Mathematical Location and Land Use Theory

Prologue.- 1 Location Theory.- 1.1 The Weber Problem.- 1.2 Pick's Construction.- 1.3 Location and Substitution.- 1.4 Non-Euclidean Metrics.- 2 Optimal Routes.- 2.1 Flows and Routes.- 2.2 Parameterized Paths.- 2.3 Shortest Paths and Euler's Equation.- 2.4 A Simpler Case.- 2.5 An Example.- 2.6 Another Example.- 2.7 Fermat's Principle and Snell's Law.- 2.8 Geodesics on Curved Surfaces.- 2.9 Generalizations: Several Functions.- 2.10 Generalizations: Constraints.- 2.11 Coordinate Transformations.- 2.12 The Isoperimetric Problem.- 3 Flows in the Space Economy.- 3.1 Flows in One Dimension.- 3.2 Flows in Two Dimensions.- 3.3 Euler's Equations Revisited.- 3.4 Minimal Surfaces.- 3.5 Generalizations.- 3.6 Beckmann's Flow Model.- 3.7 Uniqueness in the Beckmann Model.- 3.8 Aggregate Values.- 4 Market Areas.- 4.1 From Launhardt to Lösch.- 4.2 Compactness and Stability.- 4.3 Optimality Versus Stability.- 4.4 Nesting of Market Areas.- 4.5 Rank-Size Relations.- 4.6 Price Policies.- 4.7 Mill Pricing.- 4.8 Discriminatory Pricing.- 4.9 Uniform Delivery Price.- 4.10 Oligopoly Theory.- 4.11 Local Oligopoly.- 4.12 Disjoint Monopolies.- 4.13 The Hotelling Case.- 4.14 Equilibrium for Two Identical Firms.- 4.15 Crowding and Price Undercutting.- 4.16 Oligopoly in 2D: Equilibrium.- 4.17 Oligopoly in 2D: Price Cuts.- 4.18 Oligopoly in 2D: Cutting Out Competitors.- 4.19 Oligopoly in 2D: Touching Monopolies.- 4.20 Oligopoly in 2D: Partial Changes of Location.- 4.21 Public Utility Location.- 4.22 Demand: One Dimension.- 4.23 Bifurcations.- 4.24 Nonlinear Demand.- 4.25 Two Dimensions: Circles.- 4.26 Two Dimensions: Polygons.- 5 Land Use.- 5.1 Von Thünen's Model.- 5.2 Generalization: Production.- 5.3 Generalization: Transportation.- 5.4 Beckmann's Flow Model Revisited.- 5.5Differential Equations in the Plane.- 5.6 Structural Stability Defined.- 5.7 The Square Flow Grid.- 5.8 Triangular/Hexagonal Grids.- 5.9 Changes of Structure.- 5.10 Fractal Rent Landscapes.- 6 Commuting and Migrating.- 6.1 The

Extracts from reviews of the first edition:

"This book is 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. As Puu states "good science is to be easily understood. This book is, indeed, a lucid and easily readable introduction to the fundamental concepts of spatial economic theory and the differential calculus machinery of the continuous transportation model."

K. C. Mosler in "Location Science"

"This book represents an honest attempt at introducing spatial economic theory. The author does not appear to be interested in showing off his obvious mathematical skills. His intention is to summarize the accumulated knowledge in the field and present the main results in a simple manner. He does an admirable job. Of help are the high-quality graphics, the omission of semicooked ideas and messy results, and the author's extensive experience on the subject over a long period of time."

P. S. Kanaroglou in "Environment and Planning"