The Comparative Statics of Constrained Optimization Problems

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-super-l and consider the problem of maximizing f(x) when x is constrained to lie in some subset C of R-super-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. Copyright The Econometric Society 2007.

[1]  John S. Chipman,et al.  An empirical implication of Auspitz-Lieben-Edgeworth-Pareto complementarity , 1977 .

[2]  Paul R. Milgrom,et al.  Monotone Comparative Statics , 1994 .

[3]  Paul R. Milgrom,et al.  Robust Comparative Statics , 2002 .

[4]  T. Hens,et al.  Gross substitution in financial markets , 1995 .

[5]  Charles H. Whiteman,et al.  Habit formation: a resolution of the equity premium puzzle? , 2002 .

[6]  Additional Notes on the Comparative Statics of Constrained Optimization Problems , 2006 .

[7]  D. McFadden.  Cost, Revenue, and Profit Functions , 1978 .

[8]  Leonard J. Mirman,et al.  Lattice Programming and the Consumer's Problem , 2003 .

[9]  J. Quah.  Market demand and comparative statics when goods are normal , 2003 .

[10]  John Nachbar.  General equilibrium comparative statics , 2002 .

[11]  E. Antoniadou.  Lattice Programming and Consumer Theory Part I: Method and Applications to Two Goods , 2004 .

[12]  Itzhak Gilboa,et al.  Uncertainty in economic theory : essays in honor of David Schmeidler's 65th birthday , 2004 .

[13]  Massimo Marinacci,et al.  Introduction to the mathematics of ambiguity , 2004 .

[14]  Comparative Statics, English Auctions, and the Stolper-Samuelson Theorem , 2003 .

[15]  Donald M. Topkis,et al.  Minimizing a Submodular Function on a Lattice , 1978, Oper. Res..

[16]  Paul R. Milgrom,et al.  Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities , 1990 .

[17]  D. McFadden,et al.  Production Economics: A Dual Approach to Theory and Applications (I): The Theory of Production , 1978 .

[18]  D. M. Topkis.  Supermodularity and Complementarity , 1998 .

[19]  Ilya Segal,et al.  Solutions manual for Microeconomic theory : Mas-Colell, Whinston and Green , 1997 .

[20]  Paul Milgrom,et al.  Comparing Optima: Do Simplifying Assumptions Affect Conclusions? , 1994, Journal of Political Economy.

[21]  C. Gollier.  The economics of risk and time , 2001 .

[22]  Paul Milgrom,et al.  The LeChatelier Principle , 1996 .

[23]  K. Roberts.  Rationality and the LeChatelier Principle , 1999 .

[24]  A. Mas-Colell.  The Theory Of General Economic Equilibrium , 1985 .

[25]  S. Athey.  Monotone Comparative Statics under Uncertainty , 2002 .