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| Preface | |
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| Introduction | |
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| The Nature of Mathematical Economics | |
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| Mathematical versus Nonmathematical Economics | |
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| Mathematical Economics versus Econometrics | |
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| Economic Models | |
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| Ingredients of a Mathematical Model | |
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| The Real-Number System | |
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| The Concept of Sets | |
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| Relations and Functions | |
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| Types of Function | |
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| Functions of Two or More Independent Variables | |
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| Levels of Generality | |
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| Static (or Equilibrium) Analysis | |
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| Equilibrium Analysis in Economics | |
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| The Meaning of Equilibrium | |
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| Partial Market Equilibrium--A Linear Model | |
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| Partial Market Equilibrium--A Nonlinear Model | |
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| General Market Equilibrium | |
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| Equilibrium in National-Income Analysis | |
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| Linear Models and Matrix Algebra | |
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| Matrices and Vectors | |
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| Matrix Operations | |
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| Notes on Vector Operations | |
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| Commutative, Associative, and Distributive Laws | |
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| Identity Matrices and Null Matrices | |
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| Transposes and Inverses | |
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| Linear Models and Matrix Algebra (Continued) | |
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| Conditions for Nonsingularity of a Matrix | |
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| Test of Nonsingularity by Use of Determinant | |
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| Basic Properties of Determinants | |
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| Finding the Inverse Matrix | |
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| Cramer's Rule | |
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| Application to Market and National-Income Models | |
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| Leontief Input-Output Models | |
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| Limitations of Static Analysis | |
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| Comparative-Static Analysis | |
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| Comparative Statics and the Concept of Derivative | |
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| The Nature of Comparative Statics | |
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| Rate of Change and the Derivative | |
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| The Derivative and the Slope of a Curve | |
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| The Concept of Limit | |
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| Digression on Inequalities and Absolute Values | |
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| Limit Theorems | |
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| Continuity and Differentiability of a Function | |
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| Rules of Differentiation and Their Use in Comparative Statics | |
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| Rules of Differentiation for a Function of One Variable | |
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| Rules of Differentiation Involving Two or More Functions of the Same Variable | |
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| Rules of Differentiation Involving Functions of Different Variables | |
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| Partial Differentiation | |
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| Applications to Comparative-Static Analysis | |
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| Note on Jacobian Determinants | |
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| Comparative-Static Analysis of General-Function Models | |
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| Differentials | |
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| Total Differentials | |
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| Rules of Differentials | |
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| Total Derivatives | |
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| Derivatives of Implicit Functions | |
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| Comparative Statics of General-Function Models | |
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| Limitations of Comparative Statics | |
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| Optimization Problems | |
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| Optimization: A Special Variety of Equilibrium Analysis | |
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| Optimum Values and Extreme Values | |
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| Relative Maximum and Minimum: First-Derivative Test | |
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| Second and Higher Derivatives | |
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| Second-Derivative Test | |
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| Digression on Maclaurin and Taylor Series | |
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| Nth-Derivative Test for Relative Extremum of a Function of One Variable | |
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| Exponential and Logarithmic Functions | |
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| The Nature of Exponential Functions | |
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| Natural Exponential Functions and the Problem of Growth | |
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| Logarithms | |
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| Logarithmic Functions | |
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| Derivatives of Exponential and Logarithmic Functions | |
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| Optimal Timing | |
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| Further Applications of Exponential and Logarithmic Derivatives | |
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| The Case of More than One Choice Variable | |
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| The Differential Version of Optimization Conditions | |
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| Extreme Values of a Function of Two Variables | |
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| Quadratic Forms--An Excursion | |
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| Objective Functions with More than Two Variables | |
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| Second-Order Conditions in Relation to Concavity and Convexity | |
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| Economic Applications | |
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| Comparative-Static Aspects of Optimization | |
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| Optimization with Equality Constraints | |
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| Effects of a Constraint | |
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| Finding the Stationary Values | |
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| Second-Order Conditions | |
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| Quasiconcavity and Quasiconvexity | |
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| Utility Maximization and Consumer Demand | |
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| Homogeneous Functions | |
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| Least-Cost Combination of Inputs | |
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| Some Concluding Remarks | |
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| Dynamic Analysis | |
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| Economic Dynamics and Integral Calculus | |
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| Dynamics and Integration | |
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| Indefinite Integrals | |
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| Definite Integrals | |
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| Improper Integrals | |
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| Some Economic Applications of Integrals | |
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| Domar Growth Model | |
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| Continuous Time: First-Order Differential Equations | |
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| First-Order Linear Differential Equations with Constant Coefficient and Constant Term | |
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| Dynamics of Market Price | |
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| Variable Coefficient and Variable Term | |
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| Exact Differential Equations | |
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| Nonlinear Differential Equations of the First Order and First Degree | |
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| The Qualitative-Graphic Approach | |
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| Solow Growth Model | |
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| Higher-Order Differential Equations | |
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| Second-Order Linear Differential Equations with Constant Coefficients and Constant Term | |
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| Complex Numbers and Circular Functions | |
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| Analysis of the Complex-Root Case | |
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| A Market Model with Price Expectations | |
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| The Interaction of Inflation and Unemployment | |
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| Differential Equations with a Variable Term | |
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| Higher-Order Linear Differential Equations | |
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| Discrete Time: First-Order Difference Equations | |
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| Discrete Time, Differences, and Difference Equations | |
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| Solving a First-Order Difference Equation | |
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| The Dynamic Stability of Equilibrium | |
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| The Cobweb Model | |
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| A Market Model with Inventory | |
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| Nonlinear Difference Equations--The Qualitative-Graphic Approach | |
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| Higher-Order Difference Equations | |
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| Second-Order Linear Difference Equations with Constant Coefficients and Constant Term | |
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| Samuelson Multiplier-Acceleration Interaction Model | |
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| Inflation and Unemployment in Discrete Time | |
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| Generalizations to Variable-Term and Higher-Order Equations | |
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| Simultaneous Differential Equations and Difference Equations | |
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| The Genesis of Dynamic Systems | |
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| Solving Simultaneous Dynamic Equations | |
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| Dynamic Input-Output Models | |
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| The Inflation-Unemployment Model Once More | |
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| Two-Variable Phase Diagrams | |
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| Linearization of a Nonlinear Differential-Equation System | |
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| Limitations of Dynamic Analysis | |
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| Mathematical Programming | |
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| Linear Programming | |
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| Simple Examples of Linear Programming | |
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| General Formulation of Linear Programs | |
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| Convex Sets and Linear Programming | |
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| Simplex Method: Finding the Extreme Points | |
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| Simplex Method: Finding the Optimal Extreme Point | |
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| Further Notes on the Simplex Method | |
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| Linear Programming (Continued) | |
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| Duality | |
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| Economic Interpretation of a Dual | |
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| Activity Analysis: Micro Level | |
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| Activity Analysis: Macro Level | |
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| Nonlinear Programming | |
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| The Nature of Nonlinear Programming | |
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| Kuhn-Tucker Conditions | |
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| The Constraint Qualification | |
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| Kuhn-Tucker Sufficiency Theorem: Concave Programming | |
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| Arrow-Enthoven Sufficiency Theorem: Quasiconcave Programming | |
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| Economic Applications | |
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| Limitations of Mathematical Programming | |
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| The Greek Alphabet | |
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| Mathematical Symbols | |
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| A Short Reading List | |
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| Answers to Selected Exercise Problems | |
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| Index | |