Frisch demands that are separable in the budget multiplier \(\lambda\) turn out to have a surprisingly simple structure. We give a complete characterization: quantities are $λ$-separable iff utility is additively separable.

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Abstract

Frisch demands depend on prices and a multiplier \(\lambda\) associated with the consumer’s budget constraint. Subject only to standard, modest, regularity conditions, we provide a complete characterization of all Frisch demand systems and of the utility functions that rationalize these demand systems when either quantities demanded or consumption expenditures are separable in \(\lambda\). Quantities demanded are $λ$-separable if and only if the rationalizing utility function is additively separable in these quantities. In contrast, expenditures are $λ$-separable if and only if marginal utilities for these expenditures belong to one of two simple parametric families.

BibTeX

@Article{	  ligon16a,
  author	= {Ethan Ligon},
  title		= {All $\lambda$-Separable Demands and Rationalizing Utility
                Functions},
  journal	= {Economics Letters},
  year		= 2016,
  volume	= 147,
  pages		= {16--18},
  doi		= {10.1016/j.econlet.2016.08.010}
}