Trade and Welfare

Though the social welfare function was Bergson's, in the following decade it was Samuelson who defended the underlying approach to welfare economics.^g The first context for Samuelson's application of this approach was interna­tional trade.

g. Bergson's publications were focused on issues relating more directly to problems confronting the government agencies for which he was working during the war—price flexibility and the economics of the Soviet Union—and after the war he became a specialist on the latter.

economics was going through a period of controversy, it was appropriate to revisit the theory of international trade to see whether existing conclusions were valid in light of new ideas about welfare.

Samuelson’s starting point was the position that formed the basis for Bergson's social welfare function: that welfare economics implied making ethical judgments.

At the outset, it is understood of course that every discussion of wel­fare economics implies certain ethical assumptions. I do not propose, however, to discuss the philosophical grounds for holding or rejecting different ethical precepts or assumptions. Rather will the discussion be confined to the implications of different ethical assumptions and the necessary and sufficient presuppositions or the truth of various theorems.³⁰

Though he wrote in terms of utility, he had in mind ordinal utility, which meant that it was impossible to measure the difference in utility between two situations. If utility functions served only to rank alternative combinations of goods in order of preference, and could not measure how good they were, then a fortiori they could not be used to compare the well-being of different individuals.

Samuelson simplified the argument by considering trade between two individuals, so that no aggregation problems arose within each of the par­ties engaging in the trade. This meant that he could represent each trader’s behavior by a set of indifference curves. He made the assumption that if one trader preferred one outcome to another, this was better for that trader (the judgment that each individual is the judge of his or her own welfare). If both parties were better off, then this was an overall welfare gain. The problem was that if one of the two parties was made better off and the other worse off, it was impossible to know whether or not there was an overall increase in welfare, for there was no way to measure or add their utilities. This meant that, though he could show that some trade was better than no trade, he could not show that free trade was optimal; it was possible that moving from protection to free trade would benefit one person and harm another.

The following year he developed this argument, arguing that if the intro­duction of trade resulted in relative prices that were different from those pre­vailing with no trade, all parties to the trade would be better off than if the trade did not take place.³¹ This was a familiar result, but Samuelson argued that writers often claimed it could be proved only under restrictive assump­tions about production costs. In contrast, he claimed that all valid norma­tive propositions about international trade could be derived from “the most general theories of equilibrium,” without making any restrictive assump­tions about costs other than those necessary to ensure there could be perfect competition.³²

He then made what is often called the small-country assumption that the country being analyzed is too small to influence world prices—and he showed that, if all individuals were identical (removing the possibility that some would gain and others would lose), the introduction of interna­tional trade would increase welfare so long as world prices were different from those prevailing under autarky (where the prices at which goods are traded must equal world prices).

Samuelson then turned to the case where individuals were not identi­cal, conceding that it undermined the argument that everyone would benefit from the introduction of trade. However, rather than concede that nothing could be said, he turned to the idea of compensation, then being introduced into discussions of welfare. John Hicks and Nicholas Kaldor were arguing that there was an improvement in welfare if those who gained from a policy change could compensate any losers and still remain better off than before the change. Using similar reasoning, Samuelson argued that if trade were introduced, those who gained would be able to compensate those who lost and still remain better off themselves, implying that everyone could be made better off through trade. However, he refused to provide any measure of the gains from trade. Perhaps implicitly responding to John Hicks's attempts to reinstate the concept of consumers' surplus, Samuelson noted that “con­structs such as consumers' surplus are in general inadmissible,” and that in the special cases where they could be used, they were “perfectly arbitrary and conventional, adding nothing to the analysis.”^h

h. Consumers' surplus was a measure of welfare developed by Alfred Marshall, discussed in chapter 10 this volume.

Thus, although his discussions are consistent with Bergson's social wel­fare function, Samuelson confined his welfare judgments essentially to the Pareto criterion: that if at least one person is better off and no one is worse off, then there is an overall improvement in welfare. As in his previous work, he emphasized the importance of formal reasoning. He attached less importance to the results he had derived (perhaps not surprisingly, as they were very weak) than to the fact that he had demonstrated them rigorously, “with little reliance on intuition.”³⁴ The theorems, he continued, “are true consequences of the premises, and do not rest on presumption or probability.” Addressing the relevance of such formal reasoning, he concluded his article by writing,

Whether or not this [rigorous reasoning] should be done is, of course, a matter of taste.... For in pointing out the consequences of a set of abstract assumptions, one need not be committed unduly as to the relation between reality and these assumptions. On the other hand, in advancing a presumption in favour of an undeducible proposition, the suggestion is conveyed that the difficult task of interpreting reality has already been performed.³⁵

His assumptions might be unrealistic, but this had the merit of making clear that no claims were being made about the real world. The implication was that although other economists—whose theories were based on more realistic assumptions—might seem to be saying something about the world, they were making claims that did not follow from their assumptions. The use of rigorous mathematics was revealing faults in existing theories.

Ironically, it was Marion who was the first to make use of these results that Paul had derived. In 1938, the Quarterly Journal of Economics carried an article by Karl Anderson of Bryn Mawr College, attacking those Australian economists who argued that Australia's historical circumstances justified the imposition of a protective tariff.

At some point during 1939, Marion wrote a reply to Anderson, published in the November issue of the Quarterly Journal of Economics. She constructed a numerical example in which protection was shown to raise Australian consumption of both manufactured goods and primary products, and in which the income accruing to labor increased. Anderson’s claim was wrong. A central argument in Marion’s paper was that Paul had provided “a gen­eral analytical proof’ of the conclusions she had reached; it could be shown that the only critical assumption was that Australia should be able to affect the prices of its exports by imposing a tariff.^37,i Faced with her argument, Anderson conceded that his involved “a complete non sequiter" and did not try to defend it.³⁸ However, in his rejoinder he made the point that it was ques­tionable whether one should talk about supply and demand curves in inter­national trade; that is, it was impossible to devise units in which to measure goods traded that would give any meaning to supply and demand curves (or the notion of an elasticity of demand) such as she had used.

This latter remark prompted a reaction from Frank Graham, a Princeton economist who had published extensively on international trade, cited by Paul in “The Gains from International Trade” (1939a).

One point that is interesting about Marion’s article is her use of Bergson’s arguments about social welfare. Whereas Paul, in his article “The Gains from International Trade,” presumably written before hers, argued that trade was beneficial if those who gained could compensate those who lost, Marion did not use such an argument. She cited Bergson in support of her claim that no one had ever demonstrated that equilibrium under pure competi­tion represented the maximum of “some social magnitude.”⁴⁰ She noted that government subsidies to the landowners who lost through protection might “modify” the situation, but she refrained from noting that if national income had risen, this meant the laborers could still be better off if the landowners were compensated. Given that she must have known and understood the argument, it seems possible she was more skeptical about that point than Paul was.

When Samuelson did eventually publish on this topic, his co-author was not Marion but Wolfgang Stolper, a fellow graduate student who lived close by. Samuelson remembered Stolper as being his first contact with continental

i. That the elasticity of demand for Australian imports was not infinite. European culture, introducing him to Viennese waltzes and Lederhosen, and reacting indignantly when an ignorant waiter responded to a complaint about the temperature of some Chablis by adding an ice cube to the glass.⁴¹ The cultured Stolper found it incredible that Samuelson would listen to the movements of a Beethoven symphony in the order ι, 4, 2, 3, because this minimized the number of times he had to get up to turn over the 78 RPM records on which they were recorded. Stolper and his wife married in the same year as Paul and Marion, and the two couples became close friends.

Samuelson’s later memory of his early collaboration with Stolper was vivid.

One day in the late 1930s, Stolper mentioned to me a curiosity: “Old Taussig... asserts that free trade raises American wages by drawing workers into the sectors of maximum comparative advantage. How do we square this with Ohlin’s notion that the input America is most niggardly endowed with can have its return lowered by free trade in comparison with autarky?”

The point was a new one to me. I said, “You’ve got something there. Work it out.”’

He did. And in the course of his explorations we talked endlessly about the many ramifications of the problem. The analysis soon went beyond the point about free trade, which fell naturally into place after one had sorted out the issues.⁴²

It was presumably this work that placed Samuelson in a position where he could provide the more general analysis to support the numerical example Marion used in her paper, even if he and Stolper had at that point not reached the point where either of them was prepared to publish on the subject. Perhaps he still remembered Viner’s letter saying that mathematical arguments were more interesting if he could prove something that was not obvious.

Though it was Wolfgang Stolper and Paul Samuelson who were named as the authors of the paper that eventually emerged, “Protection and Real Wages” (1941), Marion was also involved in the writing. Stolper admitted that, as would have reflected the prejudices of the time, she typed the paper, though his memory that they “literally dictated alternate sentences to her”’ suggests that her role was probably much greater, involving at a minimum translation of their competing suggestions into something coherent.⁴³ What came to be known as “the Stolper-Samuelson theorem” made a sufficiently important contribution to the theory of international trade that, many years after Marion’s death, a conference was convened to celebrate its fiftieth anni­versary. On that occasion, Samuelson reflected, in terms that may reveal some guilt for not having made sufficient acknowledgment of her work at the time, “my unconscious mind must have benefited enormously in 1940—41 from knowledge of Marion's 1939 QJE findings.”⁴⁴ The crucial point in the paper was that, though much traditional theory concealed this fact by applying a labor theory of value, international trade theory actually involved two factors of production—labor and land. Though it was the Stolper-Samuelson paper that made it explicit, the same point had been implicit in Marion's paper.

In their paper, worked out after Samuelson had left Harvard, they stated that economists had repeatedly tried to show the fallacy in the popular view that protective tariffs could raise either employment or real wages, However, though that popular view might be wrong, the literature contained few unambiguous results. By making additional assumptions, Stolper and Samuelson proved that, if labor was the scarce factor of production, protec­tion could raise wages. Their starting point was to assume that there were two commodities (wheat and watches) and two factors of production (labor and capital). For each commodity there was a production function relating output to the inputs of capital and labor allocated to that sector, from which they could derive the conditions for optimal allocation of capital and labor between the two sectors. It was a model of the production side of the econ­omy. Furthermore, demand conditions did not need to be specified, because they assumed that the relative price of wheat and watches was determined in international markets. They could then work out the effect of changes in this price ratio on the allocation of capital and labor within the economy, and hence on real wages. They concluded that "JiJnternational trade necessarily lowers the real wage of the scarce factor,” a result that was true whether work­ers were assumed to consume wheat, watches, or a mixture of both.⁴⁵’’ This result would be true even if there were more than two commodities; however, it would not necessarily be true if there were more than two countries.

Their paper was submitted to the American Economic Review, where it was considered by Howard Ellis and Paul Homan, who provided the following assessment, on May 2, 1941:

We both agree that the article is a brilliant theoretical performance, and since we wish to have from time to time good and substantial theoretical articles in the Review, we very much dislike to reject it. On the other hand, we agree that it is a very narrow study in formal theory, which adds practically nothing to the literature of the subject with which it is nominally concerned. Indeed, by your own admission

j. Though the term “wage” is mostly used to refer to labor income, in this sentence it is used as a generic term to refer to the income earned by any factor of production. in the last pages, it is practically a complete “sell-out.” It does not, in other words, have anything to say about any of the real situations with which the theory of international trade has to concern itself.⁴⁶

Homan decided to return the paper despite it being “so good of its kind.” He urged them to rewrite it so as to add “something relevant that really will have some bearing upon the practical problem that you introduce at the begin­ning and end of the article.” He argued that there must be something that could be said even if it could not be reduced to the neat theoretical treatment they had used. This amounted to suggesting that they write a new paper on the same problem so, not surprisingly, they did not take his advice. Stolper and Samuelson then submitted it to the Review of Economic Studies, where the British economist Ursula Hicks accepted it for publication with the remark, “I do congratulate you on having found a new point in the theory of interna­tional trade.”⁴⁷

Though Hicks appreciated the paper, it seems likely that even she did not appreciate how significant the paper would prove to be. The paper laid the foundation on which much trade theory was built for the next thirty to forty years. As was noted in the fiftieth anniversary celebration of the paper, the significance of their result resided as much in the way they derived their result as in the result itself.⁴⁸ They worked with a formal general equilibrium model in which there were two of everything: two countries, two goods, and two factors of production. This made it possible both to write down and derive comparative statics results and to represent what was happening using diagrams. They represented the equilibrium quantities of goods produced using Leontief's diagram that combined indifference curves with Haberler's substitution curve.^k To show what happened to factor prices and the alloca­tion of capital and labor between the two industries, they used what is often called an Edgeworth or Edgeworth-Bowley box diagram, with which they would have been familiar from Wilson's course, for which Bowley's textbook had been essential reading. Such diagrams were, following their article, to become staples of international trade theory.

They had provided a formal general equilibrium model, going beyond the work of their predecessors and teachers—Taussig, Viner, Haberler, and Leontief—by describing explicitly the allocation of capital and labor between sectors. However, when it came to analyzing the effects of protection, they relied heavily on verbal arguments, for tariffs did not enter the model explic­itly and neither did production conditions in the rest of the world. Even

k. See figures 9.2 and 9.1 this volume. working out from their diagrams which good is the more capital intensive (a point critical to their arguments) required careful thought. It is therefore possible to sympathize with Homan, for there is a sense in which he and Ellis were entirely right to say that much of the article was not really about the problem that Stolper and Samuelson claimed it to be about. As the authors conceded, their results would not hold in the realistic case where there are more than two factors of production, and too much was happening “offstage.”

Another feature of their article was coining the term “Heckscher-Ohlin model” to denote a model in which countries (usually two) were assumed to have the same technology (the same production function) but different endowments of capital and labor. Trade was then determined by the rela­tive factor endowments of the two countries: the country with the highest ratio of labor to capital would export the labor-intensive good, and the other country would export the capital-intensive good. The significance of this model was that it provided a formal general equilibrium model that could be manipulated to work out what would happen to the equilibrium when one of the parameters changed. Although Stolper and Samuelson attributed the model to the Swedish economists Eli Heckscher and Bertil Ohlin, nei­ther Heckscher nor Ohlin confined themselves to the assumptions of this model.⁴⁹ Instead, Stolper and Samuelson had simplified Ohlin’s theory to the point where it could be translated into a simple set of either equations or diagrams—something neither Heckscher nor Ohlin had actually done? In attributing the model to Heckscher and Ohlin, Stolper and Samuelson understated their own originality.

l. In the subsequent literature, the model was sometimes referred to as the Heckscher- Ohlin-Samuelson model (with possible injustice to Stolper), or even the Heckscher- Ohlin-Samuelson-Jones model, Jones being one of Samuelson’s students who specialized in the field.