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Mathematical Location and Land Use ATheory: An Introduction
by
Tonu Puu
Springer-Verlag. Berlin-Heidelberg-New York, 1997
This book offers an excellent introduction to the theory of continuous location of economic activities in two-dimensional space based on differential equations and to their solution by vector calculus methods.
Continuous models of location focus on geometric aspects of the economic process in space that are not described - at least not visibly - by the standard discrete equilibrium models. In particular, the shapes of optimal routes and market areas, the patterns of population and land use, and the topographical structure of transportation networks are reflected and illustrated by the continuous approach.
Spatial phenomena are basically visual. Their display by means of continuous geometric models has a long tradition in spatial economics. Puu builds on the classic approaches of von Thunen, Launhardt, Weber and Pick, Losch, Christaller and Palander. (Tord Palander was Puu's academic teacher.) He extends and develops them in an admirable way. The classic results suffer from overly restrictive assumptions. Besides a homogeneous space, linear technologies are assumed. Using Beckmann's (1952) continuous model of transportation, which had been neglected for a long time, Puu has succeeded in generalizing the classic results (and many more) to a...