This paper develops and applies some new results in the theory of monotone comparative statics. Let be a real‐valued function defined on and consider the problem of maximizing () when is constrained to lie in some subset of . We develop a natural way to order the constraint sets and find the corresponding restrictions on the objective function 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.