| 求书:求英文版的《数理经济学的基本方法》蒋中一 Preface | ||||||
| Part 1 | Introduction | |||||
| 1 | The Nature of Mathematical Economics | 3 | ||||
| 1.1 | Mathematical versus Nonmathematical Economics | 3 | ||||
| 1.2 | Mathematical Economics versus Econometrics | 5 | ||||
| 2 | Economic Models | 7 | ||||
| 2.1 | Ingredients of a Mathematical Model | 7 | ||||
| 2.2 | The Real-Number System | 10 | ||||
| 2.3 | The Concept of Sets | 11 | ||||
| 2.4 | Relations and Functions | 17 | ||||
| 2.5 | Types of Function | 23 | ||||
| 2.6 | Functions of Two or More Independent Variables | 29 | ||||
| 2.7 | Levels of Generality | 31 | ||||
| Part 2 | Static (or Equilibrium) Analysis | |||||
| 3 | Equilibrium Analysis in Economics | 35 | ||||
| 3.1 | The Meaning of Equilibrium | 35 | ||||
| 3.2 | Partial Market Equilibrium--A Linear Model | 36 | ||||
| 3.3 | Partial Market Equilibrium--A Nonlinear Model | 40 | ||||
| 3.4 | General Market Equilibrium | 46 | ||||
| 3.5 | Equilibrium in National-Income Analysis | 52 | ||||
| 4 | Linear Models and Matrix Algebra | 54 | ||||
| 4.1 | Matrices and Vectors | 55 | ||||
| 4.2 | Matrix Operations | 58 | ||||
| 4.3 | Notes on Vector Operations | 67 | ||||
| 4.4 | Commutative, Associative, and Distributive Laws | 76 | ||||
| 4.5 | Identity Matrices and Null Matrices | 79 | ||||
| 4.6 | Transposes and Inverses | 82 | ||||
| 5 | Linear Models and Matrix Algebra (Continued) | 88 | ||||
| 5.1 | Conditions for Nonsingularity of a Matrix | 88 | ||||
| 5.2 | Test of Nonsingularity by Use of Determinant | 92 | ||||
| 5.3 | Basic Properties of Determinants | 98 | ||||
| 5.4 | Finding the Inverse Matrix | 103 | ||||
| 5.5 | Cramer's Rule | 107 | ||||
| 5.6 | Application to Market and National-Income Models | 112 | ||||
| 5.7 | Leontief Input-Output Models | 115 | ||||
| 5.8 | Limitations of Static Analysis | 124 | ||||
| Part 3 | Comparative-Static Analysis | |||||
| 6 | Comparative Statics and the Concept of Derivative | 127 | ||||
| 6.1 | The Nature of Comparative Statics | 127 | ||||
| 6.2 | Rate of Change and the Derivative | 128 | ||||
| 6.3 | The Derivative and the Slope of a Curve | 131 | ||||
| 6.4 | The Concept of Limit | 132 | ||||
| 6.5 | Digression on Inequalities and Absolute Values | 141 | ||||
| 6.6 | Limit Theorems | 145 | ||||
| 6.7 | Continuity and Differentiability of a Function | 147 | ||||
| 7 | Rules of Differentiation and Their Use in Comparative Statics | 155 | ||||
| 7.1 | Rules of Differentiation for a Function of One Variable | 155 | ||||
| 7.2 | Rules of Differentiation Involving Two or More Functions of the Same Variable | 159 | ||||
| 7.3 | Rules of Differentiation Involving Functions of Different Variables | 169 | ||||
| 7.4 | Partial Differentiation | 174 | ||||
| 7.5 | Applications to Comparative-Static Analysis | 178 | ||||
| 7.6 | Note on Jacobian Determinants | 184 | ||||
| 8 | Comparative-Static Analysis of General-Function Models | 187 | ||||
| 8.1 | Differentials | 188 | ||||
| 8.2 | Total Differentials | 194 | ||||
| 8.3 | Rules of Differentials | 196 | ||||
| 8.4 | Total Derivatives | 198 | ||||
| 8.5 | Derivatives of Implicit Functions | 204 | ||||
| 8.6 | Comparative Statics of General-Function Models | 215 | ||||
| 8.7 | Limitations of Comparative Statics | 226 | ||||
| Part 4 | Optimization Problems | |||||
| 9 | Optimization: A Special Variety of Equilibrium Analysis | 231 | ||||
| 9.1 | Optimum Values and Extreme Values | 232 | ||||
| 9.2 | Relative Maximum and Minimum: First-Derivative Test | 233 | ||||
| 9.3 | Second and Higher Derivatives | 239 | ||||
| 9.4 | Second-Derivative Test | 245 | ||||
| 9.5 | Digression on Maclaurin and Taylor Series | 254 | ||||
| 9.6 | Nth-Derivative Test for Relative Extremum of a Function of One Variable | 263 | ||||
| 10 | Exponential and Logarithmic Functions | 268 | ||||
| 10.1 | The Nature of Exponential Functions | 269 | ||||
| 10.2 | Natural Exponential Functions and the Problem of Growth | 274 | ||||
| 10.3 | Logarithms | 282 | ||||
| 10.4 | Logarithmic Functions | 287 | ||||
| 10.5 | Derivatives of Exponential and Logarithmic Functions | 292 | ||||
| 10.6 | Optimal Timing | 298 | ||||
| 10.7 | Further Applications of Exponential and Logarithmic Derivatives | 302 | ||||
| 11 | The Case of More than One Choice Variable | 307 | ||||
| 11.1 | The Differential Version of Optimization Conditions | 308 | ||||
| 11.2 | Extreme Values of a Function of Two Variables | 310 | ||||
| 11.3 | Quadratic Forms--An Excursion | 319 | ||||
| 11.4 | Objective Functions with More than Two Variables | 332 | ||||
| 11.5 | Second-Order Conditions in Relation to Concavity and Convexity | 337 | ||||
| 11.6 | Economic Applications | 353 | ||||
| 11.7 | Comparative-Static Aspects of Optimization | 364 | ||||
| 12 | Optimization with Equality Constraints | 369 | ||||
| 12.1 | Effects of a Constraint | 370 | ||||
| 12.2 | Finding the Stationary Values | 372 | ||||
| 12.3 | Second-Order Conditions | 379 | ||||
| 12.4 | Quasiconcavity and Quasiconvexity | 387 | ||||
| 12.5 | Utility Maximization and Consumer Demand | 400 | ||||
| 12.6 | Homogeneous Functions | 410 | ||||
| 12.7 | Least-Cost Combination of Inputs | 418 | ||||
| 12.8 | Some Concluding Remarks | 431 | ||||
| Part 5 | Dynamic Analysis | |||||
| 13 | Economic Dynamics and Integral Calculus | 435 | ||||
| 13.1 | Dynamics and Integration | 436 | ||||
| 13.2 | Indefinite Integrals | 437 | ||||
| 13.3 | Definite Integrals | 447 | ||||
| 13.4 | Improper Integrals | 454 | ||||
| 13.5 | Some Economic Applications of Integrals | 458 | ||||
| 13.6 | Domar Growth Model | 465 | ||||
| 14 | Continuous Time: First-Order Differential Equations | 470 | ||||
| 14.1 | First-Order Linear Differential Equations with Constant Coefficient and Constant Term | 470 | ||||
| 14.2 | Dynamics of Market Price | 475 | ||||
| 14.3 | Variable Coefficient and Variable Term | 480 | ||||
| 14.4 | Exact Differential Equations | 483 | ||||
| 14.5 | Nonlinear Differential Equations of the First Order and First Degree | 489 | ||||
| 14.6 | The Qualitative-Graphic Approach | 493 | ||||
| 14.7 | Solow Growth Model | 496 | ||||
| 15 | Higher-Order Differential Equations | 502 | ||||
| 15.1 | Second-Order Linear Differential Equations with Constant Coefficients and Constant Term | 503 | ||||
| 15.2 | Complex Numbers and Circular Functions | 511 | ||||
| 15.3 | Analysis of the Complex-Root Case | 523 | ||||
| 15.4 | A Market Model with Price Expectations | 529 | ||||
| 15.5 | The Interaction of Inflation and Unemployment | 535 | ||||
| 15.6 | Differential Equations with a Variable Term | 541 | ||||
| 15.7 | Higher-Order Linear Differential Equations | 544 | ||||
| 16 | Discrete Time: First-Order Difference Equations | 549 | ||||
| 16.1 | Discrete Time, Differences, and Difference Equations | 550 | ||||
| 16.2 | Solving a First-Order Difference Equation | 551 | ||||
| 16.3 | The Dynamic Stability of Equilibrium | 557 | ||||
| 16.4 | The Cobweb Model | 561 | ||||
| 16.5 | A Market Model with Inventory | 566 | ||||
| 16.6 | Nonlinear Difference Equations--The Qualitative-Graphic Approach | 569 | ||||
| 17 | Higher-Order Difference Equations | 576 | ||||
| 17.1 | Second-Order Linear Difference Equations with Constant Coefficients and Constant Term | 577 | ||||
| 17.2 | Samuelson Multiplier-Acceleration Interaction Model | 585 | ||||
| 17.3 | Inflation and Unemployment in Discrete Time | 591 | ||||
| 17.4 | Generalizations to Variable-Term and Higher-Order Equations | 596 | ||||
| 18 | Simultaneous Differential Equations and Difference Equations | 605 | ||||
| 18.1 | The Genesis of Dynamic Systems | 605 | ||||
| 18.2 | Solving Simultaneous Dynamic Equations | 608 | ||||
| 18.3 | Dynamic Input-Output Models | 616 | ||||
| 18.4 | The Inflation-Unemployment Model Once More | 623 | ||||
| 18.5 | Two-Variable Phase Diagrams | 628 | ||||
| 18.6 | Linearization of a Nonlinear Differential-Equation System | 638 | ||||
| 18.7 | Limitations of Dynamic Analysis | 646 | ||||
| Part 6 | Mathematical Programming | |||||
| 19 | Linear Programming | 651 | ||||
| 19.1 | Simple Examples of Linear Programming | 652 | ||||
| 19.2 | General Formulation of Linear Programs | 661 | ||||
| 19.3 | Convex Sets and Linear Programming | 665 | ||||
| 19.4 | Simplex Method: Finding the Extreme Points | 671 | ||||
| 19.5 | Simplex Method: Finding the Optimal Extreme Point | 676 | ||||
| 19.6 | Further Notes on the Simplex Method | 682 | ||||
| 20 | Linear Programming (Continued) | 688 | ||||
| 20.1 | Duality | 688 | ||||
| 20.2 | Economic Interpretation of a Dual | 696 | ||||
| 20.3 | Activity Analysis: Micro Level | 700 | ||||
| 20.4 | Activity Analysis: Macro Level | 709 | ||||
| 21 | Nonlinear Programming | 716 | ||||
| 21.1 | The Nature of Nonlinear Programming | 716 | ||||
| 21.2 | Kuhn-Tucker Conditions | 722 | ||||
| 21.3 | The Constraint Qualification | 731 | ||||
| 21.4 | Kuhn-Tucker Sufficiency Theorem: Concave Programming | 738 | ||||
| 21.5 | Arrow-Enthoven Sufficiency Theorem: Quasiconcave Programming | 744 | ||||
| 21.6 | Economic Applications | 747 | ||||
| 21.7 | Limitations of Mathematical Programming | 754 | ||||
| The Greek Alphabet | 756 | |||||
| Mathematical Symbols | 757 | |||||
| A Short Reading List | 760 | |||||
| Answers to Selected Exercise Problems | 763 | |||||
| Index | 781 | |||||



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