Comparative Statics under Uncertainty : Single Crossing Properties and Log-Supermodularity.

This paper develops necessary and sufficient conditions for monotone comparative statics predictions in several general classes of stochastic optimization problems. There are two main results, where the first pertains to single crossing properties (of marginal returns, incremental returns, and indifference curves) in stochastic problems with a single random variable, and the second class involves log-supermodularity of functions with multiple random variables (where log-supermodularity of a density corresponds to the property affiliation from auction theory).