he particular model I want to exposit is not the monopolistic competition, intraindustry-versus-interindustry story that has become emblematic of the new trade theory; you will see why shortly. Rather, it is the integration of external economies with factor proportions first suggested in Helpman and Krugman (1985), and subsequently presented in too many survey papers, including my recent survey in the Handbook of International Economics (1998).

The starting point for that model is an economy without trade, or more accurately one without borders - that is, one in which factors of production can work freely with each other, regardless of national origin. In the simplest case we think of a world with two factors of production, and (at least) three goods: X, Y, and Z, ranked in order of capital intensity. Of these, one of the goods - say X - is subject to external economies in production.

This "integrated economy" will have an equilibrium, with goods prices, factor prices, and resource allocation (assume away the possibility of multiple equilibria). In  Figure 1  - a rather cluttered picture, but the clutter has a purpose - I show the resources allocated to the three industries as the vectors OX, XY, and YZ; OZ is, given full employment, the resource endowment of the economy as a whole.

To turn this into a trade model, we now invoke Samuelson's Angel, a character who appears in his "International factor price equalization once again" (1949). The angel - presumably the same one who stopped work on the Tower of Babel - divides up the world's factors of production into different nationalities, unable to work with each other. The angel's handiwork can be represented graphically by letting O be the origin for measuring the factor endowment of one country, Z the origin for the other; then the division of the world is indicated by a single point like E.

Can this divided world still reproduce the economic outcome of the integrated economy? Yes, if it is possible to figure out an international allocation of the pre-angel industries that uses all of each country's resources while meeting two criteria: non-negative production of each good in each country (Samuelson's criterion) together with concentration of the X industry in only one country (so as not to dissipate the external economies). To do this, one must be able to put all of the factors originally producing X in one country, together with some of the factors producing Y and Z. Geometrically, the integrated economy can be reproduced as long as E lies within either of the two parallelograms in Figure 1. If E lies inside both parallelograms - as it does in this picture - there are two trading equilibria that reproduce the integrated economy, one in which X is concentrated in the country whose origin is at O, one with X concentrated in the other. (There might also be other equilibria that do not reproduce the integrated economy - but let us leave that possibility on one side). This immediately implies that the pattern of production and trade may be indeterminate - but not that one cannot say quite interesting things about it.

For one thing, we know right away that whichever country gets the increasing-returns industry X will export that good. For another, we can surmise that whichever country has a higher capital-labor ratio will tend on average to export capital-intensive goods. This surmise can be made precise if we assume identical homothetic preferences, which means that each country's consumption of embodied factor services will lie along the diagonal OZ. Draw a line with slope equal to the wage-rental ratio (WW) through the endowment point E; then the division of the world's consumption of factor services will be indicated by C, and EC will be the net trade in such embodied factor services: the capital-abundant country will on average export capital-intensive goods. Of course, even if the countries have identical capital-labor ratios they will still trade, because one will produce X and one will not. In the general case, however, trade will reflect both increasing returns and differences in resources.

Finally, this integrated-economy approach suggests that trade will almost surely increase the purchasing power of both countries. As in the causes of trade, there are two reasons, indicated in  Figure 2. The figure shows the unit isoquant II for some good before trade, with OA the resources used in producing that unit before trade and ww the factor prices. After trade the factor prices change, say to w'w'. If the industry is constant-returns, that means that only OT resources are now needed to purchase a unit of the good, so that the country's resources are clearly able to purchase more after trade than before. If the industry is increasing-returns, then as long as world production after trade (wherever it takes place) is larger than the country's own production would have been in the absence of trade, this comparative-advantage source of gains from trade is reinforced by an inward shift of the relevant unit isoquant to I'I', further reducing the resouces needed to purchase that unit to T'.

The end result, then, is a view of trade in which both differences in factor endowments and increasing returns are sources of trade - where in each case, what trade does is to allow the world economy to overcome the problem created by the dispersion of resources across countries. And both the embodied trade in resources - which allows countries in effect to trade abundant resources for scarce - and the ability, through trade, to concentrate industries (possibly arbitrarily) to achieve larger scale lead to higher purchasing power than countries would otherwise have.

For me, at least, this integration of increasing returns and comparative advantage was not easily arrived at - it was, as already suggested, not at all a view one heard in the profession circa 1977, and it took me something like 5 years (from 1978 to 1983) and a lot of help from my colleagues and friends to get it down to the simplicity you see here. So it is quite amazing, and a bit humbling, to read Ohlin. Here are some selected quotations from Chapter III of Interregional and International Trade, "Another condition of interregional trade":
 

"[T]he advantages of producing a large quantity of a single commodity instead of a little of all commodities must lead to interregional trade ... To demonstrate the importance of this, assume that a number of regions are isolated from each other, and that their factor endowments and their demand are so balanced that the relative prices of factors and commodities are everywhere the same. Under the [constant returns] assumptions of Chapter I, no trade is then possible. As a matter of fact, insofar as the market for some articles within each region is not large enough to permit the most efficient scale of production, division of trade and labor will be profitable. Each region will specialize on some of these articles and exchange them for the rest ... The tendency toward specialization because of differences in factor endowments is reinforced by the advantages of large-scale production. The location of an industry in one region and not in another might simply be due to chance ... The conclusion that interregional trade reduces the disadvantages of indivisibility corresponds to the previous conclusion that trade mitigates the disadvantages of an unequal geographical distribution of productive agents ... Thus, all interregional trade, whether due to the one cause or the other, might be regarded as a substitute for geographical mobility of productive factors."⁽¹⁾
 

Now it is always tricky to reread old texts in the light of subsequent information; knowing what actually happened, you can probably find a prophecy of Nostradamus that fits the event, and knowing subsequent developments in economic theory, you can probably find most of it hinted at in Ibn Khaldun. Still, I think that it is pretty clear that Ohlin in 1933 had a view of the role of increasing returns in trade that corresponds fairly well to the story told by Figures 1 and 2. And yet that view remained hidden in plain sight for nearly 50 years: in the late 1970s, as I have already suggested, few trade theorists thought of increasing returns as a potential independent source of trade, and they tended to think of its welfare implications as a threat to rather than a reinforcement of the argument for gains from trade.

How did so many people miss what Ohlin not only knew but said reasonably clearly in a classic monograph?
 

2. How increasing returns got lost
 

The proximate answer to how Ohlin's insights about increasing returns as a cause of international trade got misplaced is surely that from the 1940s on few people actually read Ohlin in the original. Oh, many people may have skimmed the book - but they approached it with a mind already conditioned by Paul Samuelson's interpretation, and so they more or less failed to register the other things in there. In effect, they assumed that Samuelson had extracted all the juice.

And what about Samuelson? He was quite aware that Ohlin stressed increasing returns as a subsidiary cause of international trade, but understandably chose in his models to focus on the primary argument. The trouble was that those models were so successful - successful not only in distilling a long verbal argument into a few diagrams, but in finding implications in those diagrams that the verbal exposition had missed - that they took over the whole discourse, and whatever was not in the simplest models got forgotten.

It is also worth pointing out that while Ohlin does give significant amounts of space to the discussion of increasing returns, he simultaneously downplays it. For one thing, he underestimates the extent to which increasing returns represent a break from the comparative advantage tradition, possibly because he overstates the extent to which his factor proportions approach is a repudiation of Ricardian insights. In a modern graduate course, Heckscher-Ohlin seems to follow naturally from Ricardo - both models build on the basic idea of differences in production possibilities, with Heckscher-Ohlin simply shifting the explanation of these differences to one that stresses differences in resources rather than in technology; increasing returns stories about trade, in which differences are the result rather than the cause of trade, represent a major departure. In Interregional and international trade, by contrast, resource-based explanations of trade are treated as a fundamental break with the Ricardian labor theory of value, and increasing returns as a sort of uncontroversial add-on.

At the same time, Ohlin strongly discounts the practical importance of increasing returns: "[I]t is certainly the differences in factor supplies that determine the course of interregional trade - unless regions are small - whereas the advantages of large-scale production are more in the nature of a subsidiary cause, carrying the division of labor and trade a little further than it would otherwise go, but not changing their characteristics." This may well have been true at the time he was writing (some critics of the "new trade theory" insist, indeed, that it is still true today). In the 1920s world trade was still dominated by North-South exchanges of manufactures for raw materials rather than two-way trade in manufactures among advanced countries, and the striking examples of industry agglomerations leading to international trade tended to be old-fashioned craft sectors like jewelry. The great rise in intra-industry trade among advanced countries, and of huge exporting agglomerations like Silicon Valley (or, for that matter, the City of London) still lay in the future. (Actually, Ohlin was not completely consistent: after disparaging the practical importance of increasing returns in Part One, he seemed in Part Two to suggest that increasing returns would play a growing role over time, and thereby ensure that trade did not decline even as industry spread across the world. At least that's what I think he said: the discussion of the "Trend of international trade" in Chapter VII is one of the murkiest passages in a book that is not exactly a model of crystalline clarity in any case). The point, however, is that by playing down half of his original contribution, Ohlin in effect encouraged subsequent modelers to omit that part of his insight entirely; and the next generation of trade theorists, who read Ohlin-as-modeled rather than the original, never heard about it.

But even if Ohlin had stressed increasing returns more forcefully than he did, there were some inherent reasons why the translation of his work into more formal models probably was fated to drop his insight.

First is the generic problem of market structure - the same problem that led to a temporary forgetting of insights in location theory and development economics. Ohlin, writing in a Marshallian tradition (and before the work of Chamberlin and Robinson), is cheerfully blurry about the distinction among types of increasing returns - he is aware that there is an important distinction between external and internal economies, but is not careful to separate the cases. Once more formal modeling became the norm, however, any practicing economist was bound to come to a sudden stop over that issue. When Ohlin said "increasing returns", did he mean internal economies of scale? In that case, we are in the realm of imperfect competition, and as Harry Johnson (1967) almost triumphantly declared, during the heyday of Heckscher-Ohlin-Samuelson theory imperfect competition seemed impossible to model in a general-equilibrium framework. Or did he mean external economies? In that case, as any postwar theorist was bound to realize, we were in a world of market failure, with the case for free markets in general open to question; on first thought one might expect that any theory that stressed external economies would also be a theory that challenged the case for free trade. (After all, that was the apparent implication of Frank Graham's 1923 discussion of protection under increasing returns). At the time, the natural inclination might well have been to forget about the whole thing. It was only with the development of tractable models of monopolistic competition that it became easy to think of increasing-returns trade as a beneficial overlay on comparative advantage; and only with those monopolistic competition models in hand that it also became natural to revisit external-economy models, as in the model above, and realize that they could tell a similar story.

There was also a more specific misconception that arose in trade modeling: the confusion that arose from the habit of thinking in terms of two-good models. The two-by-two version of Heckscher-Ohlin is, of course, a thing of beauty and a source of much insight when used properly. If one tries, however, to squeeze increasing returns into that same two-good framework one ends up with a seriously misplaced view. First, you tend to think that increasing returns can give rise to arbitrary, accidental specialization only if they are sufficiently strong - specifically, strong enough to turn the production possibilities frontier concave instead of convex. Second, you find yourself thinking that absent that reversal of curvature, the only remaining effect of increasing returns is to modify comparative advantage, giving large countries an advantage in scale-intensive goods. All it takes to clear the air is a three-good model; indeed, you have to wonder why it took 50 years for someone to propose Figure 1. But such was the focus on two-good models that somehow it never happened.

From my point of view, this is all a happy story. Since Figure 1 requires none of the monopolistic competition modeling technology that became available only in the 70s, there is no good reason why someone might not have read Ohlin carefully, been a bit more flexible about modeling strategy, and created much of what later became known as the new trade theory when I was still in grade school. In practice a mixture of misplaced intellectual anxieties and modeling prejudices delayed that development until the late 70s, and some of us were in a position to get a lot of professional mileage out of what in retrospect seems a fairly obvious set of ideas.
 

3. Economic geography
 

It is obvious - in retrospect - that something special happens when factor mobility interacts with increasing returns. Suppose that there are strong advantages to concentration of factors - where these advantages may take the form of true external economies, but may also be due to "linkage" effects arising from the effect of concentration on the size of markets and the availability of inputs. And suppose also that some factors are more mobile than others. Then factor mobility will tend to increase differences among regions rather than reducing them, and instead of substituting for regional specialization will promote it. Start with an exceptional concentration of nerds in the vicinity of Stanford University; the resulting industry specialization will attract more nerds, reinforcing the nerd-friendliness of the local environment, and you end up with Silicon Valley. Similar processes lead to concentrations of ambitious people in London, beautiful people in Hollywood, and so on; and more broadly, they lead most of the population of sparsely populated North America to live in a few densely populated metropolitan corridors.

This observation is, as I suggested, obvious in retrospect; but it certainly took me a while to see it. Why exactly I spent a decade between showing how the interaction of transport costs and increasing returns at the level of the plant could lead to the "home market effect" (Krugman 1980) and realizing that the techniques developed there led naturally to simple models of regional divergence (Krugman 1991) remains a mystery to me. The only good news was that nobody else picked up that $100 bill lying on the sidewalk in the interim.

But did Ohlin already know all about this, in the way that he more or less anticipated the new trade theory?

He certainly touched on all the elements. Here as in his treatment of increasing returns, Ohlin was in a way at an advantage over later economists, because it was still possible to write in the Marshallian tradition: he did not need to describe carefully worked-out models - which meant that he could simply hand-wave his way past the nasty bits, like how to describe market structure, or how to integrate transportation costs into general equilibrium. (It is the process of taming those nasty bits that accounts for most of the algebra in the recent monograph by Fujita, Krugman, and Venables (1999)). So he could and did mention almost in passing many of the key insights that modelers would confirm some 60 years later. In the new economic geography a central theme is the tension between "centripetal" forces that pull factors together, and "centrifugal" forces that push them apart; well, Ohlin describes a tension between agglomerating and "deglomerating" tendencies. (Hey, economic jargon has not entirely changed for the worse).The new economic geography stresses the role of historical accident in determining the location of industries; Ohlin writes that "Inventions may by chance lead to manufacture in one country or place when others would do just as well; yet the industry tends to remain where it was first located, for the quality of the labor factors adapt themselves and so do capital investments in production, transportation, and trade connections."

And yet it seems to me that while much of what the new economic geography says can be found in Ohlin, the case for a missed opportunity - for asserting that Ohlin had the right vision, but that subsequent readers or, perhaps more accurately, non-readers failed to appreciate it - is much less striking than in the case of the new trade theory. For while Ohlin may have had many of the elements, he was far less sure-footed than he was with increasing returns as a cause of trade, and underplayed the implications to an even greater extent. Let me in particular note three ways in which Ohlin's vision seems to have gotten a bit blurry when it came to the ideas that make up the new economic geography.

First, Ohlin's Marshallian sloppiness about internal versus external economies may have caught up with him here, in the sense that he does not seem to make a clear distinction between individual and collective rationality. In Chapter XII one encounters a section entitled "Arbitrary elements in location", which begins with this sentence: "The historical influence can lead to an uneconomical location of industry." Aha! one thinks; he is about to talk about how early decisions can be locked in by external economies. But no: what follows is a brief discussion of the likelihood that location decisions will be mistaken. Surely the point is that an industry can be in the wrong place even if nobody is making a mistake, that it might be individually rational to stay even though it is collectively irrational not to move; but somehow this point got missed.

Second, Ohlin downplayed the endogeneity of factor location, declaring that "even small and nearby districts show substantial and lasting differences in natural resources, transfer resources and facilities, and labor supply. Such differences are to a large extent causes rather than effects of location of industry." Now this may have been true in Europe at the time of writing, though it seems doubtful even there. If one considers the United States, however - and Ohlin often uses American examples of interregional trade - the location of activity in the 1920s was already largely driven by the logic of self-reinforcing concentration. After all, America was sharply divided between manufacturing belt and farm belt, with most of the manufacturing belt owing its dominance to an early start rather than inherent resource advantages; the auto industry in Detroit, the financial and garment industries in New York, the tire industry in Akron, and so forth were already famous examples of industrial concentration. Indeed, one could argue that the "economic geography" forces of concentration played a larger role in interregional trade in America when Ohlin was writing than they do now.

But perhaps Ohlin underemphasized what we now think of as new economic geography issues for the same reason that a casual reader, trying to extract a key message from his book, would probably overlook his discussion of these issues: unlike the integration of increasing returns with comparative advantage, which in effect reinforced his basic vision, the interaction of increasing returns with factor mobility actually tended to run counter to that vision. For despite its Victorian sprawl and (by post-Samuelsonian standards) untidiness, Interregional and international trade is in the main a tract animated by a single idea: the movement of goods and factors is the way the world economy tries to overcome the limitations placed upon it by the fragmentation of its resources, and the effect of that movement is one of convergence in prices. The logic of modern economic geography models, in which trade and factor mobility are often complements, and factor movements often lead to divergence in factor and even goods prices, is something that Ohlin realized could happen, but it ran counter to his main theme.
 

4. What isn't in Ohlin (at all)
 

It is a bit humbling to realize that much of what would in the 80s come to be called the new trade theory, and some of what would in the 90s be called the new economic geography, is already present in a widely cited 1933 book. One might argue that the ability of economists to miss all those insights itself makes the case for formal models, if only for their tendency to concentrate the reader's mind. But have modern trade and geography theorists been doing more than making old ideas precise? What isn't in Ohlin, at all?

Well, I think that there are three main areas that are distinctive to late-20th-century models, and are truly absent from older writing - Ohlin, for all his perceptiveness, included.

The first is the appreciation of the importance and distinctiveness of imperfect competition. As I suggested above, Ohlin had a Marshallian tendency to fuzz over the distinction between internal economies of scale and external increasing returns, and was certainly not much worried about how firms with market power would behave. Yet when increasing returns finally did begin to play a central role in international trade theory, it was precisely because theorists finally managed to "tame" imperfect competition and hence to feel comfortable talking about internal scale economies.

As a practical matter, the focus on imperfect competition, and on monopolistic competition in particular, gave the new trade theory an immediate empirical focus: the rise of intra-industry trade among advanced countries, which meshed perfectly (at least in terms of casual empiricism) with the monopolistic-competition-cum-comparative advantage models developed by Dixit and Norman, Helpman, and myself. As a theoretical matter, once one realized that internal economies of scale necessarily implied imperfect competition, it became possible to consider stories in which imperfect competition - as opposed to the increasing returns per se - were the main source of action. One example was the theory of reciprocal dumping - trade driven neither by comparative advantage nor by increasing returns, but rather as a result of the efforts of firms to raid each others' inframarginal customers. Another was the theory of strategic trade policy, in which the gap between price and marginal cost rather than the advantages of scale itself offered the potential scope for neo-mercantilist arguments.

A second aspect of modern trade theory that seems to me to be absent from Ohlin - though it might be worth a more careful reading - is the distinction between equilibria and optima. In constant-returns trade theory this is not a big issue (except when one is considering domestic distortions argument for trade and industrial policy). But in the presence of increasing returns, either internal or external, it can be deeply misleading to confuse what is with what should be. I have already noted that Ohlin seems to have gotten confused over the nature of what we would now call lock-in to the wrong location, attributing it to mistakes by individuals rather than the difference between collective and individual rationality. He also seems to be far too blase about the way in which tradeoffs involving the tension between agglomerative and "deglomerative" forces would be resolved; while that tension implies both that there is some appropriate size of industrial clusters and their market areas, and (probably) that some typical size of cluster and market area will arise in practice, there is no good reason to suppose - as Ohlin does - that the actual and appropriate sizes will be the same.

Why did Ohlin fail to make this distinction? Partly, no doubt, because Marshall and his followers had been more or less deliberately confused about such issues, preferring a diplomatic writing style that emphasized broad themes over presumably nitpicking details. Beyond this, Ohlin was attempting to offer a unified vision of trade as a way of overcoming the dispersion of factors; since in what has come to be known as "Hecksher-Ohlin" trade there is no important distinction between equilibrium and optimum, it would have spoiled the symmetry to make much of that distinction when it came to increasing returns.

Finally, I cannot find in Ohlin one of the central things that attracted me to the kinds of models used in the new economic geography: the idea of qualitative, discontinuous change. It is typical in the models now used to think about regional differentiation that small changes in underlying parameters - say, in transportation costs - sometimes bring about large changes in behavior. For example, when transport costs drop below some critical level a symmetric division of industry among regions may become unstable, and a cumulative process of concentration begin. This is, to be sure, hardly a new idea. But it is an idea whose time has, in a way, come. New models of geography, which derive the agglomerative or centripetal forces from an underlying interaction among more basic determinants, are better suited to considering how the whole geographical logic of an economy might change than older accounts - like Ohlin's - that simply assumed agglomerative tendencies. And the availability of easy computation, letting us explore nonlinear dynamics quickly and cheaply, also probably encourages the exploration of such themes. Anyway, whatever the reason, the sorts of dramatic stories that I like in geography - the way that railroads may have precipitated the division of Italy into industrial north and depressed Mezzogiorno, or the discovery of oil may have pushed California over a critical threshold and started a self-reinforcing process of industrial development - are more or less new, at least to trade theorists.

So there is a reasonable amount of modern theory that is not in Ohlin, even in rough form. But it is still amazing how much is in there, if you really look.
 

5. What do trade theorists know, and when do they know it?
 

At the risk of offending many people living and dead, I think it might be fair to say that there have been no more than, say, five Big Ideas in international trade theory. They might include:
 

- Comparative advantage

- Determination of the terms of trade by reciprocal demand

- The interaction between factor abundance and factor intensity

- The interaction between domestic distortions and trade policy

- Arbitrary specialization driven by increasing returns
 

(I am open to suggestions about other Big Ideas that might belong on the list).

We know both from intellectual historians (Douglas Irwin in particular) and from the personal experience of many people at this conference that getting each of these Big Ideas into mainstream thinking required a major intellectual struggle, in general involving new techniques (offer curves, Edgeworth boxes, Dixit-Stiglitz) and a painful process of changing not only the way one answered questions but the questions themselves. And yet the funny thing is that once the intellectual struggle had reached a certain point, the central idea came to seem obvious - the sort of thing one could summarize in a paragraph or two, and make comprehensible to any reasonably bright Congressional staffer (though probably not the Congressman himself)⁽²⁾. What is more, once the idea was clearly expressed, it generally turned out to be an idea that had been expressed not quite so clearly by a number of older economists.

The moral, surely, is that the next Big Idea in international economics - the idea that will transform the field - is something simple, something already out there, something that all of us will later claim to have known all along. And that idea is ....
 

REFERENCES
 

Chacoliades, M. (1970), "Increasing returns and the theory of comparative advantage", Southern Economic Journal
 

Fujita, M., Krugman, P. and Venables, A. (1999), The spatial economy, MIT Press
 

Graham, F. (1923), "Some aspects of protection further considered", Quarterly Journal of Economics.
 

Grossman, G. and Rogoff, K. (1998), Handbook of International Economics, Vol. 3 North Holland
 

Helpman, E. and Krugman, P. (1985), Market Structure and Foreign Trade, MIT Press
 

Johnson, H. (1967), "International trade theory and monopolistic competition theory" in Kuenne, R., ed., Monopolistic competition theory: studies in impact, Wiley.
 

Krugman, P. (1980), "Scale economies, product differentiation, and the pattern of trade", American Economic Review
 

Krugman, P. (1991), "Increasing returns and economic geography", Journal of Political Economy
 

Krugman, P. (1995), Development, Geography, and Economic Theory, MIT Press
 

Krugman, P. (1996), "How to be a crazy economist", in S. Medema and W. Samuels, eds., Foundations of Research in Economics: How do Economists do Economics?, Edward Elgar.
 

Matthews, R.C.O. (1950), "Reciprocal demand and increasing returns", Review of Economic Studies
 

Ohlin, B. (1933), Interregional and International Trade
 

Samuelson, P. (1949), "International factor price equalization once again",
 

Samuelson, P. (1971), "Ohlin was right", Scandinavian Journal of Economics

1. Ohlin also stated, more or less clearly, the idea that if the increasing returns industry is capital-intensive the country that gets it will shift to a labor-intensive mix of constant-returns goods, and conversely. True, he argues in terms of factor prices, missing the Samuelsonian point about factor price equalization. But it is still amazingly close to what I regarded as a fresh discovery when I finally worked it out.

2. Richard Feynman once told a reporter who wanted a 5-minute summary of his work that if it could have been summarized in 5 minutes, it wouldn't have warranted a Nobel. Yet the Big Ideas in trade theory probably can be summarized in not much more than 5 minutes.