Economic dynamics:
Gespeichert in:
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| Format: | Buch |
| Sprache: | English |
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Heidelberg [u.a.]
Springer
2010
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| Ausgabe: | Study ed., 4. ed. |
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| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XXV, 829 S. graph. Darst. |
| ISBN: | 9783642038624 9783642135033 |
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| 250 | |a Study ed., 4. ed. | ||
| 264 | 1 | |a Heidelberg [u.a.] |b Springer |c 2010 | |
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Datensatz im Suchindex
| _version_ | 1805094152144158720 |
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IMAGE 1
CONTENTS
PREFACE VII
INTRODUCTION 1
1.1 DEFINITION 1
1.2 FUNCTIONAL EQUATIONS 2
1.3 ECONOMIC DYNAMICS: PAST AND FUTURE 3
1.4 REFERENCES 5
LINEAR DIFFERENCE EQUATIONS 7
DIFFERENCE EQUATIONS: GENERAL PRINCIPLES 9
2.1 DEFINITIONS 9
2.2 LINEAR DIFFERENCE EQUATIONS WITH CONSTANT COEFFICIENTS 11 2.2.1 THE
HOMOGENEOUS EQUATION 12
2.2.2 THE NON-HOMOGENEOUS EQUATION 14
2.3 DETERMINATION OF THE ARBITRARY CONSTANTS 15
2.4 REFERENCES 16
FIRST-ORDER DIFFERENCE EQUATIONS 19
3.1 SOLUTION OF THE HOMOGENEOUS EQUATION 19
3.2 PARTICULAR SOLUTION OF THE NON-HOMOGENEOUS EQUATION 23 3.2.1 G(T) IS
A CONSTANT 23
3.2.2 G(T) IS AN EXPONENTIAL FUNCTION 24
3.2.3 G(T) IS A POLYNOMIAL FUNCTION OF DEGREE M 25
3.2.4 G(T) IS A TRIGONOMETRIC FUNCTION OF THE SINE-COSINE TYPE . 25
3.2.5 G(T) IS A COMBINATION OF THE PREVIOUS FUNCTIONS 26 3.2.6 THE CASE
WHEN G(T) IS A GENERIC FUNCTION OF TIME. BACK- WARD AND FORWARD
SOLUTIONS 26
3.3 GENERAL SOLUTION OF THE NON-HOMOGENEOUS EQUATION 29 3.4 A DIGRESSION
ON DISTRIBUTED LAGS AND PARTIAL ADJUSTMENT EQUA- TIONS 30
3.5 EXERCISES 33
3.5.1 EXAMPLE 33
3.5.2 OTHER EXERCISES 34
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1002539897
DIGITALISIERT DURCH
IMAGE 2
XII CONTENTS
3.6 REFERENCES 35
4 FIRST-ORDER DIFFERENCE EQUATIONS IN ECONOMIC MODELS 37 4.1 THE COBWEB
THEOREM 37
4.1.1 THE COBWEB MODEL AND EXPECTATIONS 40
4.1.1.1 THE NORMAL PRICE 41
4.1.1.2 ADAPTIVE EXPECTATIONS 42
4.2 THE DYNAMICS OF MULTIPLIERS 45
4.2.1 THE BASIC CASE 45
4.2.2 OTHER MULTIPLIERS 47
4.2.2.1 A FOREIGN TRADE MULTIPLIER 48
4.2.2.2 TAXATION 49
4.3 EXERCISES 50
4.4 REFERENCES 53
5 SECOND-ORDER DIFFERENCE EQUATIONS 55
5.1 SOLUTION OF THE HOMOGENEOUS EQUATION 55
5.1.1 POSITIVE DISCRIMINANT (A 0) 56
5.1.2 NULL DISCRIMINANT (A = 0) 57
5.1.3 NEGATIVE DISCRIMINANT (A 0) 58
5.1.4 STABILITY CONDITIONS 60
5.2 SOLUTION OF THE NON-HOMOGENEOUS EQUATION 62
5.2.1 THE OPERATIONAL METHOD 63
5.3 DETERMINATION OF THE ARBITRARY CONSTANTS 65
5.4 EXERCISES 67
5.4.1 EXAMPLE 67
5.4.2 OTHER EXERCISES 70
5.5 REFERENCES 71
6 SECOND-ORDER DIFFERENCE EQUATIONS IN ECONOMIC MODELS 73 6.1
MULTIPLIER-ACCELERATOR INTERACTION: THE PROTOTYPE MODEL (HANSEN-
SAMUELSON) 73
6.1.1 GRAPHICAL LOCATION OF THE ROOTS 75
6.2 MARKET ADJUSTMENTS AND RATIONAL EXPECTATIONS 77
6.3 HICKS' TRADE CYCLE MODEL 78
6.3.1 THE WORKINGS OF THE MODEL 83
6.4 EXERCISES 88
6.5 REFERENCES 90
7 HIGHER-ORDER DIFFERENCE EQUATIONS 93
7.1 SOLUTION OF THE HOMOGENEOUS EQUATION 93
7.2 PARTICULAR SOLUTION OF THE NON-HOMOGENEOUS EQUATION 94 7.2.1 THE
OPERATIONAL METHOD 95
7.3 DETERMINATION OF THE ARBITRARY CONSTANTS 97
IMAGE 3
CONTENTS XIII
7.4 STABILITY CONDITIONS 97
7.4.1 NECESSARY AND SUFFICIENT STABILITY CONDITIONS (SAMUELSON'S FORM)
98
7.4.2 NECESSARY AND SUFFICIENT STABILITY CONDITIONS (SCHUR-COHN FORM) 99
7.5 EXERCISES 102
7.5.1 EXAMPLE 102
7.5.2 OTHER EXERCISES 103
7.6 REFERENCES 103
8 HIGHER-ORDER DIFFERENCE EQUATIONS IN ECONOMIC MODELS 105 8.1 INVENTORY
CYCLES (METZLER) 105
8.2 DISTRIBUTED LAGS AND INTERACTION BETWEEN THE MULTIPLIER AND THE
ACCELERATOR (HICKS) 108
8.3 EXERCISES 110
8.4 REFERENCES 112
9 SIMULTANEOUS SYSTEMS OF DIFFERENCE EQUATIONS 113
9.1 FIRST-ORDER 2X2 SYSTEMS IN NORMAL FORM 113
9.1.1 GENERAL SOLUTION OF THE HOMOGENEOUS SYSTEM: FIRST METHOD 113
9.1.2 GENERAL SOLUTION OF THE HOMOGENEOUS SYSTEM: SECOND (OR DIRECT)
METHOD 116
9.1.2.1 UNEQUAL REAL ROOTS 116
9.1.2.2 EQUAL REAL ROOTS 118
9.1.2.3 COMPLEX ROOTS 119
9.1.3 PARTICULAR SOLUTION. DETERMINATION OF THE ARBITRARY CONSTANTS 120
9.2 FIRST ORDER NXN SYSTEMS IN NORMAL FORM 121
9.2.1 DIRECT MATRIX SOLUTION. THE JORDAN CANONICAL FORM . . 124 9.2.2
STABILITY CONDITIONS 127
9.2.2.1 A DIGRESSION ON NOT-WHOLLY-UNSTABLE SYSTEMS . 130 9.2.2.2 PROOF
OF THE STABILITY CONDITIONS 132
9.2.3 PARTICULAR SOLUTION 134
9.2.3.1 THE OPERATIONAL METHOD 134
9.2.4 DETERMINATION OF THE ARBITRARY CONSTANTS 137
9.3 GENERAL SYSTEMS 138
9.3.1 FIRST-ORDER SYSTEMS NOT IN NORMAL FORM 138
9.3.2 HIGHER-ORDER SYSTEMS 140
9.3.2.1 AN EXAMPLE 140
9.3.2.2 THE GENERAL CASE 141
9.3.2.3 TRANSFORMATION OF A HIGHER-ORDER SYSTEM INTO A FIRST-ORDER
SYSTEM IN NORMAL FORM 142
9.3.2.4 STABILITY CONDITIONS FOR HIGHER-ORDER SYSTEMS . 144
IMAGE 4
XIV CONTENTS
9.4 EXERCISES 145
9.4.1 EXAMPLE 145
9.4.2 OTHER EXERCISES 145
9.5 REFERENCES 146
10 SIMULTANEOUS DIFFERENCE SYSTEMS IN ECONOMIC MODELS 149 10.1 COURNOT
OLIGOPOLY 149
10.2 MULTIPLIER EFFECTS IN AN OPEN ECONOMY 152
10.3 OLIGOPOLY AND INTERNATIONAL TRADE 155
10.3.1 THE EQUILIBRIUM SOLUTION 156
10.3.2 STABILITY 158
10.4 EXERCISES 159
10.5 REFERENCES 160
11 LINEAR DIFFERENTIAL EQUATIONS 161
11 DIFFERENTIAL EQUATIONS: GENERAL PRINCIPLES 163
11.1 DEFINITIONS 163
11.2 LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS 164 11.2.1
THE HOMOGENEOUS EQUATION 165
11.2.2 THE NON-HOMOGENEOUS EQUATION 166
11.3 DETERMINATION OF THE ARBITRARY CONSTANTS 168
11.4 REFERENCES 170
12 FIRST-ORDER DIFFERENTIAL EQUATIONS 171
12.1 SOLUTION OF THE HOMOGENEOUS EQUATION 171
12.2 PARTICULAR SOLUTION OF THE NON-HOMEGENEOUS EQUATION 174 12.2.1 G(T)
IS A CONSTANT 174
12.2.2 G(T) IS AN EXPONENTIAL FUNCTION 175
12.2.3 G(T) IS A POLYNOMIAL FUNCTION OF DEGREE M 175
12.2.4 G(T) IS A TRIGONOMETRIC FUNCTION OF THE SINE-COSINE TYPE . 176
12.2.5 G(T) IS A COMBINATION OF THE PREVIOUS FUNCTIONS 176 12.2.6 G(T)
IS A GENERIC FUNCTION OF TIME. THE METHOD OF VARI- ATION OF PARAMETERS
177
12.3 GENERAL SOLUTION OF THE NON-HOMOGENEOUS EQUATION 178 12.4
CONTINUOUSLY DISTRIBUTED LAGS AND PARTIAL ADJUSTMENT EQUATIONS 179 12.5
EXERCISES 181
12.5.1 EXAMPLE 181
12.5.2 OTHER EXERCISES 183
12.6 REFERENCES 183
IMAGE 5
CONTENTS XV
13 FIRST-ORDER DIFFERENTIAL EQUATIONS IN ECONOMIC MODELS 185 13.1
STABILITY OF SUPPLY AND DEMAND EQUILIBRIUM 185
13.2 THE NEOCLASSICAL GROWTH MODEL 191
13.2.1 EXISTENCE OF A GROWTH EQUILIBRIUM 192
13.2.2 STABILITY OF GROWTH EQUILIBRIUM 194
13.2.3 REFINEMENTS 197
13.2.3.1 DEPRECIATION AND TECHNICAL PROGRESS 197 13.2.3.2 GOLDEN RULE
199
13.2.4 FURTHER DEVELOPMENTS 200
13.2.4.1 ADJUSTMENT TIME OR, HOW LONG IS THE LONG RUN? 200 13.2.4.2
/^-CONVERGENCE, CR-CONVERGENCE, AND ALL THAT . . 203 13.2.4.3 ENDOGENOUS
GROWTH 205
13.3 EXERCISES 205
13.4 REFERENCES 208
14 SECOND-ORDER DIFFERENTIAL EQUATIONS 209
14.1 SOLUTION OF THE HOMOGENEOUS EQUATION 209
14.1.1 POSITIVE DISCRIMINANT (A 0) 210
14.1.2 NULL DISCRIMINANT (A = 0) 211
14.1.3 NEGATIVE DISCRIMINANT (A 0) 212
14.1.4 STABILITY CONDITIONS 214
14.2 PARTICULAR SOLUTION OF THE NON-HOMOGENEOUS EQUATION 215 14.2.1
VARIATION OF PARAMETERS 216
14.3 GENERAL SOLUTION OF THE NON-HOMOGENEOUS EQUATION 218 14.4
DETERMINATION OF THE ARBITRARY CONSTANTS 219
14.5 EXERCISES 219
14.5.1 EXAMPLES 219
14.5.2 OTHER EXERCISES 221
14.6 REFERENCES .221
15 SECOND-ORDER DIFFERENTIAL EQUATIONS IN ECONOMIC MODELS 223 15.1 THE
SECOND-ORDER ACCELERATOR 223
15.2 EXERCISES 226
15.3 REFERENCES 228
16 HIGHER-ORDER DIFFERENTIAL EQUATIONS 229
16.1 SOLUTION OF THE HOMOGENEOUS EQUATION 229
16.2 SOLUTION OF THE NON-HOMOGENEOUS EQUATION 231
16.2.1 VARIATION OF PARAMETERS 231
16.3 DETERMINATION OF THE ARBITRARY CONSTANTS 234
16.4 STABILITY CONDITIONS 235
16.4.1 NECESSARY AND SUFFICIENT STABILITY CONDITIONS (ROUTH-HURWITZ) 239
IMAGE 6
XVI CONTENTS
16.4.2 NECESSARY AND SUFFICIENT STABILITY CONDITIONS (LIENARD-CHIPART)
240
16.5 EXERCISES 241
16.5.1 EXAMPLE 241
16.5.2 OTHER EXERCISES 242
16.6 REFERENCES 242
17 HIGHER-ORDER DIFFERENTIAL EQUATIONS IN ECONOMIC MODELS 243 17.1
FEEDBACK CONTROL AND STABILISATION POLICIES 243
17.1.1 INTRODUCTION 243
17.1.2 THREE TYPES OF STABILISATION POLICY 244
17.1.2.1 PROPORTIONAL STABILISATION POLICY 247 17.1.2.2 MIXED
PROPORTIONAL-DERIVATIVE STABILISATION POL- ICY 248
17.1.2.3 INTEGRAL STABILISATION POLICY 249
17.2 EXERCISES 250
17.3 REFERENCES 251
18 SIMULTANEOUS SYSTEMS OF DIFFERENTIAL EQUATIONS 253 18.1 FIRST-ORDER
2X2 SYSTEMS IN NORMAL FORM 253
18.1.1 GENERAL SOLUTION OF THE HOMOGENEOUS SYSTEM: FIRST METHOD 254
18.1.2 GENERAL SOLUTION OF THE HOMOGENEOUS SYSTEM: SECOND (OR DIRECT)
METHOD 256
18.1.2.1 UNEQUAL REAL ROOTS 257
18.1.2.2 EQUAL REAL ROOTS 259
18.1.2.3 COMPLEX ROOTS 260
18.1.3 PARTICULAR SOLUTION. DETERMINATION OF THE ARBITRARY CONSTANTS 261
18.2 FIRST ORDER NXN SYSTEMS IN NORMAL FORM 261
18.2.1 SOLUTION OF THE HOMOGENEOUS SYSTEM 263
18.2.1.1 THE MATRIX EXPONENTIAL AND THE JORDAN CANON- ICAL FORM 265
18.2.2 STABILITY CONDITIONS 269
18.2.2.1 D-STABILITY, AND STABILISATION OF MATRICES . . . 272 18.2.2.2
SENSITIVITY ANALYSIS 274
18.2.2.3 A DIGRESSION ON NOT-WHOLLY-UNSTABLE SYSTEMS . 277 18.2.2.4
PROOF OF THE STABILITY CONDITIONS 281
18.2.3 PARTICULAR SOLUTION 282
18.2.3.1 VARIATION OF PARAMETERS 283
18.2.4 DETERMINATION OF THE ARBITRARY CONSTANTS 283
18.3 GENERAL SYSTEMS 285
18.3.1 FIRST-ORDER SYSTEMS NOT IN NORMAL FORM 285
18.3.2 HIGHER-ORDER SYSTEMS 287
IMAGE 7
CONTENTS XVII
18.3.2.1 AN EXAMPLE 287
18.3.2.2 THE GENERAL CASE 288
18.3.2.3 TRANSFORMATION OF A HIGHER-ORDER SYSTEM INTO A FIRST-ORDER
SYSTEM IN NORMAL FORM 289
18.3.2.4 STABILITY CONDITIONS FOR HIGHER-ORDER SYSTEMS . 292 18.4
EXERCISES 292
18.4.1 EXAMPLE 292
18.4.2 OTHER EXERCISES 294
18.5 REFERENCES 295
19 DIFFERENTIAL EQUATION SYSTEMS IN ECONOMIC MODELS 297 19.1 STABILITY
OF WALRASIAN GENERAL EQUILIBRIUM OF EXCHANGE 297 19.1.1 STATIC STABILITY
299
19.1.2 DYNAMIC STABILITY 301
19.2 HUMAN CAPITAL IN A GROWTH MODEL 304
19.3 A DIGRESSION ON 'ARROW DIAGRAMS' 309
19.4 BALANCED GROWTH IN A MULTI-SECTOR ECONOMY 311
19.5 EXERCISES 316
19.6 REFERENCES 319
III ADVANCED TOPICS 323
20 COMPARATIVE STATICS AND THE CORRESPONDENCE PRINCIPLE 325 20.1
INTRODUCTION 325
20.2 THE METHOD OF COMPARATIVE STATICS 326
20.2.1 PURELY QUALITATIVELY COMPARATIVE STATICS 330
20.2.2 THE INVERSE COMPARATIVE STATICS PROBLEM 330
20.3 COMPARATIVE STATICS AND OPTIMIZING BEHAVIOUR 331
20.4 COMPARATIVE STATICS AND THE DYNAMIC STABILITY OF EQUILIBRIUM . 334
20.4.1 CRITICISM AND QUALIFICATIONS 336
20.5 EXTREMA AND DYNAMIC STABILITY 338
20.5.1 AN APPLICATION TO THE THEORY OF THE FIRM 343
20.6 ELEMENTS OF COMPARATIVE DYNAMICS 344
20.7 AN ILLUSTRATIVE APPLICATION OF THE CORRESPONDENCE PRINCIPLE: THE
IS-LM MODEL 345
20.8 EXERCISES 349
20.9 REFERENCES 349
21 STABILITY OF EQUILIBRIUM: A GENERAL TREATMENT 351
21.1 INTRODUCTION 351
21.2 BASIC CONCEPTS AND DEFINITIONS 353
21.2.1 STABILITY 353
21.2.2 FURTHER DEFINITIONS 357
IMAGE 8
XVIII CONTENTS
21.2.3 STRUCTURAL STABILITY 359
21.3 QUALITATIVE METHODS: PHASE DIAGRAMS 363
21.3.1 SINGLE EQUATIONS 364
21.3.2 TWO-EQUATION SIMULTANEOUS SYSTEMS 368
21.3.2.1 INTRODUCTION: PHASE PLANE AND PHASE PATH . . 368 21.3.2.2
SINGULAR POINTS 369
21.3.2.3 GRAPHICAL CONSTRUCTION OF THE TRAJECTORIES . . 372 21.3.2.4
LINEAR SYSTEMS 378
21.4 QUANTITATIVE METHODS 382
21.4.1 LINEARISATION 382
21.5 ELEMENTS OF THE QUALITATIVE THEORY OF DIFFERENCE EQUATIONS . . .
387 21.5.1 SINGLE DIFFERENCE EQUATIONS 388
21.5.2 TWO SIMULTANEOUS DIFFERENCE EQUATIONS 393
21.5.2.1 LINEAR SYSTEMS 394
21.6 ECONOMIC APPLICATIONS 396
21.7 EXERCISES 396
21.8 REFERENCES 398
22 LIAPUNOV'S SECOND METHOD 401
22.1 GENERAL CONCEPTS 401
22.2 THE FUNDAMENTAL THEOREMS 402
22.3 SOME ECONOMIC APPLICATIONS 407
22.3.1 GLOBAL STABILITY OF WALRASIAN GENERAL EQUILIBRIUM . . . 407
22.3.2 RULES OF THUMB IN BUSINESS MANAGEMENT 414
22.3.3 PRICE ADJUSTMENT AND OLIGOPOLY UNDER PRODUCT DIFFER- ENTIATION
415
22.4 EXERCISES 419
22.5 REFERENCES 420
23 INTRODUCTION TO NONLINEAR DYNAMICS 423
23.1 PRELIMINARY REMARKS 423
23.1.1 A DIGRESSION ON EXISTENCE AND UNIQUENESS THEOREMS . . 425 23.2
SOME INTEGRABLE DIFFERENTIAL EQUATIONS 426
23.2.1 FIRST-ORDER AND FIRST-DEGREE EXACT EQUATIONS 426 23.2.2 LINEAR
EQUATIONS OF THE FIRST ORDER WITH VARIABLE COEFFI- CIENTS 429
23.2.3 THE BERNOULLI EQUATION 431
23.2.4 THE RICCATI EQUATION 432
23.3 LIMIT CYCLES AND RELAXATION OSCILLATIONS 434
23.3.1 LIMIT CYCLES: THE GENERAL THEORY 434
23.3.2 LIMIT CYCLES: RELAXATION OSCILLATIONS 436
23.3.3 KALDOR'S NON-LINEAR CYCLICAL MODEL 439
23.3.3.1 THE MODEL 439
23.3.3.2 KALDOR VIA RELAXATION OSCILLATIONS 443
IMAGE 9
CONTENTS XIX
23.3.3.3 KALDOR VIA POINCARE'S LIMIT CYCLE 446
23.4 THE LOTKA-VOLTERRA EQUATIONS 448
23.4.1 CONSTRUCTION OF THE INTEGRAL CURVES 453
23.4.2 CONSERVATIVE AND DISSIPATIVE SYSTEMS, AND IRREVERSIBILITY 455
23.4.3 GOODWIN'S GROWTH CYCLE 457
23.4.3.1 THE MODEL 457
23.4.3.2 THE PHASE DIAGRAM OF THE MODEL 460
23.4.4 PALOMBA'S MODEL 463
23.4.4.1 THE MODEL 463
23.4.4.2 CONCLUSION 466
23.5 EXERCISES 466
23.6 REFERENCES 469
24 BIFURCATION THEORY 473
24.1 INTRODUCTION 473
24.2 BIFURCATIONS IN CONTINUOUS TIME SYSTEMS 473
24.2.1 CODIMENSION-ONE BIFURCATIONS 475
24.2.2 THE HOPF BIFURCATION 479
24.2.3 SENSITIVITY ANALYSIS AND BIFURCATIONS: A REMINDER . . . 484
24.2.4 KALDOR'S NON-LINEAR CYCLICAL MODEL AGAIN 485
24.2.5 OSCILLATIONS IN OPTIMAL GROWTH MODELS 486
24.2.5.1 THE MODEL 486
24.2.5.2 THE OPTIMALITY CONDITIONS 488
24.2.5.3 EMERGENCE OF A HOPF BIFURCATION 489
24.2.6 CYCLES IN AN IS-LM MODEL WITH PURE MONEY FINANCING . 491 24.3
BIFURCATIONS IN DISCRETE TIME SYSTEMS 493
24.3.1 CODIMENSION-ONE BIFURCATIONS 494
24.3.2 THE HOPF (OR NEIMARK-SACKER) BIFURCATION IN DISCRETE TIME 496
24.3.3 KALDOR'S CYCLICAL MODEL IN DISCRETE TIME 498
24.3.4 LIQUIDITY COSTS IN THE FIRM 499
24.3.4.1 THE MODEL 499
24.3.4.2 THE DYNAMICS 502
24.3.5 EXPECTATIONS AND MULTIPLIER-ACCELERATOR INTERACTION . . 504 24.4
HYSTERESIS AND BIFURCATIONS 507
24.4.1 GENERAL 507
24.4.2 DYNAMICAL SYSTEMS 509
24.4.3 ECONOMICS 510
24.5 SINGULARITY-INDUCED BIFURCATIONS 511
24.6 EXERCISES 513
24.7 REFERENCES 515
IMAGE 10
XX CONTENTS
25 COMPLEX DYNAMICS 519
25.1 INTRODUCTION 519
25.2 DISCRETE TIME SYSTEMS AND CHAOS 522
25.2.1 THE LOGISTIC MAP 522
25.2.2 INTERMITTENCY 528
25.2.3 THE BASIC THEOREMS 529
25.2.4 DISCRETE TIME CHAOS IN ECONOMICS 531
25.2.4.1 CHAOS IN GROWTH THEORY 531
25.2.4.2 EXCHANGE RATE DYNAMICS AND CHAOS 533 25.3 CONTINUOUS TIME
SYSTEMS AND CHAOS 535
25.3.1 THE LORENZ EQUATIONS, STRANGE ATTRACTORS, AND CHAOS . . 535
25.3.2 OTHER ROUTES TO CONTINUOUS TIME CHAOS 537
25.3.2.1 THE ROESSLER ATTRACTOR 537
25.3.2.2 THE SHIL'NIKOV SCENARIO 538
25.3.2.3 THE FORCED OSCILLATOR 538
25.3.2.4 THE COUPLED OSCILLATOR 539
25.3.3 INTERNATIONAL TRADE AS THE SOURCE OF CHAOS 542
25.3.4 A CHAOTIC GROWTH CYCLE 544
25.4 SIGNIFICANCE AND DETECTION OF CHAOS: STOCHASTIC DYNAMICS OR CHAOS?
545
25.5 CONTROL OF CHAOS 549
25.6 OTHER APPROACHES 552
25.6.1 INTRODUCTION 552
25.6.2 FAST AND SLOW, AND SYNERGETICS 552
25.6.3 CATASTROPHE THEORY 556
25.7 EXERCISES 558
25.8 REFERENCES 560
26 MIXED DIFFERENTIAL-DIFFERENCE EQUATIONS 567
26.1 GENERAL CONCEPTS 567
26.2 CONTINUOUS VS DISCRETE TIME IN ECONOMIC MODELS 568 26.3 LINEAR
MIXED EQUATIONS 573
26.4 THE METHOD OF SOLUTION 574
26.5 STABILITY CONDITIONS 579
26.6 APPROXIMATE METHODS 580
26.7 DELAY DIFFERENTIAL EQUATIONS AND CHAOS 581
26.8 SOME ECONOMIC APPLICATIONS 582
26.8.1 KALECKI'S BUSINESS CYCLE MODEL 583
26.8.1.1 THE MODEL 583
26.8.1.2 THE DYNAMICS 585
26.8.2 A FORMALIZATION OF THE CLASSICAL PRICE-SPECIE-FLOW MECH- ANISM OF
BALANCE OF PAYMENTS ADJUSTMENT 589
26.8.2.1 THE MODEL 589
26.8.2.2 STABILITY 591
IMAGE 11
CONTENTS XXI
26.9 EXERCISES 593
26.10REFERENCES 594
27 DYNAMIC OPTIMIZATION 597
27.1 INTRODUCTION 597
27.2 CALCULUS OF VARIATIONS 599
27.2.1 PARTICULAR CASES 601
27.2.2 GENERALIZATIONS 603
27.3 THE MAXIMUM PRINCIPLE 604
27.3.1 STATEMENT 604
27.3.2 PROOF 606
27.3.3 TRANSVERSALITY CONDITIONS 610
27.3.3.1 THE CASE WITH INFINITE TERMINAL TIME 611 27.3.4 EFFECTS OF
PARAMETER CHANGES ON THE OPTIMAL SOLUTION: THE COSTATE VARIABLES 612
27.3.5 DISCOUNTING 614
27.3.6 PARTICULAR CASES 615
27.3.6.1 THE BANG-BANG CONTROL CASE 615
27.3.6.2 LINEAR-QUADRATIC PROBLEMS 616
27.3.7 THE MAXIMUM PRINCIPLE IN DISCRETE TIME 618
27.4 DYNAMIC PROGRAMMING 619
27.4.1 DYNAMIC PROGRAMMING IN DISCRETE TIME: MULTI-STAGE OPTIMIZATION
PROBLEMS 622
27.4.2 DYNAMIC PROGRAMMING AND NONLINEAR PROGRAMMING . . 626 27.4.3
INFINITE TERMINAL TIME 627
27.4.3.1 SOLUTION BY CONJECTURE 628
27.4.3.2 SOLUTION BY ITERATION 632
27.4.3.3 SOLUTION BY THE ENVELOPE THEOREM 633 27.5 MAXIMUM PRINCIPLE VS.
DYNAMIC PROGRAMMING 637 27.6 EXERCISES 639
27.7 REFERENCES 641
28 SADDLE POINTS AND ECONOMIC DYNAMICS 643
28.1 SADDLE POINTS IN OPTIMAL CONTROL PROBLEMS 644
28.2 OPTIMAL ECONOMIC GROWTH 644
28.2.1 OPTIMAL GROWTH: TRADITIONAL 644
28.2.1.1 THE SETTING OF THE PROBLEM 644
28.2.1.2 THE OPTIMALITY CONDITIONS IN THE BASIC NEO- CLASSICAL MODEL 647
28.2.1.3 SADDLE-POINT TRANSITIONAL DYNAMICS IN THE BA- SIC NEOCLASSICAL
MODEL 651
28.2.1.4 OPTIMAL AND SUB-OPTIMAL FEEDBACK CONTROL . . 653 28.2.1.4.1 THE
SUB-OPTIMAL FEEDBACK CONTROL RULE 655
IMAGE 12
XXII CONTENTS
28.2.2 OPTIMAL GROWTH: ENDOGENOUS 656
28.2.2.1 A MODEL OF OPTIMAL ENDOGENOUS GROWTH . . . 656 28.2.2.2 THE
CONDITIONS FOR OPTIMAL ENDOGENOUS GROWTH 658 28.2.2.3 OPTIMAL ENDOGENOUS
GROWTH: SADDLE-POINT TRAN- SITIONAL DYNAMICS 660
28.3 OPTIMAL ENDOGENOUS GROWTH IN AN OPEN ECONOMY 664 28.3.1 THE NET
BORROWER NATION 669
28.3.1.1 STEADY-STATE STABILITY AND COMPARATIVE DY- NAMICS 671
28.4 RATIONAL EXPECTATIONS AND SADDLE POINTS 674
28.4.1 INTRODUCTION 674
28.4.2 RATIONAL EXPECTATIONS, SADDLE POINTS, AND OVERSHOOTING 677
28.4.2.1 A DISCRETE-TIME EQUIVALENT 682
28.4.3 RATIONAL EXPECTATIONS AND SADDLE POINTS: THE GENERAL CASE 684
28.5 INDETERMINACY AND SUNSPOTS 686
28.5.1 INDETERMINACY AND FISCAL POLICY 688
28.5.1.1 FIRMS 688
28.5.1.2 HOUSEHOLDS 689
28.5.1.3 GOVERNMENT 689
28.5.1.4 THE OPTIMALITY CONDITIONS 690
28.5.1.5 THE SINGULAR POINT AND ITS NATURE 693
28.6 EXERCISES 697
28.7 REFERENCES 699
BIBLIOGRAPHY 701
INDEX 731
ANSWERS TO EXERCISES 751 |
| any_adam_object | 1 |
| author | Gandolfo, Giancarlo |
| author_GND | (DE-588)170260941 |
| author_facet | Gandolfo, Giancarlo |
| author_role | aut |
| author_sort | Gandolfo, Giancarlo |
| author_variant | g g gg |
| building | Verbundindex |
| bvnumber | BV036493086 |
| classification_rvk | QH 300 QH 310 |
| ctrlnum | (OCoLC)845756271 (DE-599)DNB1002539897 |
| dewey-full | 339 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 339 - Macroeconomics and related topics |
| dewey-raw | 339 |
| dewey-search | 339 |
| dewey-sort | 3339 |
| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| edition | Study ed., 4. ed. |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV036493086 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T10:38:51Z |
| institution | BVB |
| isbn | 9783642038624 9783642135033 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020415669 |
| oclc_num | 845756271 |
| open_access_boolean | |
| owner | DE-M382 DE-355 DE-BY-UBR DE-20 DE-1043 DE-634 DE-384 DE-2070s |
| owner_facet | DE-M382 DE-355 DE-BY-UBR DE-20 DE-1043 DE-634 DE-384 DE-2070s |
| physical | XXV, 829 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| spelling | Gandolfo, Giancarlo Verfasser (DE-588)170260941 aut Economic dynamics Giancarlo Gandolfo Study ed., 4. ed. Heidelberg [u.a.] Springer 2010 XXV, 829 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Dynamische Makroökonomie (DE-588)4200428-7 gnd rswk-swf Dynamik (DE-588)4013384-9 gnd rswk-swf Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Wirtschaftstheorie (DE-588)4079351-5 gnd rswk-swf Ökonometrie (DE-588)4132280-0 gnd rswk-swf Dynamisches Modell (DE-588)4150932-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Dynamische Makroökonomie (DE-588)4200428-7 s DE-604 Differentialgleichung (DE-588)4012249-9 s Ökonometrie (DE-588)4132280-0 s Mathematisches Modell (DE-588)4114528-8 s 1\p DE-604 Dynamik (DE-588)4013384-9 s Wirtschaftstheorie (DE-588)4079351-5 s 2\p DE-604 Wirtschaftsmathematik (DE-588)4066472-7 s Dynamisches Modell (DE-588)4150932-8 s 3\p DE-604 Erscheint auch als Online-Ausgabe 978-3-642-03871-6 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3476697&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020415669&sequence=000001&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 | Gandolfo, Giancarlo Economic dynamics Mathematisches Modell (DE-588)4114528-8 gnd Dynamische Makroökonomie (DE-588)4200428-7 gnd Dynamik (DE-588)4013384-9 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd Differentialgleichung (DE-588)4012249-9 gnd Wirtschaftstheorie (DE-588)4079351-5 gnd Ökonometrie (DE-588)4132280-0 gnd Dynamisches Modell (DE-588)4150932-8 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4200428-7 (DE-588)4013384-9 (DE-588)4066472-7 (DE-588)4012249-9 (DE-588)4079351-5 (DE-588)4132280-0 (DE-588)4150932-8 (DE-588)4123623-3 |
| title | Economic dynamics |
| title_auth | Economic dynamics |
| title_exact_search | Economic dynamics |
| title_full | Economic dynamics Giancarlo Gandolfo |
| title_fullStr | Economic dynamics Giancarlo Gandolfo |
| title_full_unstemmed | Economic dynamics Giancarlo Gandolfo |
| title_short | Economic dynamics |
| title_sort | economic dynamics |
| topic | Mathematisches Modell (DE-588)4114528-8 gnd Dynamische Makroökonomie (DE-588)4200428-7 gnd Dynamik (DE-588)4013384-9 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd Differentialgleichung (DE-588)4012249-9 gnd Wirtschaftstheorie (DE-588)4079351-5 gnd Ökonometrie (DE-588)4132280-0 gnd Dynamisches Modell (DE-588)4150932-8 gnd |
| topic_facet | Mathematisches Modell Dynamische Makroökonomie Dynamik Wirtschaftsmathematik Differentialgleichung Wirtschaftstheorie Ökonometrie Dynamisches Modell Lehrbuch |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3476697&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020415669&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gandolfogiancarlo economicdynamics |