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'l'he papers contained in this volume were originally presented at the International symposium on New Directions in Urban Systems Modelling held at the University of Waterloo in July, 1983. The papers have been reviewed and rewritten since that time. The exception is the introductory paper written specially by Manfred Fischer and Peter Nijkamp as an introduction to this volume. The manuscript was prepared in the word processing unit in the nepartment of Civil Engineering, university of Waterloo. The sustained work of Mrs. I. Steffler in preparing this manuscript is gratefully acknowledged. "'r. R. K. Kumar provided excellent assistance with the editorial process. The svrnposium and the preparation of this manuscript were supporteö financially by the Natural Sciences and Engineering Research Council of Canada, The Academic Development Fund and the Department of Civil Engineering, TTniversity of waterloo. TABLE OF CONTENTS PREFACE •....••...•..•...•..........•..••.•....•.•••.••.••.•..•••••.•.••.. III Categorical Data and Choice Analysis in a Spatial Context Manfred Fischer and Peter Nijkamp .•••....•.......•.•.....•.......•.......
This monograph deals with various classes of deterministic continuous time optimal control problems wh ich are defined over unbounded time intervala. For these problems, the performance criterion is described by an improper integral and it is possible that, when evaluated at a given admissible element, this criterion is unbounded. To cope with this divergence new optimality concepts; referred to here as "overtaking", "weakly overtaking", "agreeable plans", etc. ; have been proposed. The motivation for studying these problems arisee primarily from the economic and biological aciences where models of this nature arise quite naturally since no natural bound can be placed on the time horizon when one considers the evolution of the state of a given economy or species. The reeponsibility for the introduction of this interesting class of problems rests with the economiste who first studied them in the modeling of capital accumulation processes. Perhaps the earliest of these was F. Ramsey who, in his seminal work on a theory of saving in 1928, considered a dynamic optimization model defined on an infinite time horizon. Briefly, this problem can be described as a "Lagrange problem with unbounded time interval". The advent of modern control theory, particularly the formulation of the famoue Maximum Principle of Pontryagin, has had a considerable impact on the treatment of these models as well as optimization theory in general.
1.1. Scope of the Book This book is a contribution to the area of "dynamic models of the firm". The motivation for this kind of research is the following: Empirical studies (e.g. Albach (1976)) have shown that the development of the firm over time can be divided into different stages. such as growth. stationarity and contraction. In order to understand and evaluate these stages in a proper way. it is important to develop a suitable theoretical framework. To that end. economists have applied dynamic mathematical techniques. such as optimal control theory. calculus of variations and dynamic programming to design and analyse dynamic models of the firm. In this way. the economic theory of the firm is extended to a dynamic context. Within the field of the dynamics of the firm this book - develops a general investment decision rule. based on the concept "net present value of marginal investment". which is applicable in deterministic dynamic models of the firm; - studies the influence of adjustment costs of investment on optimal dynamic firm behavior; - extends the stochastic dynamic theory of the firm by connecting it with a dynamic version of the Capital Asset Pricing Model. Before elaborating on "the dynamics of the firm". we first review the subject of net present value in the classical analysis.
This volume presents the results of the 6th Input-Output Meeting, organized in Warsaw, Poland, December 16-18, 1985 by IIASA and the Institute of Econometrics and Statistics, University of Lodz. The main aim of the meeting was to demonstrate the use of integrated input-output models in economic policy making, both at the national and the industrial level.
Organization design has been discussed by many authors in management and organization theory. They have obtained intuitive and prescriptive propositions appealing that the best organization design is contingent on the environmental conditions. But their studies, called contingency theory, are mostly based on empirical research. Most of the "propositions" are drawn as only inferences from the results of them. On the other hand, decision theoretic models of "organizations" in the stochastic environment have been studied by some economists and management scientists independently of contingency theory. In this book, important aspects of organization design problems are formulated as statistical decision problems in the framework of management and organization theory. Part One of this book analyzes a short-run adaptive problems of the organization design. Part One contains an expanded exposition of the ideas and results published in the professional journals, and I would like to thank the anonymous reviewers of the following journals: Behaviormetrika, Human Relations, Behavioral Science. Part Two of this book considers a long-run adaptive process in the organization, and has not previously been published in its IV present form, although a version of this part is to appear in Journal of the Department of Liberal Arts, March 1987, The University of Tokyo. The resul ts of Part One and Part Two are supported by the empirical research on Japanese firms in Part Three. This research was financially supported by Nippon Telegraph and Telephone Public Corporation (NTT). I acknowledge this gratefully.
The present study is a preliminary draft on nonlinear economic dynamics, with which the author has been concerned the last years. It grew out from the joint work by Professor Martin Beckmann and the present author on nonlinear statics in spatial economics, Beckmann and Puu, "Spatial Economics" (North-Holland 1985). The monograph mentioned contains sections on price waves and business cycles, but in a linear format. The rest is static theory. The author has finally come to the conviction that linear dynamic modelling has very little to yield. This is due to the poor set of alternatives -decay or explosion of motion -pertinent to linear models. Therefore, the pr~sent work centres on non-linearity. Another distinction is that only purely causal models are dealt with, as those formatted as inter-temporal equilibria hardly belong to the more restricted field of dynamics. The spatial origin is visible in the choice of models. Chapter 2 summarizes the work by the author on the stmctural stability of continuous spatial market equilibrium models. Chapter 3 deals with a re-formulation of the ingenious population growth and diffusion model invented by the young Hotelling in 1921. Chapter 4 is a detailed digression on business cycle models in a continuous spatial format with interregional trade.
Redistribution is one of the most fundamental issues in welfare economics. In connection with this term the following questions directly arise: What is a good redistribution ? Which (governmental) instruments should be used to attain it ? Is there a "best instrument" if several of them are available? Or, to express it more generally, which allocations are at all attainable if special instruments are at hand ? All these questions are formulated in an extremely vague way. It will be the task of the following work to make these questions precise and to give answers - as far as possible. It is a matter of course that these answers will not be exhaustive because redistribution is too wide a field. I have used the word "instrument" intentionally. In doing so, Iwanted to indicate that it is not necessary to restrict oneself to income - or commodity taxes as is common place in public finance when aiming at redistribution.