig. 2a describes the reduction in food-land rent and probable1 increase in the real wage and real clothing-land rents. Summary. An increase in food-land lowers its real rent and the relative price of food. It will necessarily raise the real rent return of one other factor, labour- or clothing-land; it must raise their combined return. Elasticity-of-substitution of final demand tends to bring down clothing-land rent as food-land increases. Although food-land abundance always raises the real wage in terms of food, clothing might become so dear that the real wage in clothing could fall, and fall enough to reduce the real wage in terms of social product. 1 Real social product is a concave homogenous-first-degree function of labour, food-land, clothing-land, q = q( V0, V1, V2), with real factor prices in terms of social product given by [85q/V] = [wo, w1, w,] and [aw/aV ] = [82a'q/8VaV ]= [aw8V/V]. For any i, one aw f3Vi must be positive. The symmetry of this Hessian matrix tells us that the case described two footnotes back, in which an increase in labour reduces real food-land rent, must here invoke a reduction in food land. Swed. J. of Economics 1971 This content downloaded from 147.251.185.127 on Wed, 21 Jun 2017 11:22:30 UTC All use subject to http://about.jstor.org/terms Ohlin was Right 371 Factor shares. So far I have been discussing effects of a factor change on relative-factor and good prices. What about relative factor shares? Classical economists of Ricardo's day were perhaps susceptible to the confusion that an increase in a factor-price, as e.g. land rent, also means an increased share of rent in national income. We know that shares can move in any direction, depending upon elasticities of productivity and on elasticities of substitution. How relative shares are affected by factor-augmenting substitution, in which one of a factor now does the work of more than one, will depend on those same elasticities. Cobb-Douglas case. Before leaving the closed economy, I should describe the double Cobb-Douglas case in which the proportions of the consumer dollar spent on the different goods are constant and the proportions of each industry's costs going to labour are also constant. In this case social output is itself a simple Cobb-Douglas function of the three factors 2 0 Thus, suppose labour always gets three-fourths of national income with foodland getting 0.15 and clothing-land 0.10. Then [ko, kIc, kE,] =[0.75, 0.15, 0.10]. This would result from a 0.70 labour share in food, a 0.80 labour share in clothing, and fifty-fifty expenditure on the two goods. If [21, 22] are labour's shares in the two industries and [aLx1, cc2] are the good's share of consumption dollar, k0-x121?cc222z, Ic1=oc1(1-2), k2 a2(122L) 1c = oci(1 -As) In general, for any double Cobb-Douglas model, not necessarily Ric Viner in technology, the factor shares in national income, [klc], are relat the factor shares in the jth industry, [kL,], and the shares of the j i of the consumption dollar, [2,], by the matrix identity, [ks] = [Icu][ccl The Cobb-Douglas case displays no perverse properties, as the fol shows. Summary. Increasing any factor lowers its real return, raises the real re all other factors, and lowers the relative price of the good in which its f cost-share is relatively largest. V. Various Geographical Endowments and Trade Identical Endowments. If two regions have the same endowments of Swed. JT. of Economics 1971 This content downloaded from 147.251.185.127 on Wed, 21 Jun 2017 11:22:30 UTC All use subject to http://about.jstor.org/terms 372 P. A. Samuelson food-land, and clothing-land, uniformity of tastes will produce id tor-prices, commodity prices and of course no international trade. If the two regions differ in scale, but all factor proportions are the same absolute equalisation will result under our assumption of (homothetic) tastes. Not only will there be no international trade even if factors could move between regions, there would be no in them to do so. Disproportionate endowments. Suppose Region A has relatively more foodland, Region B has relatively more clothing-land. Before trade, A will have relatively cheap food and B will have relatively cheap clothing. Real wages could be about equal in the two regions, the cheapness of one good just balancing the dearness of the other. Regional real outputs could also happen to be equal; but of course food-land rents would still be relatively low in A and clothing-land rents relatively low in B. If free trade is allowed, A will export food in exchange for B's exporting clothing. Both regions will be better off at the equalised commodity prices With the international price ratio of clothing to food lower than Region A's autarky prices, A will shift labour from clothing to food thereby somewhat easing the redundancy and cheapness of its abundant factor, food-land. In B, trade has the opposite effect causing it to produce for export the good for which it has factor abundance: shifting labour from food to clothing tends to relieve the dearness of its scarce factor and relieve the cheapness of its plentiful factor. All this leads, in the Ohlin manner, to partial but not complete factor-price equalisation. To depict this Fig. 4 shows the autarky equilibrium for Region A at a, and for Region B at b. Region B happens to have the higher national product by virtue of its superabundance of, say, food-land. Perhaps its autarky real wage is also higher. Fig. 4 also shows the effects of the free interregional trade. A's final equilibrium is at Ea and and a'; B's final equilibrium is at E, and b'; the common international price ratio, which is intermediate between the two autarky prices, is found on that common ray-from-the-origin, OE, E,, at which the regions' trade vectors a'Ea and Eb' exactly match. Both regions get improved national products, GNP's, from trade. But in each region there is a shift in production toward greater specialization on the good which is relatively intensive in its abundant factor; these trade-induced shifts in production raise the relative factor prices of each region's relatively abundant factor from its autarky cheapness, thereby tending to equalise factor prices internationally. If Region A ends up with a real wage higher than in autarky but still lower than that in Region B, the tendency toward equalisation will not have gone all the way; it will have been only partial, in vindication of Ohlin's original contention. Swed. J. of Economics 1971 This content downloaded from 147.251.185.127 on Wed, 21 Jun 2017 11:22:30 UTC All use subject to http://about.jstor.org/terms Ohlin was Right 373 Q1 a' clothin Q2 clothing Fig. 4. Region B, above, has more food-land than Region A. In autarky, A at a has higher clothing-land price than B; at its autarky point b, Region B has relatively lower real rent of food-land. Free trade leads to equilibrium at Ea and Eb, where trade vectors a'Ea and Ebb' exactly match, and where the common international price ratio is between the autarky price ratios. Each region increases production of that good which has much of its relatively abundant factor: the move from b to b' involves shift of labour in B to food production, thereby relieving the cheapness of food-land and the dearness of clothingland there; the move from a at a' has similar Ohlin influence, relieving the cheapness of A's relatively plentiful resource. Trade in goods partially equalises factor prices. [Alternate interpretation of diagram: suppose B has more labour than A, and food is more labour intensive than clothing. The production shifts due to trade then alleviate the dearness of A's labour and the cheapness of B's abundant labour.] VI. Need for Factor Mobility Mobility of goods has not been able to serve as a complete substitute for factor mobility in equalising all factor prices. With after-trade real wages lower in A than in B (in all goods!), labour has motivation to migrate from A to B if there are now no costs to such migration. As more and more labour migrates, A's real wage rises and B's falls. Finally, they must come into equality, at which point migration will cease. The present Viner-Ricardo technology has the remarkable property that none of the factors other than labour need migrate to achieve optimal world production and complete factor-price equali- sation! Theorem. In a general technology, when goods' prices are equalised by free trade, all the different factors may have unequal factor returns; factor-mobility in all but one of the factors will generally be needed to achieve full factor-price equalisation and maximal world production. In a Viner-Ricardo technology, where labour is the only resource transferable between industries, it will always suffice for labour alone to be capable of migration to achieve full factor-price equalisation. To prove this strong result, note that if the real wage at Ea is less (in every good) than at E,, the fact that each region produces every good implies that rSwed. J. of Economics 1971 This content downloaded from 147.251.185.127 on Wed, 21 Jun 2017 11:22:30 UTC All use subject to http://about.jstor.org/terms 374 P. A. Samuelson every real rent is greater in Region A than in B. A glance back confirms that, within each and every industry, there is a uniqu between its real wage and real rent.1 By the same token, as migration from A to B proceeds far enough to achieve real-wage equality, it all of A's real rents into exact equality with B's rising real rents, The point is that if the mountains will not come to Mohammed, Mo can go to the mountains. It does not matter that there are now m of mountains-food-land, clothing-land, etc. For, these mountains d to interact with each other, but each need only interact with labour. ity of labour migration to compensate by itself for immobility of all factors will hold in a Viner-Ricardo technology for any number n > 2, provided labour works with one specialized resource in each It fails to hold wherever one or more industries involve more than one nonlabour factor, which are distributed in unequal proportions among th gions: e.g., suppose the food-industry in Region A involves a different of (food-land)' to (food-land)" than the ratio prevailing in Region B; t complete factor-price equalisation would involve, if you can imagine it, gration of one of these food-lands as well as labour. VII. The Singular Case of Complete Equalisation By Trade The case in the previous section, in which Region B begins with relati more of food-land but in which labour migrates from A to B to equalis factor prices, alerts us to an interesting possibility. Evidently there ca situations in which free trade in goods will alone suffice to equlaise fac returns all the way. Consider the geographical configuration after labour has migrated eno to equalise the free-trade real wage. Region B still has more of food-l than does Region A. Suppose trade in goods is now prohibited, then aut regimes will involve lower food-land rents in B, lower clothing-land ren A, and lower food-clothing price ratio in B than A.2 x This suggests a slight paradox. Region A began with relatively much clothing-lan hence at autarky a presumably began with lower real clothing-land rent than a autarky point b. But free trade ended A with higher real clothing-land rent, rs, than Hence, goods' mobility caused on overshoot in which this factor-price went from d gence in one direction over to divergence in the opposite direction. On reflectio perceive no reason why this should not occur. 2 The autarky real wage in terms of clothing will presumably be higher in A; in B autarky real wage will presumably be higher in terms of food. Which region will have higher autarky real wage in terms of social product---that is, which region will workers "better off"-we cannot say. Suppose the real wage, w = WIP, happens the same in both regions. Then even if labour could migrate, it would not choose to Why should it? Consequently, in the absence of goods' trade, the world will be stuck manently in a geographical configuration which fails to maximize total world produ of food and clothing. More precisely, we are not out on the world's maximal producA B A B possibility frontier of (Q = QAA B A B A B LA + LB, = V1 + V1, V = Va + Vs). But, if goods cannot be freely moved, what signi-ficance is there to a sum like Qj + QI? Swed. J. of Economics 1971 This content downloaded from 147.251.185.127 on Wed, 21 Jun 2017 11:22:30 UTC All use subject to http://about.jstor.org/terms Ohlin was Right 375 ,9, b labour labour (a) Lerner-Samuelson Model (b) Fig. 5. In the 5(a) model, all have complete factor-priceIn the present 5(b) model, o razor's edge will have equali These geographical diverg two out of three factors o would world total produc frontiers, be maximized in In short, only with free migrate in order to maxim rem about Ricardo-Viner for them, some mountain tain. But now revert to the s the complete equalisation movements from this po trade will equalise all fac all factor returns, and sinc produced a case in which happens to lead to complete This singular case resem it contradicts the Uzawa complete factor-price equ re-examines Ohlin's argu terpret him to believe t likely rather than that c sible.' Ohlin, as a followe wise. Ohlin's weaker dictum, that partial rather than complete equalisation most likely, is confirmed, not refuted, by the present singular case. Thus, t 1 It is Ellsworth's textbook, in its attempt to provide a proof for Ohlin, that does purp to demonstrate the logical impossibility of complete equalization. Cf. my 1948 discu of P. T. Ellsworth, International Economics (MacMillan, London 1937). In a real sense present singular case does refute what might be called the Ellsworth-Uzawa content Swed. J. of Economics 1971 This content downloaded from 147.251.185.127 on Wed, 21 Jun 2017 11:22:30 UTC All use subject to http://about.jstor.org/terms 376 P. A. Samuelson present Ricardo-Viner example, precisely because it is singular, does differ from the Lerner-Samuelson model in which all-the-way equalisation is the rule rather than the exception. Fig. 5b shows how the present example differs from 5a's Lerner-Samuelson three-good three-factor model. In both cases, three factors, (V0, V1, V2), are represented by points inside the equilateral triangles: the amount of Vi is proportional to the distance from any point to the ith side; and for all points the sum of the distances add up to the same normalization constant. Consider the point a in 5a. All other regions, that have geographical endowments "near to" those of Region A, in the sense of falling into the two dimen sional shaded are around a, will come into complete factor-price equalisat with Region A. By contrast, look at 5b. Here, only on a singular razor's edge, the locu a'ab, will there be complete factor-price equalisation from trade alone. El where near a, and that means for "almost all" nearby points, the factor-pr equalisation will be at best partial. How do we recognize this singular locus along which free trade can achie full factor-price equalisation. It is easy. Imagine both countries initially ali at a. Now, take some fraction of the labour and food-land that work toget in A's food industry and, without altering their proportion, send them bo in a dose to Region B to work along with that same labour/food-land ra in B's food industry. And, if you like, take some fraction of the labour a clothing-land in Region B and send them in a dose to A. Then the "new will be at b in Fig. 5b and the "new A" will be at a'. But with free trade i goods, it will be the case that the final equilibrium for a' and b will invo the same world productions (and consumptions) as at a's autarky; and exact the same (equalised) factor returns; from a' clothing will be exported in r turn for an equal value of the food exported from b. It is no accident th the now-unbalanced productions of each region can be worked off by tra By contrast, contemplate what happens at a' and b under autarky. At a' th would be too much clothing produced, if-as will actually happen under tarky--some labour were not shifted to the food-land there. Similarly, n Region B will, under autarky, shift some labour from food to clothing produc tion. Hence, the pre-trade prices would, under uniform tastes, have been quite different at a' and b: the former has lower clothing and clothing-land pric the latter, lower food and foodland prices. And it is free trade in goods t suceeds in restoring the complete equality of all relative prices that had p vailed at a. (The mathematical appendix explains why a'ab is linear.)1 'Ricardo-Viner technology aside, such a singular case can always be found. Pro start Regions A and B alike, with r factors and n goods. Send from A to B doses of facto in the proportions of one (or more) industry. Under autarky, this will hurt the over well-being of both regions as domestic productions are distorted toward a "more b anced" configuration. But with free trade in goods, all regional productions can take p with the same factor-proportions of the original equal-endowment configuration. Q.E Swed. J. of Economics 1971 This content downloaded from 147.251.185.127 on Wed, 21 Jun 2017 11:22:30 UTC All use subject to http://about.jstor.org/terms Ohlin was Right 377 VIII. Conclusions 1. The simple Ricardo-Viner model, involving n goods, will involve r =n factors, labour plus a specialised land for each good. We know from the ard analysis of factor-price equalisation that, when the number of exceeds the number of goods, no complete factor-price equalisation c pected from trade alone. (E.g., with one good and two factors, corn by labour and land, no one expects regions of different labour/land ments to end up with equal wages or rents in the absence of factor mob 2. Nonetheless, taste differences aside, free trade in goods will benefit region and all regions in the aggregate. Within this Ricardo-Viner the patterns of trade will, in the Ohlin fashion, involve each region' ing the good whose input requirements it happens to have in special abu Production adaptations to trade will thus tend to raise the factor-prices most abundant inputs, which would otherwise be cheapest under a The trade-induced movement of factor-prices toward equality, and from geographically-induced diversity, will generally be only partially e ing. With labour's post-trade real wage ending up different in two goods' trade falls short of permitting that maximal world productio migration of labour (of labour alone!) could effectuate. 3. If labour works with more than one immobile land, and if such not occur in the same proportions geographically, we have r > n +1, and is no useful sense in which we can say labour produces within the production functions internationally. Hence, no factor-price equalis to be expected. Also, in real life, taste differences must be expected to c cate the analysis, particularly when they are not random. Mathematical Appendix 1. Let the (i= 1, 2, ..., n) outputs of the (j= 1, 2, ..., J) countries be d by [Q{]. Each is produced by the inputs (L, Vi), according to the co homogeneous-first-degree production functions Qf = F,(L{, V) = V{ Q,(LI/ VY) The total factor endowments of the jth country are given by (Lt, V{~, . .., V~) = (CL, fi, V{ ..., `V). 2. Tastes and demand are summarized by a uniform homothetic set of indifference contours in terms of the n goods consumed, either in a region or in the world, x When labour works with more than one specialized land, we need the Inada conditions to rule out the shutting down of production of some goods in some regions. Such specializations are actually realistic. Swed. J. of Economics 1971 This content downloaded from 147.251.185.127 on Wed, 21 Jun 2017 11:22:30 UTC All use subject to http://about.jstor.org/terms 378 P. A. Samuelson S- u[C1,., *-->Cn] where u is a homogeneous-first-degree concave function. For simplicity, regularity conditions are placed on the u and F, functions so that they are smooth, with positive partial derivatives for positive arguments, and satisfying so-called Inada conditions whereby the partial derivative with respect to any variable goes from + cc to 0 as that variable goes from 0 to + 00 for any positive levels of the other variables.' 3. Autarky equilibrium for any region with (L, V,, ..., Vn) endowment is defined by PJW = Q(L,/V,)-1= S,(Q,) (i = 1, ..., n) L, +... + Ln= L PilW _Su[Qi, .., Qn]/S i= ,.. ) Pi/W au[Qx, -..., Qn]/sQ Here W is the wage rate, [Ps] the prices, [WIP,] the real wages in terms of the respective goods, and S,(Q,) the rising marginal cost functions easily derivable from the production functions Q&,(L,/V), with S,(0)=0 and S,(c)=oo. The 3n variables, [Q,,L, P,/W] are uniquely defined by the 2n+1+(n-1) equations of (1). The comparative statics of the equilibrium, as we change any or all of (L, V,, ..., Vn), can be largely summarized in terms of the derivable functionof social product U=q(L) V,,... , Vn) = Maxu[VQ,(L,/V,), ..., Vn Qn(Ln/Vn)1 Lt subject to L,= L--0; (2)5-1 namely, by w = ro = qo(L, VI, ..., Vn) = 8aqaL = 9q/8 Vo r, = q,(L, Vi, .*= ..,Vn)= a/ Vi ar5IaV,=~2qIaVavj=, -=-iqf (i,j=O,, 1,..., n) (3) Here w is the real wage in terms of social product, r, the similar real rents, and, by convention, L and V0 are used interchangeably. By concavity and homogeneity (qp,] is negative semi-definite. 1 Inada conditions are more popular in the textbook than in the real world. If marginal productivities and marginal costs begin at positive intercepts, the equations below must be qualified by inequalities. When specialization causes some goods not to be produced at all in a particular region, that enhances Ohlin's case for partial rather than complete equalisation, just as in the Lerner-Samuelson model. Swed. J. of Economics 1971 This content downloaded from 147.251.185.127 on Wed, 21 Jun 2017 11:22:30 UTC All use subject to http://about.jstor.org/terms Ohlin was Rigth 379 Continuing to use real social product, q, as numeraire, with Pq--1, the real prices Pj/Pq =p, are equal to p, = Bu[Q1, ..., Q0]/iQ, = qo(L, V, ...., Vn)/Q'(L,/V4) (i = 1 ...., n) (4)Also w = W/P, = ro rf = R,/P, = (R,/P,)p~, = [Q,(L,/V) -(WI/P,) (L,/V)]p, For n= 2, it is not hard to show that 8( W/P,)/8L O. (i = 1, 2) For the limiting cases where the indifference contours are respectively of oo and 0 elasticities of substitution, the matrix [q00o qo01 q02 [ar1/ V,] = qlo q11 q12 q20 q21 q22 [ + +] + +has sign patterns + - - and + - + , + - _ + + but I do not see that, for intermediat pattern - + 4. Free trade in good P,/I = Q&(LifV L + ... + L= L' (5 b) P1(C{ - Q{) +... + P,(CO - Q) = 0 (5 c) P,/pI = u,[ Q&, ..., Q ]/ux[ Q{, ..., C Q&] P,/W PJ/ W = I~I, ..., 01/u , ... o,] (5 e) Here [Cl] is the amount consumed of the ith good in the jth country and 25 - 714814 Srwedish Journal of Economics No. 4 1971 Swed. J. of Economics 1971 This content downloaded from 147.251.185.127 on Wed, 21 Jun 2017 11:22:30 UTC All use subject to http://about.jstor.org/terms 380 P. A. Samuelson u,[ ] stands for Bu[ ]/SC0. The P's denote prices in any common in unit. It is of interest to note that, if one is interested only in the equilib international prices and real wages, and not in the pattern of tra regional consumption breakdown, all the relations of (5) invo namely (5c) and (5 e) can be ignored in this homothetic case: the (5a), (5b), (5d), which are 2nJ+J+(n-1) in number, suffice to uniquely the nJ [Q1], the nJ [Li], the J [P1/W'] and the (n-1) [P,/ If we then add the J balance-of-payments equations of (5c) and t domestic consumption-demand equations of (5e), we further uniquely the remaining Jn consumption unknowns [Ci]. Heuristically, and for that matter rigorously, we can determi post-trade real wages and rents from the following maximum problem U*(L1,~ V1 ..... Vl ..; LJ, Vr ...v~n) J J - Max u 1 V{ I(L, V'x), ..., C Vfn Qn(L(, Vn)L{ t= 1 f =1 n subject to >L(=L' (j= 1 ..., J) (6)t=1 If all prices, wages, and rent are expressed in a single currency unit, can prove W/W W = (a U*/DL)/(aU*/Ll) (. = 2, ... , J) R {/ WI= (a U*/a V{)/(a U*/aL) (i = 1, ..., J; i = 1, . n) (7 Here R, denotes the rent of the ith land in the jth country. 5. Equilibrium with factor mobility, which the text has shown need involve only labour mobility in the Ricardo-Viner model, is defined by the sam equations as (5), but with the allocation of total L among regions now to b determined by the additional equations involving geographically-equalise real wages. In a free-trade world, if the real wage in terms of any good, say th first, is equalised regionally, all real wages are equalised. Hence, we c adjoin to (5) P1/ W =P1l /W2 = ... = P1/ W (5f) These are the J-1 new equations needed to deter terregional allocations [L'] of the given world labor supp equalisation and efficiency. 6. Again, heuristically, we can determine the equil real rents when both factors and goods are mobile, w but merely from (1) applied to world totals Swed. J. of Economics 1971 This content downloaded from 147.251.185.127 on Wed, 21 Jun 2017 11:22:30 UTC All use subject to http://about.jstor.org/terms Ohlin was Right 381 w = go(, LI, 5VI, ..., V n,)I I r, = Sl,( LI I I 7. A valuab partial fact paper. Full partial; par competitio All these w productionthetic dem The follow price equal Q Lt, `'i _ns, +T*T'I 71 jl. TJ rJ TJ )(9 a) - Max U*(L1, V , ...., V; ...; LLt labour mobility and free trade >f U*(L1, V1, ..., V ; ...; L', V(, ..., Vt) = Max u[1 Fx(Ll, 'V), ..., C F,(LL, Vi)] (9 b)L1 free trade = Maxu[F,(L(, V{, ..., F,(L~, Vi)] (9 c) autarky Fig. 6 shows, symbolically, these relations. The outer frontier shows the situation when all factors are mobile, migrating to equalise all factor returns and give the world maximal production possibilities. The middle frontier shows the results of free trade in goods. As each nation is improved by trade, total world GNP (reckoned at the homothetic tastes) is higher than it is at autarky; however, if labour cannot move to wipe out any post-trade geographical differences in the real wage, the aggregate GNP under goods trade falls short of that under factor mobility. These two frontiers are the productions that would be observed as the homothetic tastes changed their food-clothing intensities, running the gamut from one extreme to the other. What then is the inner frontier? It represents the world sums of all autarky productions that would be engendered by the Swed. J. of Economics 1971 This content downloaded from 147.251.185.127 on Wed, 21 Jun 2017 11:22:30 UTC All use subject to http://about.jstor.org/terms 382 P. A. Samuelson Q1 clothing Fig. 6. The outer frontier shows world production possibilities when factors can move optimally--or, in the Ricardo-Viner case, when labour can move to equalise the posttrade real wage rate. The intermediate frontier shows world totals produced when goods can move freely in trade but factors are immobile. The inner curve shows what world production totals would be, as tastes changed uniformly in each county toward one good or the other, and when neither goods nor factors can move between regions. If resource endowments were the same in all regions, all three curves would coincide. In singular cases, the present Ricardo-Viner model could have the intermediate curve tangential to the outer frontier. This is in contrast to the Lerner-Samuelson model in which the two outer curves coincide for all regions that are near enough alike. same change in tastes.1 The fact that that this inner locus lies inside the middle one, represents the production inefficiency attributable to autarky. But, in a sense, there is a further consumption inefficiency as well: thus, suppose all countries under autarky have the same well-being. That "average level" will be less than the average level that would be read off the homothetic indifference contour going through the relevant point on the inner curve, even after proper allowance is made for the number of people: people are, so to speak, forced under autarky to consume "unbalanced" diets. It is possible, as we have seen, for the singular case to occur in which free trade in goods is a full substitute for factor mobility. In such a case the middle frontier must touch the outer frontier in at least one place. However, save in the uninteresting case of identical geographical endowments-when all these curves are identical and no mobility will ever be used-the inner curve can never touch the intermediate frontier. The mathematical condition for the singular case to occur can be written down briefly for the case of two regions, A and B. Suppose with balanced SE.g., write a Cobb-Douglas u =Qk Q-k and let k go from zero to one. Or write a fixed proportions u=Min[Ql/k, Q2/(1 -k)] with O