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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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Revealed Preference Revealed

Revealed Preference Revealed

(p.178) 6 Revealed Preference Revealed
The Index Number Problem

S. N. Afriat

Oxford University Press

The revealed preference method of Samuelson and Houthakker, dealing with the existence of a numerical utility fitting a given demand function, is examined again. After discussion of the method and proof of a related theorem, another development is proposed, resolving defects in the original approach which have persisted despite repeated attention. Their argument depends on invertibility of the demand function and is readapted to be free of that restriction. Also it needs to be taken a step further to reach the required conclusion. Besides providing the wanted gain in generality, a monotonicity argument with a dual approach, depending on mathematical auxiliaries which, together with the monotonicity, are a main contribution of this chapter, settles problematic convergence questions.

Keywords:   choice, order, preference, revealed preference, Samuelson, Houthakker, price index, price level, Index Number Problem, consumption, demand, demand function, standard of living, utility structure

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