Economic Evolution and Equilibrium

by Lehmann-Waffenschmidt, Marco

• ISBN13: 9783540686620
• ISBN10: 3540686622
• Edition: 1st
• Format: Paperback
• Copyright: 2007-05-04
• Publisher: Springer Nature

Summary

This work uses various model frameworks to study the evolution of equilibria in an open loop evolving economy in which the model characteristics evolve without any directional restrictions except for continuity. Applying mathematical methods, it is shown that equilibria can always be adapted in a piecewise gradual, non bang-bang way. Furthermore, the analysis provides a complete characterization of the structure of the equilibrium price set of evolving exchange economies. The results allow to derive policy implications for a gradual, frictionless tuning of equilibrium values for open loop evolving economies. The analysis is innovative in both its approach and its results. It contributes to bridging the gap between the traditional static, closed loop, dynamic equilibrium approach and the idea of open loop evolution which has become an attractive concept in economics in recent years.

Table of Contents

General Introduction	p. 1
Notations and Mathematical Preliminaries	p. 13
Conceptualization and Definition of Evolutions of Economies in Four General Equilibrium Frameworks
Introduction to Part I	p. 27
Evolutions in the Traditional Walrasian Exchange Equilibrium Framework	p. 29
Evolutions Based on the Model of an Exchange Economy by Arrow and Hahn	p. 30
Evolutions Based on Dierker's Version of the Model of an Exchange Economy	p. 34
Evolutions Based on a Model of a Large Exchange Economy	p. 37
Evolutions in an Exchange Equilibrium Framework Without Walras' Law and Homogeneity	p. 41
Evolutions Based on a Model of an Exchange Economy Without Walras' Law and Homogeneity	p. 42
Evolutions Based on a Model With Weakened Boundary Assumptions	p. 54
Evolutions in a General Equilibrium Framework With Production, Taxes, and Subsidies	p. 61
Evolutions Based on a General Equilibrium Model With Production and Taxes	p. 62
Evolutions Based on a General Equilibrium Model With Production, Taxes, and Subsidies	p. 68
Evolutions in the Temporary Fixprice Equilibrium Framework	p. 71
Evolutions Based on a Quantity Constrained Micromodel With Effective Demand à la Benassy	p. 72
Evolutions Based on a Quantity Constrained Multi-Sectoral Model	p. 77
Conclusions	p. 87
Formal Analysis
Introduction to Part II	p. 91
Near-Equilibrium Paths	p. 95
Existence of Joining Equilibrium Components and of Near-Equilibrium Paths for Each Type of Evolution From Part I	p. 96
A Criterion for Identifying Points on Joining Equilibrium Components	p. 103
Equilibrium Paths	p. 105
Approximating Evolutions of Exchange Economies With Nice Equilibrium Paths Based on Dierker's Model from Section 4.2	p. 106
Polynomial Approximating Exchange Evolutions	p. 107
Piecewise Linear Approximating Exchange Evolutions	p. 115
Approximating Evolutions With Equilibrium Paths for the Other Basic Models From Part I	p. 120
A Strong Connectedness Result for the Graphs of the Equilibrium Correspondences of the Basic Models From Part I	p. 126
Economic Refinements of the Notion of an Evolution of Economies	p. 141
Course Evolutions and Connection Evolutions	p. 142
New and Old Commodities	p. 149
The Structure of the Equilibrium Price Set of an Evolution of Exchange Economies	p. 155
Comparison With Related Results in the Literature	p. 161
Studies of the Graph of the Walras Correspondence	p. 161
The Regular Approach	p. 164
Conclusions	p. 175
Economic Analysis
Introduction to Part III	p. 179
Applications of the Analytical Results From Part II in the Economist's Laboratory	p. 183
Extending the Path-Following Method to the Computation of Equilibria of Non-Regular Economies	p. 184
Generalizing Comparative Statics to Economies With Multiple Equilibria	p. 187
The Method of Kinetic Analysis of Evolving Economies in Historical Time	p. 189
Evolving Economies in Historical Time	p. 199
Evolving Economies in Discrete Historical Time	p. 203
Alternative Models of Evolving Economies in Continuous Historical Time	p. 204
Flow Commodity Models of Piecewise Continuously Balanced Evolving Economies	p. 204
The Frequency Model of a Piecewise Continuously Balanced Evolving Economy	p. 210
Time Consuming Equilibrium Adjustment Processes	p. 214
Frictionless Tuning of Coordination Signals in Evolving Economies in Continuous Historical Time	p. 217
General Conceptualization	p. 217
Frictionless Tuning in the Quantity Constrained Multi-Sectoral Model From Chapter 4	p. 221
Frictionless Tuning in the General Equilibrium Framework With Production, Taxes, and Subsidies From Chapter 3	p. 222
Conclusions	p. 223
General Conclusions and Outlook
General Conclusions and Outlook	p. 227
Appendix A	p. 231
Appendix B	p. 241
Appendix C	p. 259
References	p. 263
Subject Index	p. 271
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