The comparative statics of constrained optimization problems

Abstract: The objective of this paper is to develop and apply 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 of ordering constraint sets and identify the conditions on f which guarantee that the solution to the maximization problem increases as the constraint set changes. We apply this to a variety of problems in economic theory