Mathematical optimization and economic theory /

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Bibliographic Details
Author / Creator:	Intriligator, Michael D.
Imprint:	Philadelphia : Society for Industrial and Applied Mathematics, ©2002.
Description:	1 online resource (xix, 508 pages) : illustrations
Language:	English
Series:	Classics in applied mathematics ; 39 Classics in applied mathematics ; 39.
Subject:	Economics, Mathematical. Mathematical optimization. Economics, Mathematical Mathematical optimization
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/12577174

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ISBN:	0898715113 9780898715118 9780898719215 0898719216
Notes:	Originally published: Englewood Cliffs, N.J. : Prentice-Hall, 1971. Includes bibliographical references and index. Also available in print version.
Summary:	Mathematical Optimization and Economic Theory provides a self-contained introduction to and survey of mathematical programming and control techniques and their applications to static and dynamic problems in economics, respectively. It is distinctive in showing the unity of the various approaches to solving problems of constrained optimization that all stem back directly or indirectly to the method of Lagrange multipliers. In the 30 years since its initial publication, there have been many more applications of these mathematical techniques in economics, as well as some advances in the mathematics of programming and control. Nevertheless, the basic techniques remain the same today as when the book was originally published. Thus, it continues to be useful not only to its original audience of advanced undergraduate and graduate students in economics, but also to mathematicians and other researchers interested in learning about the applications of the mathematics of optimization to economics. The book covers in some depth both static programming problems and dynamic control problems of optimization and the techniques of their solution. It also clearly presents many applications of these techniques to economics, and it shows why optimization is important for economics. Audience: mathematicians and other researchers who are interested in learning about the applications of mathematical optimization in economics, as well as students at the advanced undergraduate and beginning graduate level. A basic knowledge of analysis and matrix algebra is recommended. Two appendices summarize the necessary mathematics.
Other form:	Print version: Intriligator, Michael D. Mathematical optimization and economic theory. Philadelphia : Society for Industrial and Applied Mathematics, ©2002 0898715113
Publisher's no.:	CL39 siam

Table of Contents:

Preface to the Classics Edition
Preface
Part 1. Introduction
1. Economizing and the Economy
1.1. The Economizing Problem
1.2. Institutions of the Economy
1.3. Economics
Part 2. Static Optimization
2. The Mathematical Programming Problem
2.1. Formal Statement of the Problem
2.2. Types of Maxima, the Weierstrass Theorem, and the Local-Global Theorem
2.3. Geometry of the Problem
3. Classical Programming
3.1. The Unconstrained Case
3.2. The Method of Lagrange Multipliers
3.3. The Interpretation of the Lagrange Multipliers
Problems
4. Nonlinear Programming
4.1. The Case of No Inequality Constraints
4.2. The Kuhn-Tucker Conditions
4.3. The Kuhn-Tucker Theorem
4.4. The Interpretation of the Lagrange Multipliers
4.5. Solution Algorithms
Problems
5. Linear Programming
5.1. The Dual Problems of Linear Programming
5.2. The Lagrangian Approach; Existence, Duality and Complementary Slackness Theorems
5.3. The Interpretation of the Dual
5.4. The Simplex Algorithm
Problems
6. Game Theory
6.1. Classification and Description of Games
6.2. Two-person, Zero-sum Games
6.3. Two-person Nonzero-sum Games
6.4. Cooperative Games
6.5. Games With Infinitely Many Players
Problems
Part 3. Applications of Static Optimization
7. Theory of the Household
7.1. Commodity Space
7.2. The Preference Relation
7.3. The Neoclassical Problem of the Household
7.4. Comparative Statics of the Household
7.5. Revealed Preference
7.6. von Neumann-Morgenstern Utility
Problems
8. Theory of the Firm
8.1. The Production Function
8.2. The Neoclassical Theory of the Firm
8.3. Comparative Statics of the Firm
8.4. Imperfect Competition: Monopoly and Monopsony
8.5. Competition Among the Few: Oligopoly and Oligopsony
Problems
9. General Equilibrium
9.1. The Classical Approach: Counting Equations and Unknowns
9.2. The Input-Output Linear Programming Approach
9.3. The Neoclassical Excess Demand Approach
9.4. Stability of Equilibrium
9.5. The von Neumann Model of an Expanding Economy
Problems
10. Welfare Economics
10.1. The Geometry of the Problem in the 2 x 2 x 2 Case
10.2. Competitive Equilibrium and Pareto Optimality
10.3. Market Failure
10.4. Optimality Over Time
Problems
Part 4. Dynamic Optimization
11. The Control Problem
11.1. Formal Statement of the Problem
11.2. Some Special Cases
11.3. Types of Control
11.4. The Control Problem as One of Programming in an Infinite Dimensional Space; the Generalized Weierstrass Theorem
12. Calculus of Variations
12.1. Euler Equation
12.2. Necessary Conditions
12.3. Transversality Condition
12.4. Constraints
Problems
13. Dynamic Programming
13.1. The Principle of Optimality and Bellman's Equation
13.2. Dynamic Programming and the Calculus of Variations
13.3. Dynamic Programming Solution of Multistage Optimization Problems
Problems
14. Maximum Principle
14.1. Costate Variables, the Hamiltonian, and the Maximum Principle
14.2. The Interpretation of the Costate Variables
14.3. The Maximum Principle and the Calculus of Variations
14.4. The Maximum Principle and Dynamic Programming
14.5. Examples
Problems
15. Differential Games
15.1. Two-Person Deterministic Continuous Differential Games
15.2. Two-Person Zero-Sum Differential Games
15.3. Pursuit Games
15.4. Coordination Differential Games
15.5. Noncooperative Differential Games
Problems
Part 5. APPLICATIONS OF DYNAMIC OPTIMIZATION
16. Optimal Economic Growth
16.1. The Neoclassical Growth Model
16.2. Neoclassical Optimal Economic Growth
16.3. The Two Sector Growth Model
16.4. Heterogeneous Capital Goods
Problems
Appendices
Appendix A. Analysis
A.1. Sets
A.2. Relations and Functions
A.3. Metric Spaces
A.4. Vector Spaces
A.5. Convex Sets and Functions
A.6. Differential Calculus
A.7. Differential Equations
Appendix B. Matrices
B.1. Basic Definitions and Examples
B.2. Some Special Matrices
B.3. Matrix Relations and Operations
B.4. Scalar Valued Functions Defined on Matrices
B.5. Inverse Matrix
B.6. Linear Equations and Linear Inequalities
B.7. Linear Transformations; Characteristic Roots and Vectors
B.8. Quadratic Forms
B.9. Matrix Derivatives
Index

Mathematical optimization and economic theory /

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