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Preface to the Classics Edition | |
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Preface | |
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Introduction | |
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Economizing and the Economy | |
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The Economizing Problem | |
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Institutions of the Economy | |
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Economics | |
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Static Optimization | |
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The Mathematical Programming Problem | |
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Formal Statement of the Problem | |
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Types of Maxima, the Weierstrass Theorem, and the Local-Global Theorem | |
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Geometry of the Problem | |
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Classical Programming | |
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The Unconstrained Case | |
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The Method of Lagrange Multipliers | |
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The Interpretation of the Lagrange Multipliers | |
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Problems | |
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Nonlinear Programming | |
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The Case of No Inequality Constraints | |
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The Kuhn-Tucker Conditions | |
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The Kuhn-Tucker Theorem | |
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The Interpretation of the Lagrange Multipliers | |
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Solution Algorithms | |
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Problems | |
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Linear Programming | |
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The Dual Problems of Linear Programming | |
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The Lagrangian Approach; Existence, Duality and Complementary Slackness Theorems | |
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The Interpretation of the Dual | |
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The Simplex Algorithm | |
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Problems | |
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Game Theory | |
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Classification and Description of Games | |
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Two-person, Zero-sum Games | |
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Two-person Nonzero-sum Games | |
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Cooperative Games | |
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Games With Infinitely Many Players | |
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Problems | |
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Applications of Static Optimization | |
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Theory of the Household | |
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Commodity Space | |
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The Preference Relation | |
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The Neoclassical Problem of the Household | |
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Comparative Statics of the Household | |
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Revealed Preference | |
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von Neumann-Morgenstern Utility | |
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Problems | |
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Theory of the Firm | |
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The Production Function | |
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The Neoclassical Theory of the Firm | |
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Comparative Statics of the Firm | |
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Imperfect Competition: Monopoly and Monopsony | |
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Competition Among the Few: Oligopoly and Oligopsony | |
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Problems | |
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General Equilibrium | |
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The Classical Approach: Counting Equations and Unknowns | |
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The Input-Output Linear Programming Approach | |
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The Neoclassical Excess Demand Approach | |
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Stability of Equilibrium | |
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The von Neumann Model of an Expanding Economy | |
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Problems | |
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Welfare Economics | |
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The Geometry of the Problem in the 2 x 2 x 2 Case | |
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Competitive Equilibrium and Pareto Optimality | |
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Market Failure | |
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Optimality Over Time | |
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Problems | |
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Dynamic Optimization | |
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The Control Problem | |
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Formal Statement of the Problem | |
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Some Special Cases | |
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Types of Control | |
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The Control Problem as One of Programming in an Infinite Dimensional Space; the Generalized Weierstrass Theorem | |
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Calculus of Variations | |
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Euler Equation | |
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Necessary Conditions | |
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Transversality Condition | |
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Constraints | |
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Problems | |
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Dynamic Programming | |
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The Principle of Optimality and Bellman's Equation | |
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Dynamic Programming and the Calculus of Variations | |
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Dynamic Programming Solution of Multistage Optimization Problems | |
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Problems | |
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Maximum Principle | |
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Costate Variables, the Hamiltonian, and the Maximum Principle | |
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The Interpretation of the Costate Variables | |
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The Maximum Principle and the Calculus of Variations | |
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The Maximum Principle and Dynamic Programming | |
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Examples | |
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Problems | |
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Differential Games | |
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Two-Person Deterministic Continuous Differential Games | |
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Two-Person Zero-Sum Differential Games | |
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Pursuit Games | |
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Coordination Differential Games | |
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Noncooperative Differential Games | |
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Problems | |
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APPLICATIONS OF DYNAMIC OPTIMIZATION | |
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Optimal Economic Growth | |
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The Neoclassical Growth Model | |
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Neoclassical Optimal Economic Growth | |
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The Two Sector Growth Model | |
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Heterogeneous Capital Goods | |
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Problems | |
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Appendices | |
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Analysis | |
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Sets | |
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Relations and Functions | |
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Metric Spaces | |
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Vector Spaces | |
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Convex Sets and Functions | |
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Differential Calculus | |
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Differential Equations | |
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Matrices | |
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Basic Definitions and Examples | |
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Some Special Matrices | |
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Matrix Relations and Operations | |
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Scalar Valued Functions Defined on Matrices | |
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Inverse Matrix | |
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Linear Equations and Linear Inequalities | |
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Linear Transformations; Characteristic Roots and Vectors | |
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Quadratic Forms | |
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Matrix Derivatives | |
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Index | |