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Bibliographic Details
Main Author:	Gandolfo, Giancarlo (Author)
Format:	Book
Language:	English
Published:	Heidelberg [u.a.] Springer 2009
Edition:	4. ed.
Subjects:	Mathematisches Modell Wirtschaft Economics > Mathematical models Economics, Mathematical Statics and dynamics (Social sciences) Dynamische Makroökonomie Dynamik Wirtschaftsmathematik Differentialgleichung Wirtschaftstheorie Ökonometrie Dynamisches Modell Lehrbuch
Online Access:	Inhaltstext Inhaltsverzeichnis
Item Description:	Literaturangaben
Physical Description:	XXV, 749 S. graf. Darst. 24 cm
ISBN:	9783642038624

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adam_text	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- TION BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/995338779 DIGITALISIERT DURCH 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. 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. 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. 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 /3-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. 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. 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. 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- CIENT 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. 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. 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 27A.I 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. INDEX 731 XXII CONTENTS 28.2.2 OPTIMAL GROWTH: ENDOGENOUS 28.2.2.1 A MODEL OF OPTIMAL ENDOGENOUS GROWTH . . . .050 28.2.2.2 THE CONDITIONS FOR OPTIMAL ENDOGENOUS GROWTH 058 28.2.2.3 OPTIMAL ENDOGENOUS GROWTH: SIULDLE-JRJMT TRAN- SITIONAL DYNAMICS GGO 28.3 OPTIMAL ENDOGENOUS GROWTH IN AN OJKMI CMNUNIY . . . . . . . . 66-1 28.3.1 THE NET BORROWER NATION 669 28.3.1.1 STEADY-STATE STABILITY AND COMPARATIVI DY- NAMICS 071 28.4 RATIONAL EXPECTATIONS AND SADDLE POINT 07 I 28.4.1 INTRODUCTION 67-1 28.4.2 RATIONAL EXPECTATIONS, .SADDLE POINTS, AND OVERSHOOTING 077 28.4.2.1 A DISCRETE-TIME EQUIVALENT 6S2 28.4.3 RATIONAL EXPECTATIONS AND SADDLE POINTS: THE GENERAL CAST? OSI 28.5 INDETERMINACY AND SUNSPOTS NSQ 28.5.1 INDETERMINACY AND FISCAL POLICY OSS 28.5.1.1 FINNS OSS 28.5.1.2 HOUSEHOLDS 089 28.5.1.3 GOVERNMENT OS'J 28.5.1.4 THE OPTIMALITY CONDITIONS 090 28.5.1.5 THE SINGULAR POINT AND ITS NATURE 093 28.6 EXERCISES 097 28.7 REFERENCES 699 BIBLIOGRAPHY 701
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genre_facet	Lehrbuch
id	DE-604.BV035852714
illustrated	Not Illustrated
indexdate	2024-07-20T10:24:36Z
institution	BVB
isbn	9783642038624
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-018710726
oclc_num	436030865
open_access_boolean
owner	DE-473 DE-BY-UBG DE-N2 DE-188
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physical	XXV, 749 S. graf. Darst. 24 cm
publishDate	2009
publishDateSearch	2009
publishDateSort	2009
publisher	Springer
record_format	marc
spelling	Gandolfo, Giancarlo Verfasser (DE-588)170260941 aut Economic dynamics Giancarlo Gandolfo 4. ed. Heidelberg [u.a.] Springer 2009 XXV, 749 S. graf. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Literaturangaben Mathematisches Modell Wirtschaft Economics Mathematical models Economics, Mathematical Statics and dynamics (Social sciences) 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 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3333209&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=018710726&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 Wirtschaft Economics Mathematical models Economics, Mathematical Statics and dynamics (Social sciences) 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 Wirtschaft Economics Mathematical models Economics, Mathematical Statics and dynamics (Social sciences) 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 Wirtschaft Economics Mathematical models Economics, Mathematical Statics and dynamics (Social sciences) Dynamische Makroökonomie Dynamik Wirtschaftsmathematik Differentialgleichung Wirtschaftstheorie Ökonometrie Dynamisches Modell Lehrbuch
url	http://deposit.dnb.de/cgi-bin/dokserv?id=3333209&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=018710726&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT gandolfogiancarlo economicdynamics

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