Focusing on the location of industries and economic activities, this book presents a contemporary perspective rooted in the (neo-)classical tradition. It explores market areas, spatial price distribution, and urban systems through elementary economic reasoning and straightforward mathematical models. The author, with extensive experience since 1950, includes numbered Mathematical Notes to clarify the methods used, blending classical and innovative approaches to spatial interaction and locational specialization.
Exploring the emergence and survival of spatial structures, this collection of essays delves into how economic forces shape markets within a two-dimensional continuum. It examines the necessity of spatial concentration for achieving increasing returns to scale and the implications of Adam Smith's assertion regarding the division of labor's dependence on market size. Each essay, while distinct in its approach, contributes to a cohesive understanding of spatial economic analysis and the dynamics of markets over distances.
To start with we describe two applications of the theory to be developed in this monograph: Bernoulli's free-boundary problem and the plasma problem. Bernoulli's free-boundary problem This problem arises in electrostatics, fluid dynamics, optimal insulation, and electro chemistry. In electrostatic terms the task is to design an annular con denser consisting of a prescribed conducting surface 80. and an unknown conduc tor A such that the electric field 'Vu is constant in magnitude on the surface 8A of the second conductor (Figure 1.1). This leads to the following free-boundary problem for the electric potential u. -~u 0 in 0. \A, u 0 on 80., u 1 on 8A, 8u Q on 8A. 811 The unknowns are the free boundary 8A and the potential u. In optimal in sulation problems the domain 0. \ A represents the insulation layer. Given the exterior boundary 80. the problem is to design an insulating layer 0. \ A of given volume which minimizes the heat or current leakage from A to the environment ]R. n \ n. The heat leakage per unit time is the capacity of the set A with respect to n. Thus we seek to minimize the capacity among all sets A c 0. of equal volume.
