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All \lambda-separable Frisch demands and corresponding utility functions

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  • Ligon, Ethan

Abstract

Frisch demands depend on prices and a multiplier \(\lambda\)associated with the consumer's budget constraint. The case in whichdemands or expenditures are separable in $\lambda$ is the case ofgreatest empirical interest, since in this case latent variablemethods can be adopted to control for consumer wealth when estimatingdemands. Subject only to standard, modest, regularity conditions, we provide a completecharacterization of all Frisch demand systems and of the utilityfunctions that rationalize these demand systems when either quantitiesdemanded or consumption expenditures is separable in $\lambda$. Quantities demanded are \(\lambda\)-separable if and only if therationalizing utility function is additively separable in thesequantities. In contrast, expenditures are \(\lambda\)-separable ifand only if marginal utilities for these expenditures belong to one oftwo simple parametric families. With $n$ goods, the first family has$2n$ parameters, and corresponds to Houthakker's "direct addilog"utility function. The second family has $3n$ parameters and is new.It corresponds to a family of utility functions which have Stone-Gearyutility as a limiting case.

Suggested Citation

  • Ligon, Ethan, 2016. "All \lambda-separable Frisch demands and corresponding utility functions," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt1w13q2f1, Department of Agricultural & Resource Economics, UC Berkeley.
  • Handle: RePEc:cdl:agrebk:qt1w13q2f1
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    Keywords

    Social and Behavioral Sciences; Frisch demands; separability; Pexider equations;
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