Note on the Measurement of Spatial Imbalance

This note presents a new measure of spatial imbalance that uses the center of gravity (or the mean center) of a distribution and the geometric center (or the centroid) of a region to define a vector indicating the relative position of the distribution in the region. The spatial imbalance of a distribution in a region is defined as the distance and directional deviation of the center of gravity of the distribution from the geometric center of the region. The convex hull of a region is introduced as the reference for maximum spatial imbalance of the distribution in the region. The spatial imbalance is measured in terms of (1) the relative distance of the center of gravity between the geometric center and the convex hull; and (2) the direction from the geometric center to the center of gravity. This new measure is tested by quantifying the westward movement of the contiguous U.S. population between 1790 and 1950. It describes the well‐known observation that the U.S. population was moving westward across the contiguous United States and toward reduced spatial imbalance.     

Enduring Partnership

Book reviewed in this article:
Michael Schaller, Altered States: The United States and Japan since the Occupation     

Book reviews

Dynamique de l'espace français et aménagement du territoire. (The Dynamics of French Space and Spatial Planning), Michel Rochefort. Paris: L'Harmattan, 1995, 138 pp, £15.00, ISBN 2 7384 3338 3

Urban Process and Power. Peter Ambrose. London and New York: Routledge, 1994, 245 pp, £12.00 pb, ISBN 1 415 00850 6; £40.00 hb, ISBN 0 415 00850 4

Transport Systems, Policy and Planning: a Geographical Approach. R. Tolley and B. Turton. Harlow: Longman, 1995, xviii + 401 pp, £20.99 pb, ISBN 0 582 00562 0

Transport Policy—Ways into Europe's Future (Strategies and Options for the Future of Europe: Basic Findings 8). K. Button, with contributions by W. Weidenfeld, G. Wolfgang Heinze, H. H. Kill, R. Münch, N. Walter, G. Topmann, H. Holzapfel and K. O. Schallaböck. Gütersloh: Bertelsmann Foundation Publishers, 1994, 227 pp, £9.00, ISBN 3 89204 065 6

The European Challenge: Geography and Development in the European Community. M. Blacksell and A. M. Williams (Eds). Oxford: Oxford University Press, 429 pp, 1994, £45.00 hb, ISBN 0 19 874176 6; £15.95 pb, ISBN 0 19 874177 4     

STACKELBERG GAMES ON A NETWORK WITH COURNOT-NASH OLIGOPOLISTIC COMPETITORS

ABSTRACT. We formulate the spatial Stackelberg-Nash-Cournot competitive network equilibrium problem as a variational inequality constrained mathematical program. Our model differs from previous models of Stackelberg oligopolistic competition in that it employs explicit shipping decision variables and a general network topology. That is, the production and distribution decisions of the Stackelberg firm are determined simultaneously over a discrete network. We explore the existence of solutions to the proposed model, and we also numerically test a sensitivity analysis based algorithm. In particular, we illustrate how sensitivity analysis results can be used to generate the Cournot reaction necessary to solve the Stackelberg problem.     

A Generalization of the Utility Theory Approach To the Problem of Spatial Interaction

The derivation of the gravity model from utility theory is reformulated and generalized in order to show (1) how both the number of trips to individual destinations and the total travel budget may be determined simultaneously, and (2) how the effect of both distance and destination quality on trip distribution and total budget may be analyzed. Results are compared with the revealed space preference approach and are found to be superior in dealing theoretically with trip frequency and the effects of spatial context. For empirical applications, however, the revealed preference approach is advantageous.