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The Index Number ProblemConstruction Theorems$
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Sydney Afriat

Print publication date: 2014

Print ISBN-13: 9780199670581

Published to Oxford Scholarship Online: April 2014

DOI: 10.1093/acprof:oso/9780199670581.001.0001

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The Construction of Separable Utility Functions from Expenditure Data

The Construction of Separable Utility Functions from Expenditure Data

Chapter:
(p.133) 4 The Construction of Separable Utility Functions from Expenditure Data
Source:
The Index Number Problem
Author(s):

S. N. Afriat

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199670581.003.0010

Everything in utility theory depends on separability, either explicitly or implicitly. It is made explicit with the idea of a subgroup of goods producing a separate utility on their own which is unaffected by other goods—and by all else besides. Then it becomes a matter of the internal structure of utility. Afriat (1953) marked the decentralization effect on demand behaviour, taken up by Strotz (1957) with a departure amended by Gorman (1959). W. W. Leontief (1957a,b) approached structure for differentiable utility functions by means of conditions on the derivatives. Goldman and Uzawa (1964) deal with the utility belonging to a demand function by reference to the Slutsky coefficients. Further developments not dependent on differentiability have been shown by W. M. Gorman (1968), who has dealt most extensively with separability in this and several articles ranging from (1959) to several of 1968, 1970 and later, including (1987). The purpose in 1969 had been to deal with the matter having reference to a scheme of demand data and compatible utilities, by the finite methods. A main part of the treatment applies to the neglected matter of function construction based on separability models.

Keywords:   consumption, demand, standard of living, Afriat's Theorem, utility structure, Gorman

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