Economists commonly seek to show that one variable increases in response to changes in another variable. This paper provides sufficient conditions to draw such strict monotone comparative statics conclusions in optimization problems with and without binding constraints. These results extend the...

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...