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Multidimensional Screening

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ISBN-10: 3540239065

ISBN-13: 9783540239062

Edition: 2005

Authors: Suren Basov

List price: $179.99
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Book details

List price: $179.99
Copyright year: 2005
Publisher: Springer Berlin / Heidelberg
Publication date: 1/11/2005
Binding: Paperback
Pages: 202
Size: 6.10" wide x 9.25" long x 0.50" tall
Weight: 2.354
Language: English

Mathematical Preliminaries
Vector Calculus
The Main Operations of Vector Calculus: div, grad, and �
Conservative Vector Fields
Curvilinear Integrals and the Geometric Meaning of the Existence of a Potential
Multiple and Repeated Integrals
The Flow of a Vector Field and the Gauss-Ostrogradsky Theorem
The Circulation of a Vector Field and the Green Formula
Bibliographic Notes
Partial Differential Equations
The First Order Partial Differential Equations
The Complete Integral and the General Integral
The Singular Integral
The Quasilinear Equations and the Method of Characteristics
Compatible Systems of the First Order PDEs
The Method of Characteristics for a Non-quasilinear First Order PDE
The Second Order Partial Differential Equations
Classification of the Linear Second Order Partial Differential Equations
Boundary Value Problems for Elliptic Equations
Group Theoretic Analysis of the Systems of Partial Differential Equations
One Parameter Lie Groups
Invariance of PDEs. Systems of PDEs, and Boundary Problems under Lie Groups
Calculating a Lie Group of a PDE
Calculating Invariants of the Lie Group
Bibliographic Notes
Theory of Generalized Convexity
Definition and Properties of the Generalized Fenchel Conjugates
Generalized Convexity and Cyclic Monotonicity
Bibliographic Notes
Calculus of Variations and the Optimal Control
Banach Spaces and Polish Spaces
Hilbert Spaces
Dual Space for a Normed Space and a Hilbert Space
Frechet Derivative of a Mapping between Normed Spaces
Functionals and Gateaux Derivatives
Euler Equation
Optimal Control
Bibliographic Notes
Miscellaneous Techniques
Distributions and Generalized Solutions for the Partial Differential Equations
A Motivating Example
The Set of Test Functions and its Dual
Examples of Distributions
The Derivative of a Distribution
The Product of a Distribution and a Test Function and the Product of Distributions
The Resultant of a Distribution and a Dilation Operator
Adjoint Linear Differential Operators and Generalized Solutions of the Partial Differential Equations
Sobolev Spaces and Poincare Theorem
Sweeping Operators and Balayage of Measures
Coercive Functionals
Optimization by Vector Space Methods
Calculus of Variation Problem with Convexity Constraints
Supermodularity and Monotone Comparative Statics
Hausdorff Metric on Compact Sets of a Metric Space
Generalized Envelope Theorems
Bibliographic Notes
Economics of Multi-dimensional Screening
The Unidimensional Screening Model
Spence-Mirrlees Condition and Implementability
The Concept of the Information Rent
Three Approaches to the Unidimensional Relaxed Problem
The Direct Approach
The Dual Approach
The Hamiltonian Approach
Hamiltonian Approach to the Unidimensional Complete Problem
Type Dependent Participation Constraint
Random Participation Constraint
Bibliographic Notes
The Multi-dimensional Screening Model
The Genericity of Exclusion
Generalized Convexity and Implementability
Is Bunching Robust in the Multi-dimensional Case?
Path Independence of Information Rents
Cost Based Tariffs
Direct Approach and Its Limitations
Dual Approach for m = n
The Relaxed Problem
An Alternative Approach to the Relaxed Problem
The Complete Problem
The Geometry of the Participation Region
A Sufficient Condition for Bunching
The Extension of the Dual Approach for n > m
Hamiltonian Approach and the First Order Characterization of the Solution
The Economic Meaning of the Lagrange Multipliers
Symmetry Analysis of the First Order Conditions
Some Remarks on the Hamiltonian Approach to the Complete Problem
Examples and Economic Applications
Bibliographic Notes
Beyond the Quasilinear Case
The Unidimensional Case
The Multi-dimensional Case
Implementability of a Surplus Function
Implementability of an Allocation
The First Order Characterization of the Solution of the Relaxed Problem
Bibliographic Notes
Existence, Uniqueness, and Regularity Properties of the Solution
Existence and Uniqueness of the Solution of the Relaxed Problem
Existence of a Solution for the Complete Problem
Continuity of the Solution
Bibliographic Notes