New Quantitative Techniques for Economic Analysis

List of Contributors

Preface

Part I Models and Reality

Mathematical Methods for Economic Analysis: A Biased Review


1. Historical Background


2. Chaos and Order


3. A Reappraisal of Established Techniques


4. Conclusions

References

Dynamic Econometric Models: A System-Theoretic Critique


1. Background


2. Definition of "Model" in System Theory


3. Some Properties of Models


4. Results of Realization Theory


5. Conclusions concerning Stage (1)


6. Stage (2): Parametrization


7. Conclusion

References

Economics: Past and Future


1. Introduction: The Case of Economics


2. The Positivist Approach to Economics


3. The Neopositivist Approach to Economics


4. Economics Between Ideology and Praxeology


5. Physical Systems and the Economic System


6. The Cognitive Process by Which the Economic System Is Envisaged


7. The Ideological Prejudices (Fallacies) of the Neoclassical Definition of the Economic System


8. How Can We Assess Preanalytic Knowledge?


9. Some Fundamental Properties of the Economic and the Social Systems


10. Connections Between the Social and Economic Systems


11. Equilibrium Model and Economic Theory


12. The Normal Structure and the Law of Motion of the Economy


13. Efficiency and Equilibrium


14. Aggregation in Economic Models


15. Normative Models in Economics


16. Individual and Social Choices


17. Theory and Observation


18. Diachronic Stability and Historical Stability


19. Catastrophe Theory and Structural Changes in the Economic System


20. The Role of Expectations and Some Possible Discontinuities in the Economic Process


21. Quantitative Changes and Evolution


22. Knowledge and Behavior

References

Part II New Quantitative Techniques at Work

Ergodicity for Economists


1. Introduction


2. A Two-Dimensional Mapping Model Exhibiting Chaotic Behavior


3. Integrable Systems


4. The Transition from Integrable to Chaotic Behavior in Conservative Systems


5. Ergodic and Mixing Systems and C Systems


6. K Systems and B Systems


7. Statistical Description of Chaotic Systems


8. Closing Remarks

References

Catastrophe Theory in Banking and Finance


1. Introduction


2. Catastrophe Theory


3. Catastrophic Bank Failure


4. Conclusions and Summary

References

Order by Fluctuation and the Urban System


1. Introduction


2. Interurban Dynamics


3. Conclusion

References

The Qualitative Analysis of Nonlinear Dynamic Economic Systems by Structural Methods


1. Introduction


2. Aspects of Systems Structure


3. The Nature of Nonlinear Oscillatory Behavior


4. Economic Models

References

Part III A Reappraisal of Established Methods

Optimal Consumption Plans—A Dynamic Programming Approach


1. Consumption Planning under Certainty


2. Section 2


3. Section 3


4. Section 4


5. Section 5


6. Section 6


7. Section 7


8. Section 8


9. Risk


10. Section 10


11. Section 11

References

Generalized Separation Property for Dynamic Portfolio Models


1. Introduction


2. Revised Merton Model


3. A Complete Separation Theorem for Alternative Risks

Appendix. A Brief Outline of Stochastic Control

References

Hierarchical Control and Coordination in Dynamical Systems


1. Introduction


2. Hierarchical Optimization by Price Coordination


3. Price Coordination and Optimization of Complex Systems with Inventory Couplings


4. Two-Level Control Structure with Price Coordination for Systems with Inventory Couplings

References

Discontinuous Solutions in n-Person Games


1. Introduction


2. Weighted Majority Games


3. The Case of Three-Person Games


4. Constant-Power Sets


5. Share Trading


6. The Generating Algorithm


7. Further Outstanding Problems


8. Conclusions

References

Part IV Special Problems

Elementary Properties of Nonnegative Matrices

References

Optimal Control of Econometric Models: Some Experimental Results for the Italian Monetary Sector


1. Introduction


2. The Computational Scheme


3. Experimental Results

Appendix

References

Stability and Instability in a Two-Dimensional Dynamical System: A Mathematical Approach to Kaldor's Theory of the Trade Cycle


1. Section 1


2. Section 2


3. Section 3


4. Section 4


5. Summary

References

Competitive Equilibrium and Indivisible Commodities


1. Introduction


2. The Problem of the Existence of a Competitive Equilibrium in an Economy with Unique (or Indivisible) Commodities


3. Competitive Pseudoequilibrium in an Economy with Unique (or Indivisible) Commodities

References

New Results for a Competitive Equilibrium

References