Aggregation in the Short and Long Run
The paper begins with the short‐run aspect, giving a very brief survey of known results in aggregation theory, reminding us that the basic trick in most aggregation problems is to change the endowments of firms and to see how this changes the economy overall. Section 2 starts with the long‐run problem; the reason for calling this a long‐run problem is that the technologies do not depend upon vectors of capital stocks or endowments, which, in principle, could be used to move the firms around in the economy; the same analysis would therefore hold if firms’ technologies depend on a set of endowments that could not be moved about for the analysis. Sections 2–4 are devoted to the case in which there is only one aggregate in each firm as well as in the economy; this analysis was done in the early 1980s and presented at Mirrlees's lunchtime workshop at Nuffield College, Oxford, in 1982, and at the LSE mathematical economics seminar in 1983. The rest of the paper analyses the case when there are many aggregates both in the firms and in the economy as a whole––each of the aggregates can be one of three different types, and furthermore, these different types, in some circumstances, interact with one another to produce still further restrictions; this part of the paper existed in various handwritten forms until the present version was written for a conference at the London Business School in October 1989. The analysis here is complex and at times difficult to follow, but this seems to be inherent in the nature of the problem being analysed.
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