Strict Single Crossing and the Spence-Mirrlees Condition: A Comment on Monotone Comparative Statics

Posted: 23 Sep 1998

See all articles by Aaron S. Edlin

Aaron S. Edlin

University of California at Berkeley; National Bureau of Economic Research (NBER)

Chris Shannon

University of California, Berkeley - Department of Economics

Abstract

Milgrom and Shannon [1994] assert that under appropriate conditions the Spence-Mirrlees condition is equivalent to their single crossing property, and that the strict versions are also equivalent. In this note, however, we give counterexamples which show that their strict single crossing property may hold even though the strict Spence-Mirrlees condition fails. In fact, we show that the strict single crossing property may hold even though the strict Spence-Mirrlees condition holds only on a set of arbitrarily small measure. We also give a correct statement of the relationship between the Spence-Mirrlees condition and the single crossing property. Finally, we illustrate the fact that the strict single crossing property can allow both pooling and separating equilibria while the strict Spence-Mirrlees condition eliminates the possibility of pooling equilibria.

JEL Classification: C61, D89

Suggested Citation

Edlin, Aaron S. and Shannon, Chris, Strict Single Crossing and the Spence-Mirrlees Condition: A Comment on Monotone Comparative Statics. Econometrica. Available at SSRN: https://ssrn.com/abstract=114534

Aaron S. Edlin (Contact Author)

University of California at Berkeley ( email )

Dept of Economics 549 Evans Hall #3880
Berkeley, CA 94720
United States
510-642-4719 (Phone)
510-643-0413 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Chris Shannon

University of California, Berkeley - Department of Economics ( email )

549 Evans Hall #3880
Berkeley, CA 94720-3880
United States

Here is the Coronavirus
related research on SSRN

Paper statistics

Abstract Views
1,801
PlumX Metrics