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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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The Structure of Utility Functions

The Structure of Utility Functions

Chapter:
(p.147) 12 The Structure of Utility Functions
Source:
Separability and Aggregation
Author(s):

W. M. Gorman (Contributor Webpage)

, C. Blackorby, A. F. Shorrocks
Publisher:
Oxford University Press
DOI:10.1093/0198285213.003.0012

The central result of this paper, which was published in the Review of Economic Studies 35 (1968), is the overlapping theorem, which is developed in Sect. 2 of the paper. A special‐case example given in the editorial summary shows that the theorem is concerned with the overlapping of two separable sets that have a non‐empty intersection, and are not subsets of each other; a development of the utility function in this situation indicates that it is additive in the intersection and two set differences, conditional on the rest of the variables in the function. Examples are also given in the editorial summary to indicate the power of the overlapping theorem, and the paper itself gives two applications of the theorem in Sect. 4: one to intertemporal preferences and the other a proof of the Klein–Nataf theorem (the aggregation of production relations). Sections 3 and 5 contain alternative procedures for uncovering the structure of any utility function, and Section 6 relaxes one of the maintained hypotheses (strict essentiality). The appendix contains two lemmas that prove the separable representation theorems of Debreu.

Keywords:   aggregation of production relations, intertemporal preferences, Klein–Nataf theorem, overlapping theorem, separable representation, strict essentiality, structure of utility functions, utility functions

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