Comparative Statics With Linear Objectives: Normality, Complementarity, and Ranking Multi‐Prior Beliefs
提出一种新的约束集排序（平行四边形序），保证线性目标下最优选择随约束集扩大而增加，并据此刻画了导致正常需求与要素互补的效用/生产函数，推广了多先验模型中的一阶随机占优。
We formulate an order over constraint sets <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi>A</mi> <mo>⊆</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mi>ℓ</mi> </mrow> </msup> </math>, 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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi>p</mi> <mo>∈</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mi>ℓ</mi> </mrow> </msup> </math>. 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.