Synergetic Economics: Time and Change in Nonlinear Economics

ISBN-13: 9783642759116 / Angielski / Miękka / 2011 / 246 str.

Wei-Bin Zhang

Opis

Synergetic Economics presents a new advance in analytical economics. It deals with problems related to time and change in economic systems, including complex aspects, such as the effects of nonlinearity, instability, bifurcation and chaos in economic evolution. The author argues that economic systems may run through a hierarchy of instabilities in which more and more structural patterns evolve. Such instabilities are caused by changes in the external parameters of the system. They may lead to new spatial-temporal patterns of the system. A number of explicit examples are provided to show how such behavior can occur in various dynamic economic systems. Analytical methods are also presented to cope with nonlinear problems. Of particular interest are sudden (structural) changes, the existence of regular and irregular oscillations, the role of random factors in economic evolution, and the effects of time scales and rates of adjustment of economic variables in economic analysis. The author carefully examines the implications of nonlinear phenomena for decision making, and for economic development in general.

Spis treści

1. Introduction.- 2. Time and Change in Economics.- 2.1 Economic Evolution — An Introduction.- 2.2 Equilibrium Theories in Economic Analysis.- 2.3 Dynamic Theories in Economics.- 2.4 Samuelson’s Correspondence Principle and Its Limitations.- 2.5 Instabilities in Economic Analysis.- 3. Mathematical Aspects of Dynamic Systems.- 3.1 Dynamics and Equilibrium.- 3.2 Classifications of Two-Dimensional Differential Equations.- 3.3 The Principle of Linearized Stability.- 3.4 Lyapunov’s Direct Method.- 3.5 Structural Stability.- 3.6 Conservative Systems.- 3.7 Bifurcation Theory.- 3.8 Singularity Theory.- 3.9 Catastrophe Theory.- Appendix: Remarks on Bifurcation Theory.- 4. Multiple Equilibria and Structural Changes in Economic Systems.- 4.1 Catastrophe Theory and Comparative Statics Analysis.- 4.2 Modeling Regional Dynamics.- 4.3 Some Examples of Structural Changes.- 4.3.1 Business Cycles in the Kaldor Model.- 4.3.2 Resource Management.- 4.3.3 Dynamic Transportation Modal Choice and Bifurcation.- 4.3.4 Multiple Equilibria in Wilson’s Retail Model.- 4.4 A Bifurcation Analysis for an Economic Growth Model.- 4.5 Singularity Theory in Economic Analysis.- 4.6 Remarks.- 5. Economic Cycles.- 5.1 Theories of Economic Cycles.- 5.2 Some Mathematical Results Related to Limit Cycles.- 5.2.1 The Poincaré-Bendixson Theorem and Its Applications to Economics.- 5.2.2 The Hopf Bifurcation Theorem.- 5.3 The Simplified Keynesian Business Cycle Model.- 5.4 Non-equilibrium in a Disequilibrium Model.- 5.5 Monetary Cycles in the Generalized Tobin Model.- 5.6 Oscillations in van der Ploeg’s Hybrid Growth Model.- 5.7 Periodic Optimal Employment Policy.- 5.8 Optimal Economic Growth Associated with Endogenous Fluctuations.- 5.9 Remarks on Possible Further Bifurcations from Limit Cycles.- 5.10 Competitive Business Cycles in an Overlapping Generations Economy — A Discrete Model.- 6. Economic Chaos in Deterministic Systems.- 6.1 Chaos in Deterministic Systems.- 6.2 Economic Chaos in a Discrete System.- 6.3 Aperiodic Optimal Economic Growth.- 6.4 Urban Dynamics — The Lorenz System.- 6.5 Chaos in an International Economic Model.- 6.6 Chaos and Economic Forecasting.- 6.7 Remarks.- Appendix: Some Criteria for Distinguishing Different Attractors.- A.1 The Lyapunov Exponents for Differential Equations.- A.2 The Lyapunov Exponents for Discrete Maps.- A.3 The Signal, Power Spectrum, Autocorrelation Function and Poincaré Map.- 7. Stochastic Processes and Economic Evolution.- 7.1 Random Processes and Economic Evolution.- 7.2 Stochastic Processes — An Introduction.- 7.2.1 Some Concepts in Probability Theory.- 7.2.2 Stochastic Processes.- 7.3 Birth-Death Processes and the Master Equation.- 7.4 A Non-equilibrium Model of the Schumpeter Clock.- 7.5 Effects of Noise on the Nonlinear Stochastic Systems Close to Critical Points.- 7.6 Effects of Random Environment on a Two-Dimensional Deterministic System Near Critical Points.- 7.7 Conclusions.- 8. Urban Pattern Formation Process — Stability, Structural Changes and Chaos.- 8.1 Continuous Spatial Economics and Description of Urban Pattern Formation.- 8.2 The Implications of Structural Stability in the Two-Dimensional Economy.- 83 Economic Cycles in Puu’s Spatial Multiplier-Accelerator Business Model.- 8.4 Spatial Diffusional Effects as a Stabilizer.- 8.5 Separation and Coexistence of Residents.- 8.6 Long-Term Traveling-Wave Urban Pattern.- 8.7 Instabilities and Urban Pattern Formation.- Appendix: Structural Changes in Two Pattern Formation Models.- A.1 A Model for Morphogenesis.- A.2 The Brusselator.- 9. The Haken Slaving Principle and Time Scale in Economic Analysis.- 9.1 The Haken Slaving Principle.- 9.2 The Center Manifold Theorem.- 9.3 Singular Perturbations.- 9.4 Fast Variable Versus Slow Variable in Economic Analysis.- 9.5 The Time Scale in Economic Analysis.- 9.6 Another Problem — Understanding a Dynamic Man.- Appendix: The Slaving Principle for Stochastic Differential Equations.- 10. Implications of Synergetic Economics.- 10.1 Synergetic Economics and Its Relations to Synergetics.- 10.2 Relations to Traditional Dynamic Economics.- 10.3 Competitive and Planned Economies and Synergetic Economics.- 10.4 Implications for Developed and Developing Economies.- 10.5 Chance and Necessity in Economic Life.- 10.6 Policy Decision in a Chaotic World.- 10.7 Relations Between Microeconomics and Macroeconomics.- 11. Conclusions and Prospects for Further Research.- References.

O autorze

Synergetic Economics presents a new advance in economic analysis. The author deals with problems related to time and change in economic evolution in terms of nonlinear interactions, instability, and complexity. Analytical methods are presented to cope with nonlinear problems.