Economic Dynamics: Phase Diagrams and their Economic Application
by Ronald Shone (Author)
Paperback: 722 pages Publisher: Cambridge University Press; 2 edition (January 13, 2003) Language: English Review
"This book is written primarily for undergraduates and graduates in economics who have a good grasp of mathematics and computing...the chapters are well chosen and the book is an excellent read." Computing Reviews
Book Description
This substantially revised and restructured second edition of an essential textbook presents dynamics and phase diagrams for advanced undergraduate and graduate courses in economic theory and quantitative economics. It offers an integrated analysis of dynamics that includes many more exercises and examples and a more comprehensive range of applications to economic theory. The user-friendly text is supported by a companion website offering a solutions manual and learning tools for teachers, students and researchers.
Contents
Preface to the second edition page xi
Preface to the first edition xiii
PART I Dynamic modelling
1 Introduction 3
1.1 What this book is about 3
1.2 The rise in economic dynamics 5
1.3 Stocks, flows and dimensionality 8
1.4 Nonlinearities, multiple equilibria and local stability 12
1.5 Nonlinearity and chaos 15
1.6 Computer software and economic dynamics 17
1.7 Mathematica and Maple 20
1.8 Structure and features 24
Additional reading 25
2 Continuous dynamic systems 26
2.1 Some definitions 26
2.2 Solutions to first-order linear differential equations 37
2.3 Compound interest 39
2.4 First-order equations and isoclines 41
2.5 Separable functions 45
2.6 Diffusion models 53
2.7 Phase portrait of a single variable 54
2.8 Second-order linear homogeneous equations 59
2.9 Second-order linear nonhomogeneous equations 64
2.10 Linear approximations to nonlinear differential equations 66
2.11 Solving differential equations with Mathematica 70
2.12 Solving differential equations with Maple 73
Appendix 2.1 Plotting direction fields for a single equation
with Mathematica 77
Appendix 2.2 Plotting direction fields for a single equation
with Maple 79
Exercises 80
Additional reading 84
vi Contents
3 Discrete dynamic systems 85
3.1 Classifying discrete dynamic systems 85
3.2 The initial value problem 86
3.3 The cobweb model:an introduction 87
3.4 Equilibrium and stability of discrete dynamic systems 88
3.5 Solving first-order difference equations 99
3.6 Compound interest 105
3.7 Discounting, present value and internal rates of return 108
3.8 Solving second-order difference equations 110
3.9 The logistic equation:discrete version 118
3.10 The multiplier–accelerator model 123
3.11 Linear approximation to discrete nonlinear difference
equations 127
3.12 Solow growth model in discrete time 130
3.13 Solving recursive equations with Mathematica
and Maple 131
Appendix 3.1 Two-cycle logistic equation using Mathematica 135
Appendix 3.2 Two-cycle logistic equation using Maple 137
Exercises 138
Additional reading 141
4 Systems of first-order differential equations 142
4.1 Definitions and autonomous systems 142
4.2 The phase plane, fixed points and stability 145
4.3 Vectors of forces in the phase plane 149
4.4 Matrix specification of autonomous systems 156
4.5 Solutions to the homogeneous differential equation
system:real distinct roots 160
4.6 Solutions with repeating roots 162
4.7 Solutions with complex roots 164
4.8 Nodes, spirals and saddles 166
4.9 Stability/instability and its matrix specification 178
4.10 Limit cycles 179
4.11 Euler’s approximation and differential equations
on a spreadsheet 183
4.12 Solving systems of differential equations with
Mathematica and Maple 186
Appendix 4.1 Parametric plots in the phase plane:
continuous variables 194
Exercises 196
Additional reading 200
5Discr ete systems of equations 201
5.1 Introduction 201
5.2 Basic matrices with Mathematica and Maple 204
5.3 Eigenvalues and eigenvectors 208
Contents vii
5.4 Mathematica and Maple for solving discrete systems 214
5.5 Graphing trajectories of discrete systems 220
5.6 The stability of discrete systems 223
5.7 The phase plane analysis of discrete systems 235
5.8 Internal and external balance 239
5.9 Nonlinear discrete systems 245
Exercises 247
Additional reading 250
6 Optimal control theory 251
6.1 The optimal control problem 251
6.2 The Pontryagin maximum principle:continuous model 252
6.3 The Pontryagin maximum principle:discrete model 259
6.4 Optimal control with discounting 265
6.5 The phase diagram approach to continuous time
control models 270
Exercises 283
Additional reading 285
7 Chaos theory 286
7.1 Introduction 286
7.2 Bifurcations:single-v ariable case 287
7.3 The logistic equation, periodic-doubling bifurcations
and chaos 293
7.4 Feigenbaum’s universal constant 301
7.5 Sarkovskii theorem 302
7.6 Van der Pol equation and Hopf bifurcations 304
7.7 Strange attractors 307
7.8 Rational choice and erratic behaviour 312
7.9 Inventory dynamics under rational expectations 315
Exercises 319
Additional reading 321
PART II Applied economic dynamics
8 Demand and supply models 325
8.1 Introduction 325
8.2 A simple demand and supply model in continuous time 326
8.3 The cobweb model 332
8.4 Cobwebs with Mathematica and Maple 338
8.5 Cobwebs in the phase plane 339
8.6 Cobwebs in two interrelated markets 346
8.7 Demand and supply with stocks 349
8.8 Stability of the competitive equilibrium 353
8.9 The housing market and demographic changes 358
8.10 Chaotic demand and supply 363
viii Contents
Appendix 8.1 Obtaining cobwebs using Mathematica
and Maple 367
Exercises 371
Additional reading 374
9 Dynamic theory of oligopoly 375
9.1 Static model of duopoly 375
9.2 Discrete oligopoly models with output adjusting
completely and instantaneously 377
9.3 Discrete oligopoly models with output not adjusting
completely and instantaneously 389
9.4 Continuous modelling of oligopoly 398
9.5 A nonlinear model of duopolistic competition (R&D) 405
9.6 Schumpeterian dynamics 414
Exercises 419
Additional reading 423
10 Closed economy dynamics 424
10.1 Goods market dynamics 425
10.2 Goods and money market dynamics 429
10.3 IS-LM continuous model:v ersion 1 431
10.4 Trajectories with Mathematica, Maple and Excel 437
10.5 Some important propositions 442
10.6 IS-LM continuous model:v ersion 2 447
10.7 Nonlinear IS-LM model 453
10.8 Tobin–Blanchard model 455
10.9 Conclusion 465
Exercises 467
Additional reading 469
11 The dynamics of inflation and unemployment 470
11.1 The Phillips curve 470
11.2 Two simple models of inflation 472
11.3 Deflationary ‘death spirals’ 484
11.4 A Lucas model with rational expectations 490
11.5 Policy rules 493
11.6 Money, growth and inflation 494
11.7 Cagan model of hyperinflation 500
11.8 Unemployment and job turnover 506
11.9 Wage determination models and the profit function 509
11.10 Labour market dynamics 513
Exercises 516
Additional reading 518
12 Open economy dynamics: sticky price models 519
12.1 The dynamics of a simple expenditure model 519
12.2 The balance of payments and the money supply 524
Contents ix
12.3 Fiscal and monetary expansion under fixed
exchange rates 532
12.4 Fiscal and monetary expansion under flexible
exchange rates 539
12.5 Open economy dynamics under fixed prices and
floating 545
Exercises 551
Additional reading 552
13 Open economy dynamics: flexible price models 553
13.1 A simplified Dornbusch model 554
13.2 The Dornbusch model 559
13.3 The Dornbusch model:capital immobility 564
13.4 The Dornbusch model under perfect foresight 567
13.5 Announcement effects 573
13.6 Resource discovery and the exchange rate 581
13.7 The monetarist model 586
Exercises 589
Additional reading 592
14 Population models 593
14.1 Malthusian population growth 593
14.2 The logistic curve 596
14.3 An alternative interpretation 601
14.4 Multispecies population models:geometric analysis 603
14.5 Multispecies population models:mathematical analysis 619
14.6 Age classes and projection matrices 626
Appendix 14.1 Computing a and b for the logistic equation
using Mathematica 630
Appendix 14.2 Using Maple to compute a and b for the
logistic equation 631
Appendix 14.3 Multispecies modelling with Mathematica
and Maple 632
Exercises 634
Additional reading 637
15The dynamics of fisheries 638
15.1 Biological growth curve of a fishery 638
15.2 Harvesting function 644
15.3 Industry profits and free access 647
15.4 The dynamics of open access fishery 650
15.5 The dynamics of open access fishery:a numerical
example 654
15.6 The fisheries control problem 658
15.7 Schooling fishery 661
15.8 Harvesting and age classes 669
Exercises 673
Additional reading 676
Answers to selected exercises 677
Bibliography 688
Author index 697
Subject index 700 [此贴子已经被作者于2007-11-9 21:37:20编辑过]
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