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Shape Invariant Demand Functions

Listed author(s):
  • Arthur Lewbel


    (Boston College)

Shape invariance is a property of demand functions that is convenient for semiparametric demand modelling. All known shape invariant demands are derived from utility functions that, up to monotonic transformation, are called IB/ESE (independent of base - equivalence scale exact) utility functions, because they yield IB/ESE equivalence scales, which are widely used in welfare calculations. This paper provides a counterexample, i.e., a shape invariant demand system that is not derived from a transform of IB/ESE utility. A general theorem is then provided that characterizes all shape invariant demand systems. The usual practice of equating shape invariance with the IB/ESE utility class is shown to be not quite right, but it can be made valid by testing for the small class of exceptions noted here. In particular, all the exceptions have rank two, so any rank three or higher shape invariant system must be derived from transforms of IB/ESE utility.

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Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 669.

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Length: 18 pages
Date of creation: 13 Jun 2007
Date of revision: 26 Nov 2008
Handle: RePEc:boc:bocoec:669
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