The Comparative Statics of Constrained Optimization Problems
John K.-H Quah
This paper develops and applies some new results in the theory of monotone comparative statics. Let f be a real-valued function defined on Rl and consider the problem of maximizing f(x) when x is constrained to lie in some subset C of Rl. 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.