Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Jan, 2024, Volume 92, Issue 1

Comparative statics with linear objectives: normality, complementarity, and ranking multi-prior beliefs
p. 167-200

Paweł Dziewulski, John K.‐H. Quah

We formulate an order over constraint sets , called the parallelogram order, which guarantees that argmin{p ⋅ x:x ∈ A} increases in the product order as A increases in the parallelogram order, for any vector . Using this result, we characterize the utility/production functions that lead to normal demand as well as the closely related class of production functions with marginal costs that increase with factor prices. By generalizing the concept of supermodularity, we also characterize the class of production functions for which factors are complements. In the context of decision‐making under uncertainty, our new set order leads to natural generalizations of first‐order stochastic dominance in multi‐prior models.

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Supplemental Material

Supplement to "Comparative statics with linear objectives: normality, complementarity, and ranking multi-prior beliefs"

Pawel Dziewulski and John K.-H. Quah

This supplement contains additional results related to Dziewulski and Quah (2023). These notes should be read in conjunction with the article. In this supplement, we present proofs of some of the claims made in the main article. In addition, in Section S.11 we use the set-theoretic notion of first order stochastic dominance defined in Section 5 of the main article to study comparative statics in problems of dynamic choice under ambiguity. Throughout this supplement, we employ the notation introduced in the main article.