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Separability and AggregationThe Collected Works of W. M. Gorman, Volume I$
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W. M. Gorman, C. Blackorby, and A. F. Shorrocks

Print publication date: 1996

Print ISBN-13: 9780198285212

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198285213.001.0001

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Separable Utility and Aggregation

Separable Utility and Aggregation

(p.31) 3 Separable Utility and Aggregation
Separability and Aggregation

W. M. Gorman (Contributor Webpage)

, C. Blackorby, A. F. Shorrocks
Oxford University Press

Separability is a maintained hypothesis throughout this paper, which was published in Econometrica 27 (1959). Hence, the results of the previous paper are applicable: that is, it begins with the assumption that two‐stage budgeting is possible, but that no restrictions are imposed on the information used to discover the optimal expenditure on each group. The paper considers the implications of reducing the information available to make the intergroup allocation decision, and begins by investigating the conditions in which a consumer with a well‐behaved separable utility function can find the optimal income allocation for a group, given only the price indices for each group. In Sect. 1, Gorman posits the existence of differential price indices, and his Proposition I provides the necessary and sufficient conditions for local price aggregation, maintaining separability of the direct utility function. Section 2 of the paper considers the case of perfect price aggregates, and the conclusion makes specific remarks about an earlier paper written for the same journal by R. H. Strotz, of which this paper of Gorman's is essentially an elaboration of Gorman's referee's report.

Keywords:   aggregation, allocation, budgeting, differential prices indices, intergroup allocation, local price aggregation, optimal expenditure, perfect price aggregates, price indices, separability, separable utility function, two‐stage budgeting

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