Integrability and Generalized Separability
48 Pages Posted: 5 Feb 2018 Last revised: 22 Oct 2018
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Integrability and Generalized Separability
Date Written: January 2018
Abstract
This paper examines demand systems where the demand for a good depends only on its own price, consumer income, and a single aggregator synthesizing information on all other prices. This generalizes directly-separable preferences where the Lagrange multiplier provides such an aggregator. As indicated by Gorman (1972), symmetry of the Slutsky substitution terms implies that such demand can take only one of two simple forms. Conversely, here we show that only weak conditions ensure that such demand systems are integrable, i.e. can be derived from the maximization of a well-behaved utility function. This paper further studies useful properties and applications of these demand systems.
Keywords: integrability, non-homothetic preferences, Recoverability, Separable demand, Single aggregator
JEL Classification: D11, D40, L13
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