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...

A numerical example employing a class of increasing absolute risk averse utility functions, the incomplete Euler gamma functions, proves that the slope of indifference curves in the $\mu,\sigma$)-space can be locally decreasing in $\sigma$ (for given $\mu$). So far, this possibility has been...