, Volume 52, Issue 3, pp 1039-1060
Date: 03 Nov 2011

Monotone comparative statics: changes in preferences versus changes in the feasible set

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Let a preference ordering on a lattice be perturbed. As is well known, single crossing conditions are necessary and sufficient for a monotone reaction of the set of optimal choices from every chain. Actually, there are several interpretations of monotonicity and several corresponding single crossing conditions. We describe restrictions on the preferences that ensure a monotone reaction of the set of optimal choices from every sublattice whenever a perturbation of preferences satisfies the corresponding single crossing condition. Quasisupermodularity is necessary if we want monotonicity in every conceivable sense; otherwise, weaker conditions will do.

Financial support from the Russian Foundation for Basic Research (projects 08-07-00158 and 11-07-00162) and the Spanish Ministry of Education and Innovation (project ECO 2010-19596) is acknowledged. I have benefitted from fruitful contacts with Vladimir Danilov, Francisco Marhuenda, Paul Milgrom, Hervé Moulin, Kevin Reffett, and Alexei Savvateev. My especial gratitude is due to an anonymous referee, who carefully read two versions and suggested plenty of improvements.