Economic Evolution and Equilibrium (eBook)

Contents 5
1 General Introduction 9
2 Notations and Mathematical Preliminaries 20
Notations 20
Mathematical Preliminaries 22
Conceptualization and Definition of Evolutions of Economies in Four General Equilibrium Frameworks 32
3 Introduction to Part I 33
4 Evolutions in the Traditional Walrasian Exchange Equilibrium Framework 35
4.1 Evolutions Based on the Model of an Exchange Economy by Arrow and Hahn 36
4.2 Evolutions Based on Dierker’s Version of the Model of an Exchange Economy 40
4.3 Evolutions Based on a Model of a Large Exchange Economy 43
5 Evolutions in an Exchange Equilibrium Framework Without Walras’ Law and Homogeneity 47
5.1 Evolutions Based on a Model of an Exchange Economy Without Walras’ Law and Homogeneity 48
5.2 Evolutions Based on a Model With Weakened Boundary Assumptions 60
6 Evolutions in a General Equilibrium Framework With Production, Taxes, and Subsidies 66
6.1 Evolutions Based on a General Equilibrium Model With Production and Taxes 67
6.2 Evolutions Based on a General Equilibrium Model With Production, Taxes, and Subsidies 73
7 Evolutions in the Temporary Fixprice Equilibrium Framework 76
7.1 Evolutions Based on a Quantity Constrained Micromodel With Effective Demand `a la Benassy 77
7.2 Evolutions Based on a Quantity Constrained Multi- Sectoral Model 82
8 Conclusions 92
Formal Analysis 93
9 Introduction to Part II 94
10 Near-Equilibrium Paths 97
10.1 Existence of Joining Equilibrium Components and of Near- Equilibrium Paths for Each Type of Evolution From Part I 98
10.2 A Criterion for Identifying Points on Joining Equilibrium Components 105
11 Equilibrium Paths 107
11.1 Approximating Evolutions of Exchange Economies With Nice Equilibrium Paths Based on Dierker’s Model from Section 4.2 108
11.2 Approximating Evolutions With Equilibrium Paths for the Other Basic Models From Part I 122
11.3 A Strong Connectedness Result for the Graphs of the Equilibrium Correspondences of the Basic Models From Part I 128
12 Economic Refinements of the Notion of an Evolution of Economies 143
12.1 Course Evolutions and Connection Evolutions 144
12.2 New and Old Commodities 151
13 The Structure of the Equilibrium Price Set of an Evolution of Exchange Economies 156
14 Comparison With Related Results in the Literature 161
14.1 Studies of the Graph of the Walras Correspondence 161
14.2 The Regular Approach 164
15 Conclusions 175
Economic Analysis 177
16 Introduction to Part III 178
17 Applications of the Analytical Results From Part II in the Economist’s Laboratory 181
17.1 Extending the Path-Following Method to the Computation of Equilibria of Non- Regular Economies 182
17.2 Generalizing Comparative Statics to Economies With Multiple Equilibria 185
18 The Method of Kinetic Analysis of Evolving Economies in Historical Time 186
19 Evolving Economies in Historical Time 195
19.1 Evolving Economies in Discrete Historical Time 199
19.2 Alternative Models of Evolving Economies in Continuous Historical Time 200
19.3 Time Consuming Equilibrium Adjustment Processes 210
19.4 Frictionless Tuning of Coordination Signals in Evolving Economies in Continuous Historical Time 213
20 Conclusions 219
General Conclusions and Outlook 221
21 General Conclusions and Outlook 222
22 Appendix A1 225
Proof of Theorem 11.8 225
23 Appendix B 235
Proof of Theorem 13.1 235
Proof of Corollary 13.2 251
Proof of Proposition 13.4 251
24 Appendix C 252
Proof of Proposition 14.3 252
References 255
Subject Index 262