Variational methods in economics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
North-Holland Publ. Co.
1973
|
| Ausgabe: | 2. print. |
| Schriftenreihe: | Advanced textbooks in economics.
1. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 378 S. graph. Darst. |
| ISBN: | 072043601X |
Internformat
MARC
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| 100 | 1 | |a Hadley, George |e Verfasser |4 aut | |
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| 264 | 1 | |a Amsterdam |b North-Holland Publ. Co. |c 1973 | |
| 300 | |a IX, 378 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804120498749046784 |
|---|---|
| adam_text | Titel: Variational methods in economics
Autor: Hadley, George
Jahr: 1973
Contents
PREFACE V
CHAPTER 1 1
1.1. Introduction 1
1.2. Growth modeis in economics 1
CHAPTER 2: CALCULUS OF VARIATIONS-CLASSICAL THEORY 6
2.1. Introduction 6
2.2. Historical foundations and some classical Problems 7
2.3. Functions 10
2.4. Phase diagrams and phase Spaces 17
2.5. The simplest problem in the calculus of variations 22
2.6. The Euler equation and corner conditions 26
2.7. The Euler equation in special cases 40
2.8. Examples 41
2.9. Ramsey s problem 50
2.10. Ramsey s problem-finite planning horizons 54
2.11. Ramsey s problem-infinite planning horizons 62
2.12. Samuelson s catenary turnpike theorem 71
2.13. Generalization to n functions 78
2.14. Parametric representation 82
2.15. The Weierstrass and Legendre necessary conditions 86
2.16. An n-sector generalization of Ramsey s model 89
2.17. Sufficient conditions based on the concavity of F 96
2.18. Classical sufficiency conditions 105
2.19. Sensitivity analysis-end point changes 117
2.20. Weierstrass sufficient conditions 120
2.21. Variable end points-free boundaries 127
2.22. Variable end points-transversality 131
2.23. Transversality at infinity 137
2.24. Transversality in the model of Samuelson and Solow. 140
2.25. The connection with dynamic Programming 147
Problems 152
VIII CONTENTS
CHAPTER 3: CLASSICAL THEORY-CONSTRAINTS 175
3.1. Introduction 175
3.2. Isoperimetric constraints 177
3.3. The problem of Lagrange 183
3.4. A simplified proof of the multiplier rule for fixed end points 186
3.5. Transversality 192
3.6. Free boundary conditions 197
3.7. Examples 197
3.8. Preliminary results 201
3.9. The comparison functions 208
3.10. The convex polyhedral cone Jf 212
3.11. The convex cone Jf * 215
3.12. The multiplier rule and the Weierstrass and Legendre necessary conditions 217
3.13. Unbounded intervals of Integration 223
3.14. Normality 225
3.15. Sufficiency based on the concavity of H 228
3.16. The problem ofBolza 230
Problems 233
CHAPTER 4: OPTIMAL CONTROL THEORY 238
4.1. Introduction 238
4.2. The basic control problem 239
4.3. Necessary conditions-the maximum principle 241
4.4. The conversion of a nonautonomous System into an autonomous System 246
4.5. An heuristic derivation of the necessary conditions 249
4.6. The Ramsey model: finite planning horizon 255
4.7. A phase diagram using conjugate variables 257
4.8. The Ramsey model: infinite planning horizon 261
4.9. A Situation in which it may be optimal to reach bliss in a finite time 264
4.10. The Ramsey model with discounting 267
4.11. Optimal transfer from K0 to Ki with Z -»¦ 0 as K - Ki 270
4.12. The conversion of classical problems into control Problems 270
4.13. The synthesis problem 271
4.14. The model of Samuelson and Solow again 273
Problems 280
CHAPTER 5: CONNECTIONS WITH THE CLASSICAL THEORY 282
5.1. Introduction 282
5.2. Valentine s procedure 284
5.3. The conversion of a control problem into a problem of Lagrange 285
5.4. Necessary conditions 286
5.5. The time Variation of H 292
5.6. Examples 294
5.7. Sufficiency 297
5.8. Linear control problems 299
5.9. Constrained State variables-introduction 304
5.10. The control problem and the equivalent problem of Lagrange 306
5.11. Necessary conditions for the problem of Lagrange 308
CONTENTS IX
5.12. An interior segment 312
5.13. A boundary segment 315
5.14. Transition conditions 319
Problems 322
CHAPTER 6: TWO-SECTOR MODELS OF OPTIMAL ECONOMIC GROWTH 326
6.1. Introduction 326
6.2. The capital good freely transferable between industries 327
6.3. The capital good immobile between industries 347
6.4. Final remarks 361
Problems 363
appendix i: Uniqueness of the Utility functional and the Utility function 364
Appendix n: Implicit function theorems 367
appendix in. Existence theorems for Systems of ordinary differential equations 370
REFERENCES 374
|
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| author | Hadley, George Kemp, Murray C. 1926-2021 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. print. |
| format | Book |
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| genre | Lehrbuch - Variationsrechnung - Wirtschaftsmathematik |
| genre_facet | Lehrbuch - Variationsrechnung - Wirtschaftsmathematik |
| id | DE-604.BV006283071 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:43:03Z |
| institution | BVB |
| isbn | 072043601X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003971188 |
| oclc_num | 256136716 |
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| owner_facet | DE-739 DE-20 DE-634 DE-83 DE-706 DE-188 |
| physical | IX, 378 S. graph. Darst. |
| publishDate | 1973 |
| publishDateSearch | 1973 |
| publishDateSort | 1973 |
| publisher | North-Holland Publ. Co. |
| record_format | marc |
| series | Advanced textbooks in economics. |
| series2 | Advanced textbooks in economics. |
| spelling | Hadley, George Verfasser aut Variational methods in economics G. Hadley ; M. C. Kemp 2. print. Amsterdam North-Holland Publ. Co. 1973 IX, 378 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advanced textbooks in economics. 1. Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Lehrbuch - Variationsrechnung - Wirtschaftsmathematik Variationsrechnung (DE-588)4062355-5 s DE-604 Kemp, Murray C. 1926-2021 Verfasser (DE-588)11917166X aut Advanced textbooks in economics. 1. (DE-604)BV000012327 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003971188&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hadley, George Kemp, Murray C. 1926-2021 Variational methods in economics Advanced textbooks in economics. Variationsrechnung (DE-588)4062355-5 gnd |
| subject_GND | (DE-588)4062355-5 |
| title | Variational methods in economics |
| title_auth | Variational methods in economics |
| title_exact_search | Variational methods in economics |
| title_full | Variational methods in economics G. Hadley ; M. C. Kemp |
| title_fullStr | Variational methods in economics G. Hadley ; M. C. Kemp |
| title_full_unstemmed | Variational methods in economics G. Hadley ; M. C. Kemp |
| title_short | Variational methods in economics |
| title_sort | variational methods in economics |
| topic | Variationsrechnung (DE-588)4062355-5 gnd |
| topic_facet | Variationsrechnung Lehrbuch - Variationsrechnung - Wirtschaftsmathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003971188&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012327 |
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