Puu Mathematical Location and Land Use Theory

An Introduction
2. Auflage 2003
ISBN: 978-3-540-24785-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 362 Seiten, eBook

Reihe: Advances in Spatial Science

Covers all main topics of spatial economics, plant location, the theory of nested market areas, including rank-size relations, spatial competition and pricing, land use theory and the emergence of specialization and trade, commuting and traffic distributions according to the gravity and entropy hypotheses, migration, and the layout of transportation networks. A strong focus is on the continuous two dimensional geographical space, with Beckmann's continuous flow model as central piece. Another feature is a focus on structural stability rather than optimality of emergent patterns. All the specific mathematical tools needed are developed within context. The whole approach is intuitive, and supported by lavish computer graphics. The new edition contains extensive material on spatial competition, oligopoly theory in Hotelling's setup. The Hotelling case is formally worked out with elastic demand, which limits the occurrence of some of the confusing paradoxes Hotelling found for inelastic demand.

Zielgruppe

Research

Autoren/Hrsg.

Puu, Tönu

Inhaltsverzeichnis

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 Gravity Model.- 6.2 Traffic: Linear Routes.- 6.3 Traffic: Spiral Routes.- 6.4 The Entropy Model.- 6.5 Hotelling’s Migration Model.- 6.6 Stability of Hotelling’s Model.- 6.7 Hotelling’s Model with Production.- 6.8 Pure Growth in the Model with Production.- 6.9 Stationary Solutions for the Model with Production.- 6.10 Travelling Waves for the Model with Production.- 7 Cycles, Growth, and Equilibrium.- 7.1 Spatial Growth.- 7.2 Spatial Business Cycles.- 7.3 Equilibrium of the Beckmann Model.- 7.4 Stability.- 8 Transportation Networks.- 8.1 Transportation Cost Metrics.- 8.2 Nested Networks.- 8.3 Detours and Accessibility.- 8.4 Topological Considerations.- 8.5 Networks in Reality.- 8.6 Fractal Networks.- 8.7 Central Networks.- 8.8 The Number of Radials.- 8.9 Approximations.- 8.10 Bifurcations of Radials.- 8.11 Curved Bifurcations.- 8.12 Accessibility.- Epilogue.- List of Figures.- Author Index.- Glossary of Formulas.