Monotone Comparative Statics under Uncertainty
نویسنده
چکیده
This paper analyzes monotone comparative statics predictions in several classes of stochastic optimization problems. The main results characterize necessary and sufficient conditions for comparative statics predictions to hold based on properties of primitive functions, that is, utility functions and probability distributions. The results apply when the primitives satisfy one of the following two properties: (i) a single crossing property, which arises in applications such as portfolio investment problems and auctions, or (ii) log-supermodularity, which arises in the analysis of demand functions, affiliated random variables, stochastic orders, and orders over risk aversion.
منابع مشابه
On Price Caps under Uncertainty
This paper shows how standard arguments supporting the imposition of price caps break down in the presence of demand uncertainty. In particular, though in the deterministic case the introduction or lowering of a price cap (above marginal cost) results in increased production, increased total welfare, decreased prices, and increased consumer welfare, we show that all of the above comparative sta...
متن کاملMonotone Comparative Statics for Games With Strategic Substitutes
Under some conditions, parameterized games with strategic substitutes exhibit monotone comparative statics of equilibria. These conditions relate to a tradeoff between a direct parameter effect and an opposing, indirect strategic substitute effect. If the indirect effect does not dominate the direct effect, monotone comparative statics of equilibria are guaranteed. These conditions are availabl...
متن کاملMonotone Comparative Statics: Geometric Approach
We consider the comparative statics of solutions to parameterized optimization problems. A geometric method is developed for finding a vector field that, at each point in the parameter space, indicates a direction in which monotone comparative statics obtains. Given such a vector field, we provide sufficient conditions under which the problem can be reparameterized on the parameter space (or a ...
متن کاملRatio Orderings and Comparative Statics
Monotone ratio orderings are refinements of first order stochastic dominance that allow monotone comparative statics results in games of incomplete information. We develop analogous refinements for second order stochastic dominance based on the monotonicity of the cumulative probability ratio and the unimodality of the likelihood and probability ratios. We go on to investigate comparative stati...
متن کاملAn Introduction to Monotone Comparative Statics
1. Overview Comparative statics (called sensitivity analysis in engineering fields) means characterizing how the endogenous outcomes of a model change with its exogenous parameters. The " statics " in the name is because one is simply comparing two versions of the model, for two different values of exogenous parameters, rather than tracing out a dynamic process of change. One can do comparative...
متن کامل