An Interaction Model

Methodologically, the IIASA research program on Regional Development reflects the general attitude of the majority of regional scientists. Among other things, this means that the models developed deal with discrete sets of regions or locations. For planning purposes, this approach is extremely efficient, due to computational advantages. On the other hand, systematic information about regional structures, of the geometric flavor associated with classical location theory, is hard to obtain if one discretizes space from the outset. To complement this main stream of regional analysis, two scientists currently trying to revive continuous modeling of the space economy, Martin J. Beckmann and Tonu Puu, were invited to IIASA in September 1979. They started writing a comprehensive monograph intended to present the state-of-the-art in the field of continuous regional modeling. The completion of such an extensive work was not possible in the brief period of three weeks. The authors are currently continuing work on the project. This paper by Tonu Puu constitutes one chapter of the forth-coming monograph. It was completed during his visit to IIASA in August 1982 and follows the chapter circulated as CP-82-11. Whereas the preceding chapters dealt with commodity trade models with unique patterns of flow, the present one describes a simple interaction model cast in a continuous format. Given a specified need for communication and accommodation, optimal land use (balancing traffic congestion and population crowding) is discussed. In addition to the problems of optimal communication routes, the paper focuses on equilibrium population distributions such that communication and housing costs are in balance

An Attempt at Restoring von Thuenen - A Topological Model

This paper uses a topological model together with a structural stability principle as a means to identify and characterize long run solutions as regards regional specialization, direction of trade, and spatial organization. Within this setting not too restrictive assumptions are used to deduce results which shed new light on von Thunen's theory of location and spatial interaction

Long-Run Planning for Capital and Labour Allocation in Space

Methodologically, the IIASA research program on Regional Development reflects the general attitude of the majority of regional scientists. Among other things, this means that the models developed deal with discrete sets of regions or locations. For specific planning purposes, this approach is extremely efficient, due to computational advantages. On the other hand, systematic information about regional structures, of the geometric flavor associated with classical location theory, is hard to obtain if one discretizes space from the outset. To complement this main stream of regional analysis, two scientists currently trying to revive continuous modeling of the space economy, Martin J. Beckmann and Tonu Puu, were invited to IIASA in September 1979. They started writing a comprehensive monograph intended to present the state-of-the-art in the field of continuous regional modeling. The completion of such an extensive work was not possible in the brief period of three weeks. The authors currently continued to work on the project. The present paper by Tonu Puu is one chapter of the forthcoming monograph, and it was finished during his renewed visit to IIASA in April 1982. It deals with planning models for the allocation of available labor and capital resources within a continuous two-dimensional space economy. The main results of the paper concern the advantages of specialization and trade, in the absence of even comparative advantages or localized input supplies. So, the usual conditions for trade, as developed in general (spaceless) economic theory, are not needed, as specialization and trade seem to develop from the nature of bounded two-dimensional space itself. Moreover, the close parallel between the planning and competitive equilibrium solutions is brought out

Continuous Flow Modeling in Regional Science

Although discontinuous methods of regional problem analysis are now widely used, in some cases continuous models might be useful. Professor T. Puu's work is an introduction to the fundamental tools of continuous-flow modeling. Numerous possible implementations of this approach are analyzed in the paper

Structurally Stable Transport Flows and Patterns of Location

This report describes developments of the continuous model of trade and equilibrium in two-dimensional space introduced by Martin J. Beckman in the early 1950s. The original model is extended by treating several interrelated commodity flows and an explicit production activity, transforming the contents of one flow (labor services) into another (finished goods). A residential-industrial agglomeration pattern arises that corresponds to the two flows. This general model, which is capable of representing very diverse spatial organizations, but at the same time contains very little information, is specified by using the generic theory of differential equations. Therefore, if structural stability of the flows of commodities is assumed, it is possible to obtain a rather precise topological characterization of the stable flow and of the corresponding spatial organization. The main conclusion reached is that extreme care should be taken when deriving the results of classical market area from nonlinear models. The classical theory is linear and, therefore, always structurally stable. Without linearity (i.e. homogeneous space) stability is no longer guaranteed, but must be expressly assumed. The conclusions about basic spatial organization then become very different

Spatial Economics: Density, Potential, and Flow

Location theory has traditionally considered space as a two-dimensional Euclidean continuum. It has resorted to geometric constructions and emphasized geometric and geographic intuition. More recently, the emergence of linear and mathematical programming methods in regional analysis has favored an abstract indexing of locations. The matrix of spatial relationships has become the matrix of point-pairs. But the intuitive notions of two-dimensional space have been lost in the process. The purpose of this book is to reintroduce the two-dimensional continuum as the natural spatial setting of economic activities and to exploit the idea for all its worth. Economic interaction between agents are viewed as flows, of commodities or persons. These flows are generated by production and consumption activities, which represent the sources and sinks of a flow field. The direction of flow is oriented by principles of cost minimization and/or of profit or utility maximization. In this way neoclassical economics is wedded to the hydrodynamics of flow fields

Business Cycle and Conserved Quantity in Economics

We propose a dynamical model for business cycle based on an optimal DI model. In the model there exists a conserved quantity, which corresponds to the total energy in a dynamical system. We found that the business cycle with the period 6 or 7 years is nicely reproduced, since the model predicts a periodic motion in the conservative system.Comment: 13 pages and 10 figure

Introduction

This collected volume gives a concise account of the most relevant scientific results of the COST Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", a four-year project supported by COST (European Cooperation in Science and Technology). It is divided into three parts reflecting the different perspectives under which complex spatial economic systems have been studied: (i) the Macro perspective looks at the interactions among international or regional trading partners; (ii) the Meso perspective considers the functioning of (financial, labour) markets as social network structures; and, finally, (iii) the Micro perspective focuses on the strategic choices of single firms and households. This Volume points also at open issues to be addressed in future research