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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 | |