EXTENDING THE SCOPE OF MONOTONE COMPARATIVE STATICS RESULTS

Generally we can distinguish between two types of comparative statics problems that have been approached with lattice programming methods. The first type of problem considers the change of the optimal solution to a maximization problem as the objective function changes, the other type the change due to a change in the constraint set. Comparative statics theorems have been developed for both cases under cardinal and ordinal assumptions in the literature; Quah (2007) expanded existing work by making it applicable to optimization problems with a new, weaker order on the constraint sets. The idea of this paper is to extend the existing comparative statics results to an even broader class of constrained optimization problems. We combine the two previously mentioned types of maximization problems and apply the existing comparative statics theorems to cases with changes in both the objective function and non-lattice constraint sets. Examples and applications from a variety of areas in economics, such as consumer theory, producer theory and environmental economics, are provided as well.