Essays on Monotone Comparative Statics for Constrained Optimization Problems with Applications

My dissertation consists of three chapters. Chapters 1 and 2 both address extensions to existing monotone comparative statics results for constrained optimization problems using lattice programming techniques. Chapter 3 applies monotone comparative statics results to the question how environmental regulation affects investment in innovation in imperfectly competitive markets. Generally we can distinguish between two types of comparative statics problems. The first type of problem considers the change of the optimal solution to a maximization problem as the objective function changes, the other type considers the change due to a change in the constraint set. Lattice-based comparative statics theorems have been developed for both types of problems in the literature. The strengths of these latticetheoretic comparative statics results are that they don’t depend on the usual smoothness, interiority and concavity assumptions as required by the classical approach based on the Implicit Function Theorem, as well as convexity of the constraint set. Moreover, these comparative statics results also apply in the case of non-unique solutions. Quah (2007) expanded existing results by Milgrom and Shannon (1994) by making them applicable to some non-lattice constraint sets. In the first chapter, I extend existing comparative statics theorems to parametrized objective functions and non-lattice constraint sets. This generalization makes it possible to analyze a variety of economic optimization problems that fall into this class of problems which cannot be addressed using existing lattice-based techniques. I provide examples from consumer theory, producer theory and environmental economics that show the result’s broad scope of applications.