Unpacking Central Place Geometry I: Single Level Theoretical k Systems

This paper examines the spatial and potential economic consequences of relaxing the geometrical packing requirement of classical central place theory. Diagrams are wed to demonstrate that geometric packing is not necessary to satisfy demand at all discrete points at a given hierarchical level. With unpacked landscapes the same population can be smed~ fewer, me widely spaced, central places without increasing the length of journey to shop. Consumers have fewer choices in an unpacked landscape, but economies of scale may increase the away of consumer goods and services available. Relaxing the packing requirement allows the development of a range of stable k systems (i.e., firther market entry is disallowed). Between the limits of the k = 3 system (Christaller’s marketing principle) and the k = 7 system (the sociopolitical or administrative principle), a range of unpacked k systems can develop including a k = 5 and a k = 6 system. Noninteger k systems are also possible as are systems which are stable mixtures of coexisting k principh. In certain instances, it is economically advantagem for two or me entrep7eneurs to co-locate in the same central place rather than attempting monopolistic control mer a mure limited hinterland. Such a result is consistent with both Berry and Garrison’s concept of the duplication ratio and with recent trd in retail location. This paper will examine the spatial consequences of relaxing the packing requirement of classical central place theory. Complete mathematical packing in a central place context is defined as a system in which all market area boundaries are mutually shared between two or more central places. Packing has been a sine qua non in central place research; its necessity has never before been questioned. Packing was felt necessary in order to accomplish two interrelated purposes: to assure that all the population in the isotropic plain is served by at least The authors thank Will Fontanez, cartographic technician at the Cartography Services Laboratory of the University of Tennessee, Knoxville, for drafting the figures which appear in this article. The authors are indebted to Arthur Getis, Gerard Rushton, and Avijit Ghosh for reading and commenting on versions of this manuscript. Thanks are also extended to three anonymous reviewers for their helpful suggestions.