Fundamental methods of mathematical economics

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Title:

Personal Author:

Chiang, Alpha C. 1927-

Edition:

4th ed.

Publication Information:

New York : McGraw-Hill, 2005

ISBN:

9780070109100

Subject Term:

Economics, Mathematical

Added Author:

Wainwright, Kevin

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010082847	HB135 C54 2005	Open Access Book	Book	Searching... Unknown
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It has been 20 years since the last edition of this classic text. Kevin Wainwright, a long time user of the text (British Columbia University and Simon Fraser University), has executed the perfect revision---he has updated examples, applications and theory without changing the elegant, precise presentation style of Alpha Chiang. Readers will find the wait was worthwhile.

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

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