Directional Monotone Comparative Statics*

Many questions of interest can be stated in terms of monotone comparative statics: if a parameter of a constrained optimization problem “increases,” when does its solution “increase” as well. This paper studies monotone comparative statics in different directions in finite-dimensional Euclidean space. The conditions on the objective function are ordinal and retain the same flavor as their counterparts in the standard theory. They can be naturally specialized to cardinal conditions, and to differential conditions using directional derivatives. Conditions on both the objective function and the constraint set do not require new binary relations or convex domains. The results allow flexibility to explore comparative statics with respect to the constraint set, with respect to parameters in the objective function, or both. Results from Quah (2007) are included as a special case. Several examples highlight applications of the results.