Fundamental methods of mathematical economics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Auckland [u.a.]
McGraw-Hill
1984
|
| Edition: | 3. ed., internat. ed. |
| Series: | McGraw-Hill international editions : Economic series
|
| Subjects: | |
| Online Access: | Publisher description Inhaltsverzeichnis |
| Item Description: | Begleitbd. unter: Chiang, Alpha C.: Instructor's manual to accompany Fundamental methods of mathematical economics |
| Physical Description: | XII, 788 S. graph. Darst. |
| ISBN: | 0070108137 0070662193 |
Staff View
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| 245 | 1 | 0 | |a Fundamental methods of mathematical economics |c Alpha C. Chiang |
| 250 | |a 3. ed., internat. ed. | ||
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| 300 | |a XII, 788 S. |b graph. Darst. | ||
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| 490 | 0 | |a McGraw-Hill international editions : Economic series | |
| 500 | |a Begleitbd. unter: Chiang, Alpha C.: Instructor's manual to accompany Fundamental methods of mathematical economics | ||
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Record in the Search Index
| _version_ | 1805081627414495232 |
|---|---|
| adam_text |
CONTENTS
Preface
Part
1
Introduction
1
The Nature of Mathematical Economics
з
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 1
1
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
Vi
CONTENTS
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
'03
5.5
Crameťs
Rule
'07
5.6
Application to Market and National-Income Models
112
5.7 Leontief
Input-Output Models
"5
5.8
Limitations of Static Analysis
'24
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 )69
7.4
Partial Differentiation I74
7.5
Applications to Comparative-Static Analysis
178
7.6
Note on Jacobian Determinants 1
34
CONTENTS VU
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
23
1
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 Maclaunn and Taylor Series
254
9.6
Nth-Derivative Test for Relative
Extrémům
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
1
1
.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
«li
CONTENTS
12.4
Quasiconcavity
and Quasiconvexity 387
12.5
Utility Maximization and Consumer Demand 4°0
12.6
Homogeneous Functions 4J^
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 43<*
13.2
Indefinite Integrals 437
13.3
Definite Integrals w
13.4
Improper Integrals 454
13.5
Some Economic Applications of Integrals
458
13.6
Domar
Growth Model
^5
14
Continuous Time: First-Order
Differential
Equations 47°
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
CONTENTS
IX
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
65
1
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 |
| any_adam_object | 1 |
| author | Chiang, Alpha C. 1927- |
| author_GND | (DE-588)13164940X |
| author_facet | Chiang, Alpha C. 1927- |
| author_role | aut |
| author_sort | Chiang, Alpha C. 1927- |
| author_variant | a c c ac acc |
| building | Verbundindex |
| bvnumber | BV010715818 |
| callnumber-first | H - Social Science |
| callnumber-label | HB135 |
| callnumber-raw | HB135.C47 1984 |
| callnumber-search | HB135.C47 1984 |
| callnumber-sort | HB 3135 C47 41984 |
| callnumber-subject | HB - Economic Theory and Demography |
| classification_rvk | QH 100 SK 980 |
| ctrlnum | (OCoLC)11347907 (DE-599)BVBBV010715818 |
| dewey-full | 330/.01/5119 330.0151 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 330 - Economics |
| dewey-raw | 330/.01/51 19 330.0151 |
| dewey-search | 330/.01/51 19 330.0151 |
| dewey-sort | 3330 11 251 219 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 3. ed., internat. ed. |
| format | Book |
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| id | DE-604.BV010715818 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T07:19:46Z |
| institution | BVB |
| isbn | 0070108137 0070662193 |
| language | English |
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| physical | XII, 788 S. graph. Darst. |
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| publishDate | 1984 |
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| publisher | McGraw-Hill |
| record_format | marc |
| series2 | McGraw-Hill international editions : Economic series |
| spelling | Chiang, Alpha C. 1927- Verfasser (DE-588)13164940X aut Fundamental methods of mathematical economics Alpha C. Chiang 3. ed., internat. ed. Auckland [u.a.] McGraw-Hill 1984 XII, 788 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier McGraw-Hill international editions : Economic series Begleitbd. unter: Chiang, Alpha C.: Instructor's manual to accompany Fundamental methods of mathematical economics Economie gtt Wiskundige methoden gtt Wirtschaft Economics, Mathematical Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Wirtschaftswissenschaften (DE-588)4066528-8 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Wirtschaftsmathematik (DE-588)4066472-7 s DE-604 Wirtschaftswissenschaften (DE-588)4066528-8 s Mathematische Methode (DE-588)4155620-3 s 2\p DE-604 Mathematik (DE-588)4037944-9 s 3\p DE-604 http://www.loc.gov/catdir/description/mh022/83019609.html Publisher description Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007155453&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Chiang, Alpha C. 1927- Fundamental methods of mathematical economics Economie gtt Wiskundige methoden gtt Wirtschaft Economics, Mathematical Wirtschaftsmathematik (DE-588)4066472-7 gnd Mathematische Methode (DE-588)4155620-3 gnd Mathematik (DE-588)4037944-9 gnd Wirtschaftswissenschaften (DE-588)4066528-8 gnd |
| subject_GND | (DE-588)4066472-7 (DE-588)4155620-3 (DE-588)4037944-9 (DE-588)4066528-8 (DE-588)4123623-3 |
| title | Fundamental methods of mathematical economics |
| title_auth | Fundamental methods of mathematical economics |
| title_exact_search | Fundamental methods of mathematical economics |
| title_full | Fundamental methods of mathematical economics Alpha C. Chiang |
| title_fullStr | Fundamental methods of mathematical economics Alpha C. Chiang |
| title_full_unstemmed | Fundamental methods of mathematical economics Alpha C. Chiang |
| title_short | Fundamental methods of mathematical economics |
| title_sort | fundamental methods of mathematical economics |
| topic | Economie gtt Wiskundige methoden gtt Wirtschaft Economics, Mathematical Wirtschaftsmathematik (DE-588)4066472-7 gnd Mathematische Methode (DE-588)4155620-3 gnd Mathematik (DE-588)4037944-9 gnd Wirtschaftswissenschaften (DE-588)4066528-8 gnd |
| topic_facet | Economie Wiskundige methoden Wirtschaft Economics, Mathematical Wirtschaftsmathematik Mathematische Methode Mathematik Wirtschaftswissenschaften Lehrbuch |
| url | http://www.loc.gov/catdir/description/mh022/83019609.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007155453&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT chiangalphac fundamentalmethodsofmathematicaleconomics |