Economic Dynamics

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ISBN: 9780521816847 | 052181684X
Cover: Hardcover
Copyright: 1/13/2003

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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. First Edition Hb (1997): 0-521-47446-9 First Edition Pb (1997): 0-521-47973-8

Preface to the second edition

Preface to the first edition

xiii

PART I Dynamic modelling

Introduction

(23)

What this book is about

(2)

The rise in economic dynamics

(3)

Stocks, flows and dimensionality

(4)

Nonlinearities, multiple equilibria and local stability

(3)

Nonlinearity and chaos

(2)

Computer software and economic dynamics

(3)

Mathematica and Maple

(4)

Structure and features

(2)

Additional reading

(1)

Continuous dynamic systems

(59)

Some definitions

(11)

Solutions to first-order linear differential equations

(2)

Compound interest

(2)

First-order equations and isoclines

(4)

Separable functions

(8)

Diffusion models

(1)

Phase portrait of a single variable

(5)

Second-order linear homogeneous equations

(5)

Second-order linear nonhomogeneous equations

(2)

Linear approximations to nonlinear differential equations

(4)

Solving differential equations with Mathematica

(3)

Solving differential equations with Maple

(12)

Appendix 2.1 Plotting direction fields for a single equation with Mathematica

(2)

Appendix 2.2 Plotting direction fields for a single equation with Maple

(1)

Exercises

(4)

Additional reading

(1)

Discrete dynamic systems

(57)

Classifying discrete dynamic systems

(1)

The initial value problem

(1)

The cobweb model: an introduction

(1)

Equilibrium and stability of discrete dynamic systems

(11)

Solving first-order difference equations

(6)

Compound interest

105

(3)

Discounting, present value and internal rates of return

108

(2)

Solving second-order difference equations

110

(8)

The logistic equation: discrete version

118

(5)

The multiplier-accelerator model

123

(4)

Linear approximation to discrete nonlinear difference equations

127

(3)

Solow growth model in discrete time

130

(1)

Solving recursive equations with Mathematica and Maple

131

(11)

Appendix 3.1 Two-cycle logistic equation using Mathematica

135

(2)

Appendix 3.2 Two-cycle logistic equation using Maple

137

(1)

Exercises

138

(3)

Additional reading

141

(1)

Systems of first-order differential equations

142

(59)

Definitions and autonomous systems

142

(3)

The phase plane, fixed points and stability

145

(4)

Vectors of forces in the phase plane

149

(7)

Matrix specification of autonomous systems

156

(4)

Solutions to the homogeneous differential equation system: real distinct roots

160

(2)

Solutions with repeating roots

162

(2)

Solutions with complex roots

164

(2)

Nodes, spirals and saddles

166

(12)

Stability/instability and its matrix specification

178

(1)

Limit cycles

179

(4)

Euler's approximation and differential equations on a spreadsheet

183

(3)

Solving systems of differential equations with Mathematica and Maple

186

(15)

Appendix 4.1 Parametric plots in the phase plane: continuous variables

194

(2)

Exercises

196

(4)

Additional reading

200

(1)

Discrete systems of equations

201

(50)

Introduction

201

(3)

Basic matrices with Mathematica and Maple

204

(4)

Eigenvalues and eigenvectors

208

(6)

Mathematica and Maple for solving discrete systems

214

(6)

Graphing trajectories of discrete systems

220

(3)

The stability of discrete systems

223

(12)

The phase plane analysis of discrete systems

235

(4)

Internal and external balance

239

(6)

Nonlinear discrete systems

245

(6)

Exercises

247

(3)

Additional reading

250

(1)

Optimal control theory

251

(35)

The optimal control problem

251

(1)

The Pontryagin maximum principle: continuous model

252

(7)

The Pontryagin maximum principle: discrete model

259

(6)

Optimal control with discounting

265

(5)

The phase diagram approach to continuous time control models

270

(16)

Exercises

283

(2)

Additional reading

285

(1)

Chaos theory

286

(39)

Introduction

286

(1)

Bifurcations: single-variable case

287

(6)

The logistic equation, periodic-doubling bifurcations and chaos

293

(8)

Feigenbaum's universal constant

301

(1)

Sarkovskii theorem

302

(2)

Van der Pol equation and Hopf bifurcations

304

(3)

Strange attractors

307

(5)

Rational choice and erratic behaviour

312

(3)

Inventory dynamics under rational expectations

315

(10)

Exercises

319

(2)

Additional reading

321

(4)

PART II Applied economic dynamics

Demand and supply models

325

(50)

Introduction

325

(1)

A simple demand and supply model in continuous time

326

(6)

The cobweb model

332

(6)

Cobwebs with Mathematica and Maple

338

(1)

Cobwebs in the phase plane

339

(7)

Cobwebs in two interrelated markets

346

(3)

Demand and supply with stocks

349

(4)

Stability of the competitive equilibrium

353

(5)

The housing market and demographic changes

358

(5)

Chaotic demand and supply

363

(12)

Appendix 8.1 Obtaining cobwebs using Mathematica and Maple

367

(4)

Exercises

371

(3)

Additional reading

374

(1)

Dynamic theory of oligopoly

375

(49)

Static model of duopoly

375

(2)

Discrete oligopoly models with output adjusting completely and instantaneously

377

(12)

Discrete oligopoly models with output not adjusting completely and instantaneously

389

(9)

Continuous modelling of oligopoly

398

(7)

A nonlinear model of duopolistic competition (R&D)

405

(9)

Schumpeterian dynamics

414

(10)

Exercises

419

(4)

Additional reading

423

(1)

Closed economy dynamics

424

(46)

Goods market dynamics

425

(4)

Goods and money market dynamics

429

(2)

IS-LM continuous model: version 1

431

(6)

Trajectories with Mathematica, Maple and Excel

437

(5)

Some important propositions

442

(5)

IS-LM continuous model: version 2

447

(6)

Nonlinear IS-LM model

453

(2)

Tobin-Blanchard model

455

(10)

Conclusion

465

(5)

Exercises

467

(2)

Additional reading

469

(1)

The dynamics of inflation and unemployment

470

(49)

The Phillips curve

470

(2)

Two simple models of inflation

472

(12)

Deflationary `death spirals'

484

(6)

A Lucas model with rational expectations

490

(3)

Policy rules

493

(1)

Money, growth and inflation

494

(6)

Cagan model of hyperinflation

500

(6)

Unemployment and job turnover

506

(3)

Wage determination models and the profit function

509

(4)

Labour market dynamics

513

(6)

Exercises

516

(2)

Additional reading

518

(1)

Open economy dynamics: sticky price models

519

(34)

The dynamics of a simple expenditure model

519

(5)

The balance of payments and the money supply

524

(8)

Fiscal and monetary expansion under fixed exchange rates

532

(7)

Fiscal and monetary expansion under flexible exchange rates

539

(6)

Open economy dynamics under fixed prices and floating

545

(8)

Exercises

551

(1)

Additional reading

552

(1)

Open economy dynamics: flexible price models

553

(40)

A simplified Dornbusch model

554

(5)

The Dornbusch model

559

(5)

The Dornbusch model: capital immobility

564

(3)

The Dornbusch model under perfect foresight

567

(6)

Announcement effects

573

(8)

Resource discovery and the exchange rate

581

(5)

The monetarist model

586

(7)

Exercises

589

(3)

Additional reading

592

(1)

Population models

593

(45)

Malthusian population growth

593

(3)

The logistic curve

596

(5)

An alternative interpretation

601

(2)

Multispecies population models: geometric analysis

603

(16)

Multispecies population models: mathematical analysis

619

(7)

Age classes and projection matrices

626

(12)

Appendix 14.1 Computing a and b for the logistic equation using Mathematica

630

(1)

Appendix 14.2 Using Maple to compute a and b for the logistic equation

631

(1)

Appendix 14.3 Multispecies modelling with Mathematica and Maple

632

(2)

Exercises

634

(3)

Additional reading

637

(1)

The dynamics of fisheries

638

(39)

Biological growth curve of a fishery

638

(6)

Harvesting function

644

(3)

Industry profits and free access

647

(3)

The dynamics of open access fishery

650

(4)

The dynamics of open access fishery: a numerical example

654

(4)

The fisheries control problem

658

(3)

Schooling fishery

661

(8)

Harvesting and age classes

669

(8)

Exercises

673

(3)

Additional reading

676

(1)

Answers to selected exercises

677

(11)

Bibliography

688

(9)

Author index

697

(3)

Subject index

700

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Economic Dynamics

Summary

Author Biography

Table of Contents

Supplemental Materials