On the integrability problem in discrete spatial activity systems with site and network externalities

Abstract

This paper addresses the standard ‘integrability problem’ of microeconomics, in the case of discretely spatially distributed consumers, each with a randomly valued utility function, and consuming a fixed amount of a given activity/product, and in the presence of demand externalities, due, for instance, to congestion at the supply sites and/or on the access network. The aggregate direct utility of the ‘representative consumer’ representing all the individual consumers is identified. It is shown how the representative consumer's direct utility maximization provides a rigorous mathematical programming model of spatial activity allocation and travel. Also, the representative consumer's indirect utility, which explicitly measures externality effects on social welfare, is also obtained. Several areas for further investigation are identified.