Krugman's spatial economics

Development, Geography, and Economic Theory, Paul Krugman, 1995

More from Krugman. He gives a particularly good summary of various economic theories of agglomeration.

Germanic geometry
1. Weberian location theory:
Alfred Weber and his followers ... analyzed the location decision of a firm serving one or more markets and relying on one or more sources of supply, with the total number of such relevant points not less than three. The problem was that this was essentially geometry and didn't take into account who was making the decisions and how; there was no mention of competitors, pricing etc.; and there was no explanation why there should be only one production site.

2. Central-place theory (Loesch, Christaller)
This analyzed the location and roles of manufacturing/marketing/ect. centers serving a hypothetical evenly spread agricultural population. In this tradition, Loesch had the big geometric insight -- that market areas should be hexagonal -- while Christaller produced the empirically fruitful idea that tere should be a hierarchy of central places, with nested market areas. ... the trade-off between economies of scale and transportation leads producers to cluster together into a hierarchy of cities serving nested, hexagonal market areas. But on closer inspection it becomes unclear exactly what is supposed to be going on. Who is making location decisions? There is also no clear description of market structures.

Central-place theory implies that we are in a world in which there are unexhausted economies of scale, and thus in a world of imperfect competition. You can't tell a story about central-place formation unless you are prepared to offer some description, however stylized, of that imperfectly competitive market structure. And that, until relatively recently, was something economists felt unable to do.

Social physics
This is economic geography done by analogy to physics: working with the problem of balancing several discrete forces of attraction and developing new theories to explain empirical regularities (e.g. Zipf's law of city size distribution).
In the 1950s American geographers came up with the idea that firms tend, other things equal, to choose locations of maximum "market potential," where the market potential of a site was defined as some index of its access to markets, involving both the purchasing power of all the markets to which it might sell and the distance to those markets. However, it is completely unclear what is being maximized when a firm chooses a point of maximum market potential. Again, market structure is the problem. Firms cannot exhibit constant returns to scale -- otherwise one would simply establish a facility to serve every market, ... nor can they be producing goods that are perfect substitutes.

Cumulative causation
One immediately obvious implication of the market potential analysis is the possibility of circularity. Firms want to locate where market potential is high, that is, where lots of firms locate. So one is led naturally to a consideration of the possibility of self-reinforcing regional growth or decline. This line of thinking follows the "Big Push" model of high development theory. While Big Push-type stories may be implausible for the economy as a whole (since they assume perfectly elastic supply of labor), they may make perfectly good sense for a particular region since the supply of factors to any specific region will typically be very elastic because they can come from somewhere else.

Some of the authors of the classic high development tracts seem to have realized this. ... The explicit application of high development concepts to region growth, however, is something one usually associates with Alan Pred (1966). Pred's story is essentially a variant on the Big Push. Suppose that a regional economy grows to the critical point at which it becomes profitable to replace imports of some good subject to scale economies with local production. This import substitution will expand regional employment, drawing in workders from other regions; and in so doing will further expand the local market. This market expansion may, in turn, provide the market size necessary to induce a second round of import substitution, and son on -- a cascade of growth reflecting the circular relationship between market size and the range of industries that a region possesses.

(I find that this resonates very much with Jane Jacobs' ideas about how the earliest cities formed.)

Local external economies
The idea that clustering of producers in a particular lcation yields advantages, and that these advantages in turn explain such clustering, is an old one. ... Indeed, to those who imagine that increasing returns are something only recently discovered, it is startling to see how much attention is given in Marshall's 'Principles' to local externalities. They are emphasized both for their intrinsic importance and for the way they exemplify his concept of external economies in general.

What Marshall meant by an external economy was not exactly what later authors meant. In the 1940s and 1950s economists came to make a clear distinction between technological external economies -- pure spillovers -- and pecuniary externalities mediated through the market. In a world of constant returns at the level of the firm and perfect competition, pecuniary externalities don't have any particular importance, so onl technological spillovers matter. Marshall, however, did not make this distinction. ... In the light of current theory, of cours, he was right to do so. We now understand that the sharp distinction between technological and pecuniary external economies holds only in a contant-returns world; in general market-size external economies are just as real as technological spillovers. ...

Suppose that we think of positive local external economies, which tend to promote concentration of production, as being opposed by other effects -- congestion or land costs -- that tend to promote dispersal. Then we are on our way toward a story about both the optimal size of cities and, if we are prepared to make some assumptions about the process of city formation, a theory of the actual size and number of cities. (cf. Vernon Henderson, 1974).

Land rent and land use
The analysis of land rent and land use derives directly from von Thuenen's Isolated State. He envisaged an agricultural plain supplying a variety of products to an isolated central city; and he realized that one could think of the simultaneous determination of a land rent gradient declining from the center to an outer limit of cultivation, and of a series of rings in which different crops would be clutivated and/or different farming methods adopted. Thus the high-rent land near the center would be reserved for crops with high costs of transportation and/or crops yielding high value per acre; the outermost ring would consist of either land-intensive or cheaply transported crops. This model conforms surprisingly well to neo-classical economics in that it includes the idea of an equilibrium and the idea that 'value' is an emergent consequence of a market process, goods and factor prices, and efficient outcomes of markets. Unfortunately, it simply assumes the thing you want to understand: the existence of a central urban market. Indeed, the whole thrust of the model is to understand the forces that spread economic activity away from that center, the "centrifugal" forces if you will. About the "centripetal" forces that create centers, that pull economic activity together, it can and does say nothing.

The "new urban economics," which deals mainly with central business districts followed in this tradition in the late 1960s and early 1970s.

Krugman's model
In Krugman's own words: I imagine an economy with a number of separate locations. There are two sectors: agriculture, which is geographically immobile, and manufacturing, which is mobile over time. The geographic reallocation of manufacturing is, however, not instantaneous. ...

Manufacturing consists of many firms producing differentiated products; increasing returns ensure that not all potential goods are produced, and thus that each plant produces a unique good ... . The monopolistic competition assumption neatly, if implausibly, disposes of problems like strategic behavior. All that firms need to do is choose an optimal location, taking into account the spatial distribution of demand and the transportation costs they must pay. ...

The most important thing I learned is that all of my first four traditions in spatial analysis ... make perfectly good sense in terms of a rigorous economic model. ... Moreover, it turns out that all four traditions are really different aspects of the same story.