Economic dynamics and general equilibrium: time and uncertainty ; with 26 tables
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2004
|
| Subjects: | |
| Online Access: | Table of contents Inhaltsverzeichnis |
| Physical Description: | XIV, 396 S. graph. Darst. |
| ISBN: | 3540002650 |
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| 100 | 1 | |a Borglin, Anders |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Economic dynamics and general equilibrium |b time and uncertainty ; with 26 tables |c Anders Borglin |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2004 | |
| 300 | |a XIV, 396 S. |b graph. Darst. | ||
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| 650 | 4 | |a Mathematisches Modell | |
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| adam_text | Contents
1 CONSUMERS AND ECONOMIES A REVIEW 1
Introduction 1
1.1 Consumers 2
Maintained Assumptions on Consumers 3
Implications of the Maintained Assumptions 5
Solutions to the Consumer Problem 8
1.2 Walras Equilibrium and Welfare Economics 13
The First and Second Theorem of Welfare Economics 15
Summary 19
Exercises 20
2 ECONOMIES OVER TIME 25
Introduction 25
2.1 Goods and Commodities 28
2.2 A Market for all Commodities at Date 0 30
2.3 A Spot Market at Each Date and a Market for Spot
Income at Date 0 34
2.4 The Spot Market Demand Function 38
2.5 The Indirect Utility Function 43
Properties of the Indirect Utility Function 44
2.6 Decomposition of the Consumer Problem 51
2.7 Spot Market Equilibria Relative to a Set of Income Transfers 56
2.8 Marginal Analysis 60
Pareto Optimal Spot Market Equilibrium Allocations 66
Summary 68
Exercises 68
x CONTENTS
3 ASSETS AND INCOME TRANSFERS 73
Introduction 73
3.1 Nominal Assets 75
Complete and Incomplete Asset Markets 80
3.2 Arbitrage and Date 0 Prices of Income 83
Determinacy of Discount Factors* 90
3.3 Real Assets 92
3.4 Assets Traded at Future Dates 96
3.5 Radner Equilibrium 98
3.6 Applications to Economies with Production 102
Economy with Assets and Production 103
Radner Equilibrium with a Given Production Plan . . 106
The Modigliani Miller Theorem 106
Agreement about Choice of Production Plan 109
3.7 Money and the Existence of a Monetary Equilibrium . . 114
Summary 117
Exercises 118
4 ECONOMIES WITH UNCERTAINTY 125
Introduction 125
4.1 Different Kinds of Uncertainty 127
4.2 Contracts for Contingent Delivery 127
Two Dates and Uncertainty 129
4.3 Preferences and Beliefs 131
4.4 Analogy to Economies over Time. Terminology in Case of
Uncertainty 135
4.5 Increasing Information over Time 140
Partitions and Information 140
Event Trees 142
Event Tree; a General Definition* 145
4.6 Consumption Plans and Information 147
First Description 147
Second Description* 149
4.7 Walras Equilibrium 151
Equilibrium with Complete Contingent Markets .... 152
CONTENTS xi
4.8 Assets, State Prices and Arbitrage 154
Frequent Trading 156
4.9 Radner Equilibrium 161
Summary 164
Exercises 165
5 EXISTENCE AND DETERMINACY 177
Introduction 177
5.1 Real Assets and Existence of a Radner Equilibrium . . . 179
An Example of Non Existence 179
5.2 Existence of a Pseudo Equilibrium 185
The Coincidence of Pseudo Equilibria and Radner Equi¬
libria* 186
A General Existence Theorem. Real Assets* 189
A Robust Counterexample to Existence. Real Assets . 189
5.3 Nominal Assets and Existence of a Radner Equilibrium . 192
5.4 Indeterminacy of Radner Equilibrium with Nominal As¬
sets 193
An Example of Indeterminacy with Nominal Assets . 194
A General Theorem on Indeterminacy. Nominal Assets* 197
Consequences of Indeterminacy 198
Summary 200
Exercises 200
6 OPTIMALITY AND INCOMPLETE MARKETS 207
Introduction 207
6.1 Hart s Example of Pareto Domination 208
6.2 Abundance of Non optimal Equilibrium Allocations . . . 212
6.3 Welfare Properties of Spot Market Equilibria 214
Summary 217
A Summary of Results for Economies with Com¬
plete or Incomplete Markets 218
Exercises 219
xii CONTENTS
7 OVERLAPPING GENERATIONS ECONOMIES 221
Introduction 221
7.1 Structure and Assumptions 222
Allocations and Reallocations 224
7.2 Expectations and Equilibrium 226
Expectations 227
Equilibrium 229
Forward Markets 234
Summary 237
Exercises 237
8 OPTIMAL ALLOCATIONS IN OG ECONOMIES 241
Introduction 241
8.1 Notions of Optimality 243
8.2 The Theorems of Welfare Economics 247
8.3 Reduced Models 251
Allocations and Reduced Models 251
Optimality and Efficiency 255
Characterization of Efficient Reduced Models 256
8.4 Parametric Reduced Models 261
Reduced Model with Hyperbola 262
8.5 Characterization of Optimal Allocations 265
Equilibria and Strongly Optimal Allocations 268
Summary 268
Exercises 269
9 STATIONARY OG ECONOMIES 273
Introduction 273
9.1 Definition of a Stationary OG Economy 275
9.2 Demand 276
Relative Price and Demand 276
Properties of the Demand Function 277
9.3 Equilibrium and Relative Prices 283
9.4 Steady State Equilibria 287
9.5 Optimality for Stationary Economies 289
CONTENTS xiii
Support Functions 290
Approximation of Upper Contour Sets 298
Equilibrium Prices and Optimal Allocations 302
9.6 Summary 304
9.7 Exercises 305
10 GLOBAL DYNAMICS: TURNPIKE EQUILIBRIA 309
Introduction 309
10.1 The Equilibrium Equation and the Equilibrium Locus . . 311
The Equilibrium Equation 311
The Equilibrium Locus 312
10.2 Indeterminacy of Equilibrium 322
10.3 Turnpike Equilibria 324
Equilibria for Economies Close to
No Trade Economies 327
Characterization of Turnpike Equilibria 327
Summary 329
Exercises 329
11 GLOBAL DYNAMICS: CYCLICAL EQUILIBRIA 333
Introduction 333
11.1 Cycles 335
Existence of Cycles 335
Properties of Excess Demand and Dynamics 339
11.2 Sunspot Equilibrium 342
Uncertainty and the Maintained Assumptions 343
Demand under Uncertainty 346
Relating Demand under Certainty and under Uncertainty350
Existence of a Sunspot Equilibrium 352
11.3 Endowments, Cycles and Sunspot Equilibria 358
An Example 360
Summary 361
Exercises 361
xiv CONTENTS
APPENDIX 365
Appendix A Some Results from Calculus 365
Appendix B Quadratic Forms and Bordered Matrices 367
Appendix C Separation Theorems and Farkas Lemma .... 369
Appendix D Dynamical Systems 375
BIBLIOGRAPHY 381
INDEX 387
LIST OF NOTATION 396
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| language | English |
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| spelling | Borglin, Anders Verfasser aut Economic dynamics and general equilibrium time and uncertainty ; with 26 tables Anders Borglin Berlin [u.a.] Springer 2004 XIV, 396 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematisches Modell Equilibrium (Economics) -- Mathematical models Statics and dynamics (Social sciences) -- Mathematical models Time and economic reations -- Mathematical models Uncertainty -- Mathematical models Allgemeines Gleichgewichtsmodell (DE-588)4210294-7 gnd rswk-swf Dynamische Makroökonomie (DE-588)4200428-7 gnd rswk-swf Dynamische Makroökonomie (DE-588)4200428-7 s Allgemeines Gleichgewichtsmodell (DE-588)4210294-7 s DE-604 http://www.loc.gov/catdir/toc/fy044/2003069143.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010657928&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Borglin, Anders Economic dynamics and general equilibrium time and uncertainty ; with 26 tables Mathematisches Modell Equilibrium (Economics) -- Mathematical models Statics and dynamics (Social sciences) -- Mathematical models Time and economic reations -- Mathematical models Uncertainty -- Mathematical models Allgemeines Gleichgewichtsmodell (DE-588)4210294-7 gnd Dynamische Makroökonomie (DE-588)4200428-7 gnd |
| subject_GND | (DE-588)4210294-7 (DE-588)4200428-7 |
| title | Economic dynamics and general equilibrium time and uncertainty ; with 26 tables |
| title_auth | Economic dynamics and general equilibrium time and uncertainty ; with 26 tables |
| title_exact_search | Economic dynamics and general equilibrium time and uncertainty ; with 26 tables |
| title_full | Economic dynamics and general equilibrium time and uncertainty ; with 26 tables Anders Borglin |
| title_fullStr | Economic dynamics and general equilibrium time and uncertainty ; with 26 tables Anders Borglin |
| title_full_unstemmed | Economic dynamics and general equilibrium time and uncertainty ; with 26 tables Anders Borglin |
| title_short | Economic dynamics and general equilibrium |
| title_sort | economic dynamics and general equilibrium time and uncertainty with 26 tables |
| title_sub | time and uncertainty ; with 26 tables |
| topic | Mathematisches Modell Equilibrium (Economics) -- Mathematical models Statics and dynamics (Social sciences) -- Mathematical models Time and economic reations -- Mathematical models Uncertainty -- Mathematical models Allgemeines Gleichgewichtsmodell (DE-588)4210294-7 gnd Dynamische Makroökonomie (DE-588)4200428-7 gnd |
| topic_facet | Mathematisches Modell Equilibrium (Economics) -- Mathematical models Statics and dynamics (Social sciences) -- Mathematical models Time and economic reations -- Mathematical models Uncertainty -- Mathematical models Allgemeines Gleichgewichtsmodell Dynamische Makroökonomie |
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