Central Place Theory and City Size Distribution

Abstract

This article proposes a theory of city size distribution via a hierarchy approach rather than the popular random growth process. It does so by formalising central place theory using an equilibrium entry model and specifying the conditions under which city size distribution follows a power law. The force driving the city size differences in this model is the heterogeneity in economies of scale across goods. The city size distribution under a central place hierarchy exhibits a power law if the distribution of scale economies is regularly varying, which is a general class that encompasses many well‐known, commonly used distributions.

On the spatial scale of industrial agglomerations

“…One is the relation of bilateral distances for individual industries to those of the aggregate industry. As documented by Mori et al [35] and Mori and Smith [36] for Japan and Hsu [20,Appendix] and Davis and Dingel [8] for the US, clustering tends to be spatially coordinated across industries, so that clusters of many of industries tend to coincide in larger cities. (As an extreme case, Tokyo contains clusters of all industries.)…”

“…In particular, the "Hierarchy Principle" underlying this theory asserts that the set of industries found in smaller metro areas is always a subset of those found in larger metro areas. 57 Theoretical efforts to explain this phenomenon have focused mainly on the role of demand externalities in determining industrial locations (see Quinzii and Thisse [41], Fujita et al [13], Tabuchi and Thisse [47] and Hsu [20]). In particular, the types of demand externalities which induce industrial agglomeration are often shared by many different industries, so that their spatial markets overlap.…”

“…. ,155, be denoted by SD j , then our objective is to relate these indices to the average shipment distance, SD i ⌘ 1 |I i | P j2I i SD j , for each two-digit category i by employing a multiple regression approach paralleling expression (20) above. The results of this regression are shown below: log SD i = 5.812 (23.86) 0.491 ( 3.40) log GE i + 0.529 (4.11) log LD i , adj.…”

“…20 The main idea is to identify an appropriate subset of "most significant" clusters in C, and then take essential containment to be the convex solidification of this set of clusters in R. To identify "most significant" clusters, we proceed recursively by successively adding those clusters in C with maximum incremental contributions to BIC. 21 This recursion starts with the "empty" cluster scheme represented by C 0 ⌘ R 0,0 where R 0,0 denotes the full set of regions, R. If the set of (non-residual) clusters in C is denoted by C + ⌘ C\{R 0 }, then we next consider each possible "one-cluster" scheme created by choosing a cluster, C 2 C + , and forming C 0 (C) = {R 0,0 (C),C}, with R 0,0 (C) = R 0,0 \C.…”

“…For "compounding plastics materials" and "manufactured ice" in particular, this is seen to be true for all three indices (as indicated by the closeness of their respective positions, 4 · and on the horizontal axes in Figure 16. 46 Turning now to a more detailed consideration of these three indices themselves, note first from the adjusted R 2 values in Table 1 (as well as an inspection of Figure 16) that the D-index of Mori et al is most fully captured by model (20). Note in particular that since the estimated coefficients of both log(GE) and log(LD) for D are close to one, the relative values of D are well approximated by log(GE ⇥ LD).…”