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How to Eliminate Certain Defects of the Potential Formula

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  • J Bröcker

    (Institut für Theoretische Volkswirtschaftslehre der Universität Kiel, Olshausenstraße 40, D-2300 Kiel 1, FRG)

Abstract

The potential formula, defined as a sum of regional ‘masses’ weighted by a decreasing function of distance, is a conventional indicator of accessibility in spatial econometrics. If applied to a system of discrete points in space, however, the standard potential formula with an exponential distance-friction does not convey the desired information in the case of sufficiently large distance-friction parameters. The reason for this defect is that the so-called eigenpotential is inappropriately defined by the standard formula. After reviewing the theoretical foundations of the potential index and advocating its derivation from stochastic choice theory, this paper proposes a modification of the potential formula. The basic idea is to handle the region to which the potential refers as a continuous space with equally distributed density of mass. This leads to an index with desirable limiting properties with respect to the distance-friction parameter.

Suggested Citation

  • J Bröcker, 1989. "How to Eliminate Certain Defects of the Potential Formula," Environment and Planning A, , vol. 21(6), pages 817-830, June.
    • Handle: RePEc:sae:envira:v:21:y:1989:i:6:p:817-830
    DOI: 10.1068/a210817
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    Cited by:

    1. Suárez Cano, Patricia & Mayor Fernández, Matías & Cueto Iglesias, Begoña, 2011. "How important is access to employment offices in Spain? An urban and non-urban perspective," INVESTIGACIONES REGIONALES - Journal of REGIONAL RESEARCH, Asociación Española de Ciencia Regional, issue 21, pages 119-140.
    2. Pooler, James A., 1995. "The use of spatial separation in the measurement of transportation accessibility," Transportation Research Part A: Policy and Practice, Elsevier, vol. 29(6), pages 421-427, November.
    3. John R. Roy, 1998. "Areas, nodes and networks: Some analytical considerations," ERSA conference papers ersa98p94, European Regional Science Association.

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