In the preceding chapters, Micro-economic theories of the use of space were reviewed, followed by spatial interaction and entropy maximising models, and finally random utility theory was described. This chapter concludes the general theoretical framework by describing another important development from macro-economics: the input–output model. This introduces a new dimension to the problem, that of production and its relation to the urban and regional structure.

In very broad terms, the first generation of input–output models were intended as nationwide global economic accounting frameworks; the second generation of i–o models attempted a regional disaggregation; a third generation, currently in progress, attempts a more general description of the structure of a nation, and consequently these models have been defined as social accounting models. The intention of this chapter is to derive a general model to represent a spatial-economic system at any scale, capitalising on the teachings of random utility theory. Since spatial aspects become so closely linked to the economic accounting ones, the results have been termed spatial accounting models.

Keynes' theory of production and the multiplier is briefly reviewed as a starting point for later developments of regional theories such as the theory of regional rent and the study of the economic base of a region. Then the elements of the input–output model are presented and its regional disaggregation. At this point, the presentation diverts from the main stream by re-introducing random utility concepts, with related decision chains, variable costs, elasticities and hierarchies.

The theory of production and the multiplier

Keynes (1936) begins by introducing the principle of effective demand, whereby the process of production is mainly determined by consumption. According to this principle, producers determine the level of their activity according to their estimates of future demand.