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The Comparative Statics of Constrained Optimization Problems
Author(s) -
Quah John K.H
Publication year - 2007
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/j.1468-0262.2006.00752.x
Subject(s) - comparative statics , mathematical optimization , constraint (computer aided design) , monotone polygon , mathematics , function (biology) , feasible region , set (abstract data type) , mathematical economics , computer science , economics , geometry , evolutionary biology , biology , macroeconomics , programming language
This paper develops and applies some new results in the theory of monotone comparative statics. Let f be a real‐valued function defined on R l and consider the problem of maximizing f ( x ) when x is constrained to lie in some subset C of R l . We develop a natural way to order the constraint sets C and find the corresponding restrictions on the objective function f that 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.