Multidimensional Screening

The book brings into a focus all necessary mathematical knowledge necessary to understand the economics of multidimensional results screening and applies them straightaway to economic models. The first part of this book contains a review of vector calculus, the theory of partial differential equations, and the theory of generalized convexity. These techniques are extensively used in multidimensional screening models. Part II is devoted to the economics of sceening models. It starts with a detailed discussion of economics and mathematics of unidimensional screening problems and three approaches to their solution: direct, dual, and Hamiltonian. It uses the Hamiltonian approach to unify all known results, which were previously obtained using different arguments. Then the major difficulties with direct and dual approach in the multidimensional context are discussed and the Hamiltonian approach is used to provide the most complete characterization of the solution known in the literature. TOC:Part I: Mathematical Preliminaries: Vector Calculus.- Partial Differential Equations.- Theory of Generalized Convexity.- Calculus of Variations and the Optimal Control.- Miscellaneous Techniques.- Part II: Economics of Mulidimensional Screening: The Unidimensional Screening Model.- The Multidimensional Screening Model.- Beyond the Quasilinear Case.- Existence, Uniqueness, and Regularity Properties of the Solution.- Conclusions.