The ideas of this book originate from a research group at the Department of Economics in Gothenburg working with the problem of "Relations between Physical and Economic Planning". The research was financed by grants from the Swedish Council for Building Research. Among all the persons, who from time to time were associated to the project group, the author wishes to express his particular thanks to Ph.D. Rune Jungen, Ph.D.Johan L6nnroth and M.A.Lars Andersson. c' This book is also my doctoral dissertation for which professor Ake E. Andersson has acted as supervisor. It has been a privilege for me to have him as my supervisor. I have benefited a great deal from a professional as well as a personal point of view. There are other members of the Department of Economics to whom I am indebted. Professor Harald Dickson was a close reader of my last drafts. The help I got from Ph.D.Lennart Hjalmarsson and Ph.D.Olle Ohlsson has also been indispensable to me. Ph.D.Barbro Atlestam, M.A.G6sta Olavi and Ph.D.Folke Snickars have assisted with calculations and the solution of mathematical pro- blems. At last the author wishes to thank M. A . Mette Lembring who made the translation from Swedish. Jan Gunnarsson Contents V PREFACE Definition of the problem and results 1. 1.1. Some comments on the structure of systems of centres 1 A brief survey of problems 5 1.2.