A Dynamic Spatial Model

Any interesting model of economic geography must involve a tension between “centripetal” forces that tend to produce agglomerations and “centrifugal” forces that tend to pull them apart. This paper explores one such model, and shows that the model links together a number of themes in the geography literature. These include: the role of market access, as measured by a measure of “market potential”, in determining manufacturing location; the role of forward and backward linkages in producing agglomerations; the potential for “catastrophes”, i.e. , discontinuous changes in location in response to small changes in exogenous variables: and the idea that the economy is a “self-organizing system” that evolves a self-sustaining locational structure. Paul Krugman Department of Economics MIT 50 Memorial Drive Cambridge, MA 02 139 (617) 253-2655 Fax: (617) 2534096 and NRER After a generation of neglect, the last few years have seen a broad revival of interest in regional economics. Economists interested in international trade, in growth, and in macroeconomics have all turned to regional models and regional data. This revival of interest in matters regional has several sources. First, regional economic issues, though they faded from mainstream economics for more than twenty years, are of considerable importance in their own right. The importance of ~the regional dimension has been driven home by such events as the boom-bust cycle in New England and the difficulties of German reunification. So-called "spatial aspects" -a euphemism for the continuing poverty of much of Europe's periphery -are a major issue in the discussions of economic and monetary union in Europe (see Commission of the European Communities, 1990). Second, regional experience provides a valuable laboratory for empirical work. Thus Blanchard and Katz (1992) use regional evidence to investigate the process of macroeconomic adjustment, Barro and Sala-iMartin (1991) use it to investigate the characteristics of the growth process, and Glaeser et.al (1990) use it to shed light on the nature of external economies. 2 Finally, regional economics, or more broadly economic geography, is a subject of considerable intellectual interest. In particular, it is one place in which economic theory can make contact with trends in other fields of research. A number of economists, notably Brian Arthur (1990a, 1990b) have argued that increasing returns and external economies mean that real economies are characterized by strongly nonlinear dynamics. They thus argue that economic analysis should draw on the ideas of scientists like Prigogine (Nicolis and Prigogine 1989), who emphasize the possibilities of multiple equilibria, catastrophic change, and selforganization. (See Waldrop (1992) for an entertaining description of the attempts, centered on the Santa Fe Institute, to make "complexityt' into an interdisciplinary organizing principle). It is debatable how useful these ideas will turn out to be in economics at large, but it seems clear that they have their most natural application in spatial and regional economics. Indeed, geographers have been among the first social scientists to attempt to make use of trendy new concepts in nonlinear dynamics (e.g. Wilson (1981)). This paper is an exploration of the dynamic implications of a simple model of ~economic geography. I have presented versions of this model in two earlier papers (Krugman 1991, 1992). Those papers, however, restricted themselves to static analysis, asking under what conditions particular spatial economic structures were, in fact, equilibria. This paper is explicit about the dynamics. It also extends the two-region or one-city analysis of the earlier papers to the case of multiple agglomerations. While the model is simple in conception, and the results we get are quite intuitive, this dynamic analysis defies paper-and-pencil analytics. Thus the paper relies heavily on numerical examples. This is currently an unfashionable theoretical technique, but as we will see it is highly productive in this case. The paper is in seven parts. Part 1 describes the basic approach, and briefly surveys some theoretical antecedents. Part 2 lays out the assumptions of the model. Part 3 shows how short-run equilibrium is determined. Part 4 uses a static analysis of a two-region case to illustrate the nature of the "centripetal" and "centrifugal" forces in the model. Part 5 then examines dynamics in the two-region case, while Part 6 analyzes 4 the evolution of a multi-region economy. Finally, Part 7 draws some conclusions. 1. The basic aooroach Any interesting model of economic geography must exhibit a tension between two kinds of forces: l'centripetal't forces that tend to pull economic activity into agglomerations, and "centrifugal'V forces that tend to break such agglomerations up or limit their size. There is a well-developed literature in urban economics, largely deriving from the work of Henderson (1974), in which a system of cities evolves from such a tension. In Henderson-type models, the centripetal force arises from assumed localized external economies in production; the centrifugal force is urban land rent. Together with assumptions about the process of city formation, Henderson's approach yields a model of the number and sizes of cities (though not of their location relative to one another). There is a variant of this approach, represented for example by Fujita (1988), in which external economies are not assumed but instead derived from increasing returns in a