Revisiting the problem of integrability in utility theory

We revisit the problem of integrability in the consumer theory, focusing on the main difficulties. First, we look for a neat and simple local existence result, and then for a global solution. Second, observing that a utility function (or indirect utility function) cannot be determined uniquely, we p...

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Bibliographic Details
Published in:Optimization 2015-12, Vol.64 (12), p.2495-2509
Main Authors: Hadjisavvas, Nicolas, Penot, Jean-Paul
Format: Article
Language:English
Subjects:
consumer theory
Frobenius theorem
integrability problem
Mathematics
Operations research
Optimization and Control
revealed preferences
Studies
utility function
Utility functions
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Summary:We revisit the problem of integrability in the consumer theory, focusing on the main difficulties. First, we look for a neat and simple local existence result, and then for a global solution. Second, observing that a utility function (or indirect utility function) cannot be determined uniquely, we propose a means to get a kind of uniqueness result. Our approach is coordinate-free and can be used both in the classical case of a finite-dimensional commodity space and in the case an infinite-dimensional model is adopted.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2015.1080701