The dynamic systems of basic economic growth models:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer
1994
|
| Series: | Mathematics and its applications
302 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 355 S. graph. Darst. |
| ISBN: | 0792330919 |
Staff View
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| 100 | 1 | |a Jensen, Bjarne S. |d 1942- |e Verfasser |0 (DE-588)17281006X |4 aut | |
| 245 | 1 | 0 | |a The dynamic systems of basic economic growth models |c by Bjarne S. Jensen |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer |c 1994 | |
| 300 | |a XII, 355 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 302 | |
| 650 | 4 | |a Wachstumstheorie / Theorie | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Wirtschaftsentwicklung | |
| 650 | 4 | |a Economic development -- Mathematical models | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Table of Contents v
Preface xi
Introduction and Overview 1
BOOK I Basic Economic Growth Models An Axiomatic Approach
1 Basic laws of production 19
1.1 The production function 19
1.2 Homogeneity and the laws of variable proportions 20
1.3 Technical substitution possibilities 22
1.4 Factor shares and production elasticities 25
1.5 Iso marginal, iso average productivity curves 26
1.6 Special production functions 28
1.7 Literature comments 29
Part 1: Basic One Sector Growth Models
2 Classical growth models and homogeneity 33
2.1 The dynamic system 33
2.2 Ratio and coordinate solutions 34
2.2.1 Axes solutions 35
2.2.2 Directrix solutions 35
2.2.3 Non directrix solutions 37
2.3 Stability of ratio and coordinate solutions 38
2.4 The geometry of the phase portrait 39
2.5 Output, distribution and factor prices 40
2.6 CD and CES technologies 42
2.6.1 CD 42
2.6.2 CES 44
2.6.3 Linear isoquants 45
2.7 Constant returns to scale 47
2.8 Directrix solutions, steady states, and constant ratios 48
2.9 Classical comparative dynamics 52
2.9.1 Accumulation and propagation parameters 52
2.9.2 Technology parameters 54
v
vi Contents
3 Classical growth models and minimal factor rewards 57
3.1 The dynamic system 57
3.2 Decreasing returns to scale and minimal factor rewards 58
3.3 Constant returns to scale and minimal factor rewards 63
4 Aggregate endogenous growth models 67
4.1 The aggregate homogeneous dynamic system 67
4.2 Aggregate growth and critical factor productivities 69
4.2.1 Decreasing returns to scale 69
4.2.2 Constant returns to scale 71
4.2.3 One class versus two class models 71
Synopsis of endogenous growth models 73
5 Neoclassical growth models 75
5.1 The dynamic system, solutions, and stability 75
5.2 The phase portrait and the steady state path 77
5.3 Neoclassical growth and special technologies 80
5.3.1 CD technology 80
5.3.2 Leontief technology 81
5.4 Trajectory geometry and kinematics 86
6 Keynesian growth models 89
6.1 Harrodian growth models 90
6.2 Economic aspects and stability issues 96
Part 2: Basic Two Sector Growth Models
7 Leontief technology and efficient factor utilization 101
7.1 Assumptions and structure of the two sector economy 101
7.2 The dynamic system, solutions, stability, and trajectory geometry . . 105
7.3 The economic rationale of the stability conditions 109
7.4 Endogenous labor supply 117
7.5 Literature comments 121
8 Flexible technologies and proportional saving 123
8.1 The two sector economy with proportional saving 123
8.1.1 The general equilibrium model 123
8.1.2 The general equilibrium solutions 125
8.1.3 Comparative general equilibrium analysis 128
8.1.4 Literature comments 133
8.2 The dynamic system, solutions, stability, and trajectory geometry . . 136
8.3 The economic rationale of the stability conditions 140
Contents vjj
9 Flexible technologies and classical saving 142
9.1 The two sector economy with classical saving 142
9.1.1 The general equilibrium model and solutions 142
9.1.2 Comparative general equilibrium analyses 145
9.2 Dynamics, solutions, stability, and trajectory geometry 148
9.2.1 Exogenous labor supply 148
9.2.2 Endogenous labor supply 150
9.3 Comparative two sector dynamics 152
Synopsis of two sector growth models 155
Final comments 159
BOOK II Basic Dynamic Systems
10 Homogeneous Dynamics in the Plane 163
10.1 Basic framework, assumptions and definitions 164
10.2 Ratio solutions, coordinate solutions, and trajectories 170
10.3 The ratio and coordinate solutions on directrices 174
10.4 The geometry of history curves, phase curves, and trajectories .... 176
10.4.1 Vector and tangent fields 177
10.4.2 Heuristic comments on geometry, dynamics, and kinematics . 181
10.5 Miscellanea on homogeneous differential equations 184
10.5.1 Literature comment 1 184
10.5.2 The quintessence of Theorem 1 2 186
10.5.3 Literature comment 2 187
10.5.4 On solutions and their maximal time interval of existence . . . 190
10.6 The stability properties of ratio solutions 193
10.6.1 Dynamic stability concepts 193
10.6.2 Global asymptotic ratio stability 194
10.6.3 Local asymptotic ratio stability 197
10.6.4 Absence of any ratio stability 198
10.6.5 Asymptotic ratio stability and trajectory geometry 198
10.7 The stability properties of coordinate solutions 200
10.7.1 Global asymptotic ratio stability and global stabilities of co¬
ordinate solutions 200
10.7.2 Local asymptotic ratio stability and the stabilities of coordi¬
nate solutions 206
10.8 Synopsis 208
10.9 Concluding comments 209
viii Contents
11 Linear and Affine Dynamics in the Plane 211
11.1 The linear system, director function, and directrices 212
11.2 The general ratio solution 214
11.3 The general coordinate solution 216
11.4 Ratio and coordinate solutions of triangular systems 218
11.5 The calculus approach and techniques of integration 219
11.6 General coordinate solutions and initial value problems 221
11.7 Initial value problems and coordinate transformations 224
11.8 Stability of the ratio and coordinate solutions 227
11.9 The geometry of the phase portrait 232
11.9.1 Conic trajectories 232
11.9.2 Hyperconic trajectories 233
11.10Parameter space and the hyperconic phase portrait 235
11.10.1 Parameter regions and trajectory configurations 236
11.10.2 Boundary curves and trajectory configurations 236
11.11 Structural stability and bifurcations 237
11.12 Parameter space and kinematic stability properties 251
11.13 Classification of linear dynamic systems 252
11.14Affine dynamics in the plane 254
11.14.1 Nonsingular affine dynamics 254
11.14.2 Singular affine dynamics 255
11.14.3The geometry of the affine phase portrait 257
11.15 Concluding comments 258
12 Quasi Homogeneous Dynamics in the Plane 259
12.1 The class of quasi homogeneous functions 259
12.2 Quasihomogeneous differential equations 262
12.2.1 The class of quasihomogeneous differential equations 262
12.2.2 The solutions to quasihomogeneous differential equations . . . 265
12.3 Quasi homogeneous autonomous dynamic systems 268
12.3.1 Stability properties of coordinate solutions 269
12.3.2 Stability properties of ratio and quotient 272
12.4 Concluding comments 274
13 Discrete Linear Dynamics in the Plane 276
13.1 Basic framework of the discrete linear system 278
13.2 Phase plane decomposition and ratios 279
13.2.1 Stationary ratios and directrix solutions 280
13.2.2 Nonstationary ratio solutions 281
13.3 The general solution and initial value problems 282
13.4 Discrete and continuous time solutions 288
13.5 The phase portrait of discrete linear dynamics 291
13.6 Final Comment 303
13.7 Appendix: The exponential and logarithmic matrices of regular two
by two matrices 304
Contents ix
Addendum: Growth and Long Run Stability 313
A.I Introduction 313
A.2 Stability criteria and degrees of stability 314
A.3 Causality and differential equations 315
A.4 Stability conditions for autonomous differential equations 316
A.5 Rapidity of growth 320
A.6 Growth versus stability of autonomous differential equations 321
A.7 Economic applications 322
A.7.1 The multiplier accelerator growth model of Harrod 322
A.7.2 The neoclassical growth model of Solow 326
A.8 Concluding comments 328
A.9 Appendix on the logarithmic derivative 329
Bibliography: Book I 333
Bibliography: Book II 345
Index 351
|
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| dewey-sort | 3338.9 11 45118 220 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV009799749 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:41:04Z |
| institution | BVB |
| isbn | 0792330919 |
| language | English |
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| physical | XII, 355 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
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| publisher | Kluwer |
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| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Jensen, Bjarne S. 1942- Verfasser (DE-588)17281006X aut The dynamic systems of basic economic growth models by Bjarne S. Jensen Dordrecht u.a. Kluwer 1994 XII, 355 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 302 Wachstumstheorie / Theorie Mathematisches Modell Wirtschaftsentwicklung Economic development -- Mathematical models Dynamisches System (DE-588)4013396-5 gnd rswk-swf Wachstumsmodell (DE-588)4127141-5 gnd rswk-swf Wachstumsmodell (DE-588)4127141-5 s DE-604 Dynamisches System (DE-588)4013396-5 s Mathematics and its applications 302 (DE-604)BV008163334 302 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006483923&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jensen, Bjarne S. 1942- The dynamic systems of basic economic growth models Mathematics and its applications Wachstumstheorie / Theorie Mathematisches Modell Wirtschaftsentwicklung Economic development -- Mathematical models Dynamisches System (DE-588)4013396-5 gnd Wachstumsmodell (DE-588)4127141-5 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4127141-5 |
| title | The dynamic systems of basic economic growth models |
| title_auth | The dynamic systems of basic economic growth models |
| title_exact_search | The dynamic systems of basic economic growth models |
| title_full | The dynamic systems of basic economic growth models by Bjarne S. Jensen |
| title_fullStr | The dynamic systems of basic economic growth models by Bjarne S. Jensen |
| title_full_unstemmed | The dynamic systems of basic economic growth models by Bjarne S. Jensen |
| title_short | The dynamic systems of basic economic growth models |
| title_sort | the dynamic systems of basic economic growth models |
| topic | Wachstumstheorie / Theorie Mathematisches Modell Wirtschaftsentwicklung Economic development -- Mathematical models Dynamisches System (DE-588)4013396-5 gnd Wachstumsmodell (DE-588)4127141-5 gnd |
| topic_facet | Wachstumstheorie / Theorie Mathematisches Modell Wirtschaftsentwicklung Economic development -- Mathematical models Dynamisches System Wachstumsmodell |
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