Economies with a two-sector representation

Summary In both theoretical and empirical research it is a common practice to partition the economy into (at least) two sectors in order to conduct partial-equilibrium analysis. One merely hopes that general-equilibrium consequences will not obviate all of the analysis of the sector or market in question. In this paper we consider market demand functions which have a two-sector representation. In such economies the aggregate compensated demands in any one sector depend only on prices in that sector, the vector of utilities, and a scalar aggregate which in turn may depend upon everything. In particular, prices in the other sector appear only through this aggregate. In a single-consumer economy this division into two sectors carries with it no further implications. However, when there are three or more consumers, economies with a two-sector representation, which may contain public as well as private goods, must fall into a small number of broad classes which are quite restrictive. This means that the two-sector assumption is far less innocuous than one might have previously believed and that there are some phenomena which simply cannot be investigated in this framework.This research has been supported by the SSHRCC with a research grant and by leave fellowships to all three authors for the year 1984–85. Since then all three authors have been in part supported by various SSHRCC grants. In 1989–90 Blackorby was also partly supported by a Senior Killam Fellowship. The first version was written while all three of us were at CORE, Université Catholique de Louvain, 1984–85. Later versions were written at the University of British Columbia (Blackorby and Schworm), the University of Western Ontario (Schworm), Université Libre de Bruxelles (Davidson), Queen's University (Davidson), Université d'Aix-Marseille II (Davidson), Université d'Aix-Marseille III (Blackorby) and finally GREQE-EHESS (Blackorby and Davidson). We thank all of them for their support. Earlier versions of this paper have been presented at the 1986 Canadian Economic Theory Meetings, the Nuffield Conference on Measurement and Modelling in Economics-May, 1987, the Rheinische Friedrich-Wilhelms-Universität Bonn, the Université de Montréal, University of Saskatchewan, and the University of California at Riverside. We have benefited from the comments of the participants in these seminars, and from those of two anonymous referees.