Injectivity and the Law of Demand

Abstract

Establishing that a demand mapping is injective is core first step for a variety of methodologies. When a version of the law of demand holds, global injectivity can be checked by seeing whether the demand mapping is constant over any line segments. When we add the assumption of differentiability, we obtain necessary and sufficient conditions for injectivity that generalize classical Gale and Nikaido [1965] conditions for quasi-definite Jacobians. * I thank Nail Kashaev, Salvador Navarro, John Rehbeck, and David Rivers for helpful comments.

Identification of Random Coefficient Latent Utility Models

“…12 A key step to apply these methods is injectivity in a market-level observable to a vector of unobservable endogenous vectors, usually denoted ξ. See Allen [2019] or Lemma 3 in Allen and Rehbeck [2019a] for injectivity results that cover the present model when the utility index for good k is β 1 k x k `ξk . Related injectivity results have appeared in Galichon and Salanié [2015] and Chiong et al [2017].…”