Mathematical tools for economics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Malden, MA [u.a.]
Blackwell
2007
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Table of contents only Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XI, 365 S. graph. Darst. |
| ISBN: | 9781405133807 9781405133814 1405133805 1405133813 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface x
Part I Matrix Algebra and Linear Economic Models
1 Matrix Algebra
1.1 Basic Concepts 3
1.2 Determinants 11
1.3 The Inverse of a Matrix 19
1.4 Linear Dependence of Vectors and the Rank of a Matrix 28
* 1.5 Kronecker Products and Vecs of Matrices 36
2 Simultaneous Linear Equations
2.1 Definitions 40
2.2 Homogeneous Case Ax = 0 42
2.3 Nonhomogeneous Case Ax = b, b ^ 0 47
2.4 Special Case m = n 52
3 Linear Economic Models
3.1 Introduction and Definitions 58
3.2 Examples of Linear Economic Models 61
3.3 The Use of Matrix Algebra in Statistics and
Econometrics 68
4 Quadratic Forms and Positive Definite Matrices
4.1 Introduction 74
4.2 Eigenvalues of a Symmetric Matrix 76
4.3 Eigenvalues of Special Matrices 79
4.4 The Eigenvectors of a Symmetric Matrix 80
4.5 The Matrix whose Columns are the Eigenvectors of a
Symmetric Matrix 85
4.6 Diagonalization of Quadratic Forms 87
viii Contents
4.7 Eigenvalues and |A|, r(A), and tr A 89
4.8 An Alternative Approach Using Determinants 91
Part II Functions of Many Variables and Optimization
5 Functions of Many Variables
5.1 Functions in General 99
5.2 Partial Differentiation 1°
5.3 Special Sorts of Functions 107
5.4 Comparative Statics and Nonlinear Economic Models 121
5.5 Differentials and Taylor s Approximation 129
6 Optimization
6.1 Unconstrained Optimization 136
6.2 Local Optima and Global Optima I47
6.3 Constrained Optimization 150
6.4 Constrained Local Optima versus Constrained
Global Optima I57
*6.5 An Introduction to Matrix Calculus 160
7 Comparative Static Analysis in Optimization Problems
7.1 Introduction 170
7.2 Unconstrained Optimization 1™
7.3 Constrained Optimization 174
7.4 Slutsky s Equation I78
7.5 Applications of the Envelope Theorems in Economics 189
Part HI Dynamic Analysis
8 Integration
8.1 Introduction 207
8.2 Definite Integrals 208
8.3 Integration as Antidifferentiation 214
8.4 Indefinite Integrals 218
8.5 Further Considerations 221
8.6 Economic Applications 223
9 Continuous Time: Differential Equations
9.1 Definitions 232
9.2 Linear Differential Equations 233
9.3 First Order Linear Differential Equations with Constant
Coefficients 234
9.4 Economic Dynamics Using First Order Differential
Equations 240
Contents ix
9.5 Second Order Linear Differential Equations with
Constant Coefficients 250
9.6 Economic Application: A Dynamic Supply and
Demand Model 258
9.7 Higher Order Linear Differential Equations 260
9.8 Descriptive Analysis of Nonlinear Differential Equations 262
10 Discrete Time: Difference Equations
10.1 Introduction and Definitions 266
10.2 First Order Linear Difference Equations with
Constant Coefficients 269
10.3 Second Order Linear Difference Equations with
Constant Coefficients 270
10.4 Investigating the Nature of the Roots of a Quadratic
Equation 277
10.5 Economic Applications 279
10.6 Higher Order Linear Difference Equations 288
11 ^Dynamic Optimization
*11.1 Introduction 291
*11.2 Dynamic Optimization versus Static Optimization 292
* 11.3 The Basic Optimal Control Problem and Pontryagin s
Maximum Principle 294
*11.4 Extensions to the Basic Problem 302
* 11.5 Economic Application: Ramsey/Solow Model 315
Answers to exercises 325
Further Reading 359
Index 361
|
| adam_txt |
Contents
Preface x
Part I Matrix Algebra and Linear Economic Models
1 Matrix Algebra
1.1 Basic Concepts 3
1.2 Determinants 11
1.3 The Inverse of a Matrix 19
1.4 Linear Dependence of Vectors and the Rank of a Matrix 28
* 1.5 Kronecker Products and Vecs of Matrices 36
2 Simultaneous Linear Equations
2.1 Definitions 40
2.2 Homogeneous Case Ax = 0 42
2.3 Nonhomogeneous Case Ax = b, b ^ 0 47
2.4 Special Case m = n 52
3 Linear Economic Models
3.1 Introduction and Definitions 58
3.2 Examples of Linear Economic Models 61
3.3 The Use of Matrix Algebra in Statistics and
Econometrics 68
4 Quadratic Forms and Positive Definite Matrices
4.1 Introduction 74
4.2 Eigenvalues of a Symmetric Matrix 76
4.3 Eigenvalues of Special Matrices 79
4.4 The Eigenvectors of a Symmetric Matrix 80
4.5 The Matrix whose Columns are the Eigenvectors of a
Symmetric Matrix 85
4.6 Diagonalization of Quadratic Forms 87
viii Contents
4.7 Eigenvalues and |A|, r(A), and tr A 89
4.8 An Alternative Approach Using Determinants 91
Part II Functions of Many Variables and Optimization
5 Functions of Many Variables
5.1 Functions in General 99
5.2 Partial Differentiation 1°'
5.3 Special Sorts of Functions 107
5.4 Comparative Statics and Nonlinear Economic Models 121
5.5 Differentials and Taylor's Approximation 129
6 Optimization
6.1 Unconstrained Optimization 136
6.2 Local Optima and Global Optima I47
6.3 Constrained Optimization 150
6.4 Constrained Local Optima versus Constrained
Global Optima I57
*6.5 An Introduction to Matrix Calculus 160
7 Comparative Static Analysis in Optimization Problems
7.1 Introduction 170
7.2 Unconstrained Optimization 1™
7.3 Constrained Optimization 174
7.4 Slutsky's Equation I78
7.5 Applications of the Envelope Theorems in Economics 189
Part HI Dynamic Analysis
8 Integration
8.1 Introduction 207
8.2 Definite Integrals 208
8.3 Integration as Antidifferentiation 214
8.4 Indefinite Integrals 218
8.5 Further Considerations 221
8.6 Economic Applications 223
9 Continuous Time: Differential Equations
9.1 Definitions 232
9.2 Linear Differential Equations 233
9.3 First Order Linear Differential Equations with Constant
Coefficients 234
9.4 Economic Dynamics Using First Order Differential
Equations 240
Contents ix
9.5 Second Order Linear Differential Equations with
Constant Coefficients 250
9.6 Economic Application: A Dynamic Supply and
Demand Model 258
9.7 Higher Order Linear Differential Equations 260
9.8 Descriptive Analysis of Nonlinear Differential Equations 262
10 Discrete Time: Difference Equations
10.1 Introduction and Definitions 266
10.2 First Order Linear Difference Equations with
Constant Coefficients 269
10.3 Second Order Linear Difference Equations with
Constant Coefficients 270
10.4 Investigating the Nature of the Roots of a Quadratic
Equation 277
10.5 Economic Applications 279
10.6 Higher Order Linear Difference Equations 288
11 ^Dynamic Optimization
*11.1 Introduction 291
*11.2 Dynamic Optimization versus Static Optimization 292
* 11.3 The Basic Optimal Control Problem and Pontryagin's
Maximum Principle 294
*11.4 Extensions to the Basic Problem 302
* 11.5 Economic Application: Ramsey/Solow Model 315
Answers to exercises 325
Further Reading 359
Index 361 |
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| spelling | Turkington, Darrell A. 1947- Verfasser (DE-588)1012336387 aut Mathematical tools for economics Darrell A. Turkington 1. publ. Malden, MA [u.a.] Blackwell 2007 XI, 365 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Mathématiques économiques Wiskundige economie gtt Wiskundige modellen gtt Économie politique - Modèles mathématiques Mathematisches Modell Wirtschaft Economics, Mathematical Economics Mathematical models Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf Wirtschaftsmathematik (DE-588)4066472-7 s DE-604 http://www.loc.gov/catdir/toc/ecip0618/2006026293.html Table of contents only HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015602024&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Turkington, Darrell A. 1947- Mathematical tools for economics Mathématiques économiques Wiskundige economie gtt Wiskundige modellen gtt Économie politique - Modèles mathématiques Mathematisches Modell Wirtschaft Economics, Mathematical Economics Mathematical models Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| subject_GND | (DE-588)4066472-7 |
| title | Mathematical tools for economics |
| title_auth | Mathematical tools for economics |
| title_exact_search | Mathematical tools for economics |
| title_exact_search_txtP | Mathematical tools for economics |
| title_full | Mathematical tools for economics Darrell A. Turkington |
| title_fullStr | Mathematical tools for economics Darrell A. Turkington |
| title_full_unstemmed | Mathematical tools for economics Darrell A. Turkington |
| title_short | Mathematical tools for economics |
| title_sort | mathematical tools for economics |
| topic | Mathématiques économiques Wiskundige economie gtt Wiskundige modellen gtt Économie politique - Modèles mathématiques Mathematisches Modell Wirtschaft Economics, Mathematical Economics Mathematical models Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| topic_facet | Mathématiques économiques Wiskundige economie Wiskundige modellen Économie politique - Modèles mathématiques Mathematisches Modell Wirtschaft Economics, Mathematical Economics Mathematical models Wirtschaftsmathematik |
| url | http://www.loc.gov/catdir/toc/ecip0618/2006026293.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015602024&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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