The Comparative Statics of Constrained Optimization Problems
Econometrica · 2007 · Volume 75 · Issue 2
DOI: 10.1111/j.1468-0262.2006.00752.x
Abstract
This paper develops and applies some new results in the theory of monotone comparative statics. Letfbe a real-valued function defined onRland consider the problem of maximizingf(x) whenxis constrained to lie in some subsetCofRl. We develop a natural way to order the constraint setsCand find the corresponding restrictions on the objective functionfthat guarantee that optimal solutions increase with the constraint set. We apply our techniques to problems in consumer, producer, and portfolio theory. We also use them to generalize Rybcsynski's theorem and the LeChatelier principle.
Keywords
Lattices, concavity, supermodularity, comparative statics, LeChatelier principle, Rybcsynski's theorem, normality
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