1.1 The rediscovery of geography

In the last few years there has been a dramatic increase in research on economic geography -- that is, on where economic activity occurs and why. This surge of interest has been driven to some extent by real-world concerns -- the field has been given a big boost in particular by plans to unify the European market, and the attempt to understand how this deeper integration will work by comparing international economics within Europe with interregional economics within the United States. But economic geography has always been important; if it has been notably neglected by the economics profession, this is not because economists have been uninterested in the subject, but because they have regarded it as intractable. Their new willingness to work on economic geography comes from their sense that new tools -- in particular, modeling tricks that have been developed to analyze industrial organization, international trade, and economic growth -- have removed crucial technical barriers, and transformed a once inhospitable field into fertile ground for theorists.

The basic problem with doing theory in economic geography has always been the observation that any sensible story about regional and urban development must hinge crucially on the role of increasing returns. Suppose that we really lived in the constant-returns world that is still assumed in much economic theory. Then it would be hard to understand why the economy is not characterized by "backyard capitalism", in which each household or small group produces most items for itself. There would, admittedly, be some unevenness in population density and some trade between locations because of the variation in the natural environment: land differs in fertility, while differences in soil, climate, and resources mean that no one locality would produce all goods even under constant returns. Nonetheless, the dramatic spatial unevenness of the real economy -- the disparities between densely populated manufacturing belts and thinly populated farm belts, between congested cities and desolate rural areas; the spectacular concentration of particular industries in Silicon Valleys and Hollywoods -- is surely the result not of inherent differences between locations but of some set of cumulative processes, necessarily involving some form of increasing returns, whereby geographic concentration can be self-reinforcing.

Unfortunately, increasing returns have always posed difficulties for economic theorists. Except under very special circumstances they lead to a breakdown of perfect competition; even if this problem can somehow be finessed, they pose problems for the existence and uniqueness of equilibria. For the theorist determined to make some headway in understanding the location of economic activity, these difficulties have not been insurmountable. For example, one can, like much of urban economics, simply take the existence of cities (or central business districts within cities) as a given, and trace out the consequences for land rents and land use; this is the basis of the famous von Thünen model, which has given rise to a rich and productive literature. Or one can, like urban systems theorists (above all Henderson (1974, 1980, 1988)), represent increasing returns in a somewhat black-box way as localized production externalities; this approach sidesteps some important questions, but opens the door to a powerfully insightful analysis of others. Still, until a few years ago these efforts remained peripheral to the main body of economic theory, to such an extent that most textbooks in economic principles still contain literally no reference to the existence or role of cities and other geographic concentrations of economic activity.

What has happened in the last few years is the emergence of a "new economic geography" that is the fourth wave of the increasing returns revolution in economics. The revolution began in the 1970s, in the field of industrial organization, when theorists began for the first time to develop tractable models of competition in the presence of increasing returns; in particular, Dixit and Stiglitz (1977) developed a formalization of Chamberlin's concept of monopolistic competition that, while admittedly a very special case, has turned into the workhorse of theoretical modeling in a number of fields. Beginning at the end of the 1970s, the analytical tools of the new industrial organization theory were applied by a number of theorists to international trade; a few years later the same tools were applied to technological change and economic growth. In each case it was, of course, necessary to do much more than mechanically apply the Dixit-Stiglitz model to the subject at hand: new concepts needed to be developed, and at first there was a proliferation of seemingly inconsistent models and approaches, in which each author appeared to be inventing his or her own private language and notation. In time, however, it became clear in each case that a core set of useful insights had emerged; indeed, in retrospect it is remarkable how tightly integrated, how classical in feel, both the "new trade" and "new growth" theory have turned out to be.

Our sense is that the state of the "new economic geography" is currently similar to that of the "new trade theory" circa 1984, or the "new growth theory" circa 1990. That is, an exuberant and initially exhilarating growth of theory has reached the point at which it has become difficult to see the forest for the trees; and yet there is, if one looks for it, a strong element of commonality among many if not all the analyses. The integration of new trade and new growth theory was, we believe, powerfully aided by the appearance of judiciously timed monographs that endeavored to synthesize each field into a coherent whole: Helpman and Krugman's Market Structure and Foreign Trade (1985), and Grossman and Helpman's Innovation and Growth in the World Economy (1991). This book is, of course, an effort to do the same with the new economic geography.

In the remainder of this chapter, we describe what we regard as the unifying themes, methods, and questions of this new field, and set out the plan of the book.

1.2 Linkages and circular causation

We would argue that the defining issue of economic geography is the need to explain concentrations of population and/or economic activity -- the distinction between manufacturing belt and farm belt, the existence of cities, the role of industry clusters. Broadly speaking, it is clear that all these concentrations form and survive because of some form of agglomeration economies, in which spatial concentration itself creates the favorable economic environment that supports further or continued concentration. And for some purposes -- as in the urban systems literature described in Chapter 2 -- it may be enough simply to posit the existence of such agglomeration economies. But the main thrust of the new geography literature has been to get inside that particular black box, and derive the self-reinforcing character of spatial concentration from more fundamental considerations. The point is not just that positing agglomeration economies seems a bit like assuming one's conclusion -- as a sarcastic physicist remarked after hearing one presentation on increasing returns, "So you're telling us that agglomerations form because of agglomeration economies". The larger point is that by modeling the sources of increasing returns to spatial concentration, we are able to learn something about how and when these returns may change -- and then explore how the economy's behavior will change with them.

How should the returns to spatial concentration be modeled? More than a century ago Alfred Marshall suggested a threefold classification. In modern terminology, he argued that industrial districts arise because of knowledge spillovers ("the mysteries of the trade become no mysteries, but are as it were in the air"), the advantages of thick markets for specialized skills, and the backward and forward linkages associated with large local markets. While all three of Marshall's forces are clearly operating in the real world, the new geography models have generally downplayed the first two, essentially because they remain hard to model in any explicit way. Instead, they have focussed on the role of linkages.

The linkage story is easy to tell if one is willing to be a bit vague about the details. Producers, so the story goes, want to choose locations that (i) have good access to large markets and (ii) have good access to supplies of goods that they or their workers require. However, a place that for whatever reason already has a concentration of producers will tend to offer a large market (because of the demand generated by the producers and their workers) and a good supply of inputs and consumer goods (made by the producers already there). These two advantages correspond precisely to the "backward linkages" and "forward linkages" of development theory. Because of these linkages, a spatial concentration of production, once established, may tend to persist -- and a small difference in the initial economic size of two otherwise equivalent locations may tend to grow over time.

Discussions of linkage-based spatial concentration that embody more or less this story have been familiar to regional scientists for many years. In Chapter 3 we describe in particular two such stories; the dynamic extension of the base-multiplier approach largely identified with Pred (1966), and the widely used concept of "market potential" associated with such authors as Harris (1954). And provided that one is prepared to be strategically sloppy about details, it is possible to jump straight from such stories into heuristic models that are quite useful both for quick-and-dirty discussions of real-world issues and as guides to the results of more careful modeling. Such loose-jointed modeling is, we believe, under-appreciated in economics; we try to give it its due.

Nonetheless, there are certain questions that traditional discussions of linkages and economic geography do not address, yet become crucial once one tries to get beyond the simplest stories. Most important of these is the nature of competition. Linkage stories only work if there are increasing returns in production at the level of the individual firm -- otherwise the firm would not concentrate production where the market is largest, but rather establish a separate facility to serve each market. But if there are increasing returns, competition must be imperfect; how do firms compete and set prices? Models like the base-multiplier story are also sloppy about budget constraints -- it is unclear where all the money comes from or where it goes. And in any story in which transportation costs play a crucial role -- as they must in linkage stories about location, because otherwise why does location matter? -- one must worry about how the resources used in transportation fit into the picture.

The key enabling technology for the new economic geography has been the development of a basic approach that deals in a consistent, if more than a bit artificial, way with these problems -- together with an angle of approach that allows theorists to cut through what might at first sight seem be intractably complex problems of analysis.

1.3 Modeling tricks: Dixit-Stiglitz, icebergs, evolution, and the computer

We believe that the historical unwillingness of economists to address issues of economic geography was mainly due to the sense that these issues were technically intractable. As a result, we are only mildly apologetic about the fact that our analysis depends crucially on what might perhaps best be called modeling tricks -- assumptions that reflect not so much a realistic view of how the world works as a judgement about what will make the analysis of geographic issues manageable without doing too much damage to the relevance of that analysis.

The first and biggest trick of our analysis is something we have in common with the new trade and new growth literature: a heavy dependence on the Dixit-Stiglitz model of monopolistic competition. To someone unfamiliar with the exigencies of economic modeling, the popularity of the Dixit-Stiglitz model might seem baffling. The model not only assumes that there are many goods that, though constituting distinct products from the point of view of consumers, also enter perfectly symmetrically into demand; it also assumes that the individual utility function takes a particular, and fairly unlikely form. Yet the Dixit-Stiglitz model has been the basis of a huge body of economic theory in international trade, economic growth, and now economic geography. Although we step away from that model on occasion, especially in our more heuristic discussions, Dixit-Stiglitz assumptions are pervasive in this book.

We are aware that this lends the analysis a certain air of unreality -- that this book sometimes looks as if it should be entitled Games You Can Play with CES Functions. Nonetheless, we regard the advantages of the Dixit-Stiglitz model as overwhelming for our purposes. Essentially, it is a way to respect the effects of increasing returns at the level of the firm without getting bogged down in them. By assuming that those sectors of the economy subject to increasing returns also satisfy the peculiar assumptions of the Dixit-Stiglitz model, we are able to make sure that we have represented market structure in an internally consistent way without repeatedly going through a taxonomy of oligopoly models. Dixit-Stiglitz also happens to lend itself naturally to general equilibrium analysis, in which there are no loose ends about where money comes from and where it goes. Above all, because Dixit-Stiglitz-type markets have a large number of firms -- usually represented as a continuum -- we are able to reconcile two seemingly incompatible goals: respecting the integer nature of individual choices under increasing returns (each good will typically be produced in only location) while representing the aggregate of such choices with continuous variables (such as the share of production carried out in a particular location). In short, Dixit-Stiglitz lets us have our cake in discrete lumps while doing calculus on it, too.

Even with Dixit-Stiglitz, modeling a multi-location economy requires some further funny but useful assumptions, which are distinctive to the new economic geography (as opposed to the "new trade" or "new growth" literatures). One key simplification is the assumption that transportation costs take Samuelson's "iceberg" form: rather than modeling a separate transportation sector, we suppose that a fraction of a good shipped simply melts away or evaporates in transit. There turns out to be a tremendous synergy between the assumption of iceberg transport costs and the Dixit-Stiglitz model, in the sense that combining them causes many potentially nasty technical complications simply to, well, melt away.

A bigger departure from the new trade and new growth literature comes in our repeated use of a sort of evolutionary dynamics to make sense of what are mainly static models. It is very hard to talk about economic geography without using a language that suggests dynamic stories -- when one speaks of a cumulative process by which spatial concentration reinforces itself, one has a definite image of a snowballing urban or regional concentration, developing over time. Yet to insist that models of economic geography explicitly model firms and households as making intertemporal decisions based on rational expectations would greatly complicate an already difficult subject. It is very tempting to take a shortcut: to write down static models, then impose ad hoc dynamics on those models by, say, assuming that workers migrate only gradually to locations that offer higher real wage rates -- and to use this ad hoc assumption to categorize some equilibria as stable, others as unstable. We have systematically given in to this temptation.

This may require some further discussion. Ad hoc dynamics have been very much out of fashion in economics for the past 25 years; dynamics are supposed to emerge from rational, maximizing decisions by individual agents. Yet what is one to do when a model predicts the existence of multiple equilibria, as geography models usually do? Game theorists have wrestled with this question, suggesting a variety of ways to "refine" the set of equilibria. In recent years, they have increasingly come to accept the idea that it is at least useful to try to assess the stability of equilibria by imagining a process in which strategies become more or less prevalent over time based on how well they perform -- in the same way that strategies followed by organisms evolve under the pressure of natural selection. The funny thing is that modern "evolutionary game theory" often looks quite a lot like old-fashioned ad hoc dynamics. And indeed, the basic dynamic approach taken in our first model (see Chapter 5) turns out to be identical to the "replicator dynamics" now considered respectable among economic game theorists. (Game theorists in biology, of course, regard the assumption that strategies evolve myopically as a principle rather than a dubious shortcut). In short, we believe that we are right to give in to the temptation to sort out equilibria using simple, evolutionary dynamic stories, even though the models do not ground these dynamics in any explicit decision-making over time.

Finally, even with all the special assumptions we have described, models of economic geography can easily seem to be too complicated for paper-and-pencil analysis. Yet if one is prepared to assign particular numbers to the parameters, they can often be easily solved on the computer. A hallmark of the new economic geography, as compared with the new trade and new growth literatures, has been the willingness to turn where necessary to computer-assisted thinking: to use high-tech numerical examples to guide and supplement analytical results.

That said, in the course of working on this book we have found that it is often possible to learn more from pencil and paper than one might at first have thought. It often turns out that it is extemely useful to start the analysis of a model by looking at numerical examples and simulations; but that these numerical results then suggest the form of a solution that can be derived in large part analytically. We are unabashed about the use of the computer as an analytical tool; but this book has turned out to have more analytical underpinning, and to be less reliant on purely numerical results, than we expected.

1.4 The two questions

There are many questions one might ask about economic geography, and we touch on a number of issues over the course of this book. We are, however, able to stress the commonalities among a number of different models by subjecting each model to one or both of two related but not quite identical questions:

- When is a spatial concentration of economic activity sustainable? (I.e., under what conditions are the advantages created by such a concentration, should it somehow come into existence, sufficient to maintain it).

- When is a symmetric equilibrium, without spatial concentration, unstable? (I.e., under what conditions will small differences among locations snowball into larger differences over time, so that the symmetry between identical locations will spontaneously break).

Or to put it differently, the first question asks whether the economy can support something other than "backyard capitalism", whether backyard capitalism is a necessary outcome; the second whether backyard capitalism will automatically unravel, whether it is a possible outcome.

The answers to both of these questions hinge on the balance between "centripetal" forces, forces that tend to promote spatial concentration of economic activity, and "centrifugal" forces that oppose such concentration. They are not quite the same question, however, essentially because the first asks whether a situation is an equilibrium or not, and the second asks whether an equilibrium is stable. Take, for example, the case of the two-region model analyzed in Chapter 5. The first question asks whether, if we simply posit that all manufacturing is concentrated in one region, a worker who "defects" to the other region will find that doing so improves his real wage; if it does, the concentration of manufacturing is not an equilibrium. The second question asks whether, starting from an equilibrium in which manufacturing is equally divided between the two regions, a movement of a small number of workers from one region to the other will raise or lower the relative wage in the destination region; if it raises it, the symmetric initial situation will be unstable against small perturbations.

In the course of doing this book, we have discovered two important (and surprising, at least to us) things about the two questions. First, although the global behavior of new economic geography models is usually analytically intractable, and must be explored via the computer, the answers to the two questions can usually be reduced to closed-form expressions. That is, we can derive explicit formulas for the "sustain point" at which an economy with agglomeration becomes possible and the "break point" at which an economy without agglomeration becomes unstable. (Doing so typically involves guessing at the equilibrium, then confirming that guess, for the sustain point; it involves linearizing the model around the symmetric equilibrium and solving it in the case of the break point). These expressions reveal in a clear way the role of backward and forward linkages in creating and sustaining spatial concentration.

Second, across a variety of models that seem quite different on the surface, a suitable redefinition of variables leads to the same expressions for break point and sustain point. (This is particularly gratifying in the case of the break point, because the equations are possible but extremely annoying to solve; it is a great relief to find that this need only be done once). In this sense we can claim to have developed a theory of spatial concentration that is broader than any particular model, and that helps us to see a number of different models as particular cases of a more general approach.

It is not always useful to ask both questions. In some models there is no sustain point -- although symmetry does break, the result is not a full concentration of activity in one location. In the urban models of Part III, on the other hand, the economic logic makes the question of symmetry-breaking uninteresting; as we will see, it makes much more sense to posit the initial existence of one or more cities, then evolve new cities by changing the economy until that initial spatial pattern becomes unsustainable. Still, since it is always useful to ask at least one of the questions and often useful to ask both, we regard the two questions as one of the book's unifying themes.

1.5 Plan of the book

The remainder of this book is in four parts.

Part I is a selective and analytical literature review. Our main concern is with the long tradition of analysis in economic geography -- a tradition that may have been neglected by the mainstream of economic theory, but that nonetheless engaged in a process of cumulative development. We make a somewhat artificial distinction between two parts of that tradition. What we call "urban economics", surveyed in Chapter 2, consists mainly of the von Thünen model, the attempt to explain cities by invoking black-box agglomeration economies, and the use of those concepts in combination in an urban systems theory that is different from but complementary to much of what we try to do in this book. What we call "regional science" (as a catchall for an eclectic mix of approaches that are at best loosely modeled) is closer in spirit to the general approach of this book, trying to derive spatial concentration from the interactions among economies of scale, transportation costs, and factor mobility; in Chapter 3 we focus on central-place theory, the dynamic base-multiplier model, and the concept of market potential.

Part II introduces our basic approach in the context of "regional" models. These are models in which a primary sector, "agriculture", is immobile across locations, while "manufacturing", a sector subject to increasing returns, can move between regions. Chapter 4 introduces the necessary technical tools in the form of the Dixit-Stiglitz model. Chapter 5 then applies these tools to a minimal model which shows how a two-region economy can become differentiated between an industrialized core and an agricultural periphery; the chapter offers a first, and relatively simple, illustration of how numerical methods can be combined with analysis of the break and sustain points to understand the economy's dynamics. Chapter 6 applies the same basic approach to multi-region economies -- especially what we call the "racetrack" economy, a stylized economy with a large number of locations arrayed around a circle. We are able to get surprisingly clear results about this multi-region economy using an approach originally suggested by Alan Turing (1952) for the analysis of morphogenesis in biology; equally surprisingly, the Turing analysis turns out to hinge on the same analysis of symmetry-breaking that we applied in the 2-region case. Finally, both Chapter 5 and Chapter 6 relied on a simplifying assumption that is very unrealistic -- that agricultural goods can be transported costlessly. This makes a difference; Chapter 7 explores the consequences of costly agricultural transport.

Part III turns to a seemingly very different subject: the location of cities in a world in which everything, including agriculture, is mobile. Chapter 8 introduces the subject with a heuristic approach, in the spirit of the "regional science" discussion in Chapter 3, that helps to provide a guide to the more formal results. Chapter 9 develops a model that combines a von Thünen-style approach to land rent with a linkage explanation of manufacturing concentration, showing how a spatial pattern in which a single city is surrounded by an agricultural hinterland can be self-sustaining -- as long as the population is not too large. If the population does become too large, it will be in the interest of a small group of workers to move to some other location; so by using the criterion of sustainability, it is possible to develop a model of the emergence of new cities and hence of a multi-city structure, a task carried out in Chapter 10. If one then supposes that there are actually several manufacturing industries, with different costs of transportation and/or economies of scale, the process of city formation can yield a hierarchy of cities of different types and sizes, as shown in Chapter 11. Chapter 12 takes a break from the main line of argument to discuss the striking and puzzling empirical regularities that characterize actual urban hierarchies. Chapter 13 then returns to the main line of argument to show how variations in the natural landscape, such as ports and rivers, can influence urban location.

Part IV of the book, finally, turns to the analysis of international trade -- defined in this case as models in which labor is immobile between locations. What we do here, however, is to introduce the possibility that labor can move between agriculture and manufacturing, and assume that manufacturing firms use each others' outputs as intermediate inputs. What Chapter 14 shows is that this setup yields backward and forward linkages that can produce symmetry-breaking in exactly the same way that the movement of labor does in the core-periphery model; in this case, however, the breaking and restoration of symmetry drives international inequalities in wages. That model suggests that the secular decline in transport costs can explain both the initial division of the world into industrial and nonindustrial regions, and the more recent spread of manufacturing to newly industrializing economies. Chapter 15 offers an alternative explanation of that spread, focussing instead on the effects of market growth. Chapter 16 turns to the sources of international specialization within the manufacturing sector. Chapter 17, paralleling Chapter 6, offers an analysis of international trade without countries - that is, of the emergence of regions of specialization in a borderless world with continuous space. Finally, Chapter 18 examines a possible interaction between international trade and the process of urbanization within nations.

What we find remarkable and gratifying in all of this is the extent to which we are able to use the same basic modeling "architecture" to address so many issues in seemingly disparate fields. But then our point is precisely that these fields are not that disparate after all: be it urban economics, location theory, or international trade, it's all about where economic activity takes place - and why.