General equilibrium theory of value:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, NJ [u.a.]
Princeton Univ. Press
2011
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 175 S. graph. Darst. |
| ISBN: | 9780691146799 0691146799 |
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MARC
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| 100 | 1 | |a Balasko, Yves |e Verfasser |0 (DE-588)170150984 |4 aut | |
| 245 | 1 | 0 | |a General equilibrium theory of value |c Yves Balasko |
| 264 | 1 | |a Princeton, NJ [u.a.] |b Princeton Univ. Press |c 2011 | |
| 300 | |a XII, 175 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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|---|---|
| adam_text | Contents
Preface
Chapter
1
Goods and Prices
1.1
Introduction
1.2
Goods
1.3
Prices
1.4
Relative Prices
1.5
Price Normalization
1.6
Notes and Comments
Chapter
2
Preferences and Utility
2.1
Consumption Sets
2.2
Binary Relations
2.3
Consumers Preferences
2.4
Smooth Utility Functions
2.5
Conclusion
2.6
Notes and Comments
5
5
6
8
14
18
18
Chapter
3
Demand Functions
19
3.1
Introduction
19
3.2
Constrained Utility Maximization
19
3.3
The Individual Demand Function
23
3.4
Properties of Demand Functions in V
24
3.5
Demand-based Consumer Theory
31
3.6
Conclusion
36
3.7
Notes and Comments
36
Chapter
4
The Exchange Model
37
4.1
Introduction
37
4.2
The Sets
£, £„
and £c of
т
-tuples of Demand Functions Defining
the Exchange Model
38
4.3
The Exchange Model
39
4.4
Equilibrium Equation
39
vi
·
Contents
4.5
The Equilibrium Manifold and the Natural Projection
41
4.6
The Smooth Equilibrium Manifold
42
4.7
Smoothness of the Natural Projection
44
4.8
Critical and Regular Points and Values
44
4.9
Notes and Comments
46
Chapter
5
The Equilibrium Manifold
47
5.1
Introduction
47
5.2
Global Properties and Their Interest
47
5.3
The No-trade Equilibria
49
5.4
The Fibers of the Equilibrium Manifold
50
5.5
The Equilibrium Manifold as a Collection of Linear Fibers
Parameterized by the No-trade Equilibria
52
5.6
A Picture of the Equilibrium Manifold
53
5.7
Diffeomorphism with Rem
53
5.8
Conclusion
54
5.9
Notes and Comments
55
Chapter
6
Applications of the Global Coordinate System
56
6.1
Introduction
56
6.2
Coordinate System (A)
56
63
Coordinate System (B)
57
6.4
Formulas of the Natural Projection
57
6.5
The Jacobian Matrix of Aggregate Excess Demand
58
6.6
Conclusion
61
6.7
Notes and Comments
61
Chapter
7
The Broad Picture
62
7.1
Introduction
62
7.2
Properness
62
7.3
Smooth Selection at a Regular Equilibrium
63
7.4
The Equilibrium Manifold over Regular Economies
64
7.5
Genericity of Regular Economies
67
7.6
The Degrees of the Natural Projection
69
7.7
Conclusion
72
7.8
Notes and Comments
73
Contents ·
vii
Chapter
8
The Fine Picture
74
8.1
Introduction
74
8.2
Aggregate Demand at a No-trade Equilibrium
74
8.3
Regularity of the No-trade Equilibria
75
8.4
The Set of Equilibrium Allocations
75
8.5
Economies with a Unique Equilibrium
78
8.6
Degree of the Natural Projection
79
8.7
The Set of Regular Equilibria
79
8.8
Conclusion
81
8.9
Notes and Comments
81
Chapter
9
Production with Decreasing Returns
82
9.1
Introduction
82
9.2
Production Sets: Definitions
82
9.3
Production Sets: Main Properties
84
9.4
The Firm s Objective Function
89
9.5
The Strict Decreasing Returns to Scale Firm
90
9.6
The Net Supply Function as a Primitive Concept
92
9.7
Conclusion
94
9.8
Notes and Comments
95
Chapter
10
Equilibrium with Decreasing Returns
96
10.1
Introduction
96
10.2
The General Equilibrium Model with Private Ownership of
Decreasing Returns to Scale Firms
96
30.3
Production Adjusted Demand Functions
98
10.4
The Equivalent Exchange Model
101
10.5
Properness of the Natural Projection
103
10.6
Conclusion
107
10.7
Notes and Comments
107
Chapter
11
Production with Constant Returns
108
11.1
Introduction
108
11.2
Production Sets
Î09
11.3
The Net Supply Correspondence
112
11.4
Three Examples
115
11.5
Net Supply Correspondence of a Smooth Constant Returns to Scale
Firm
118
viii
· Contents
11.6
The Graph of the Net Supply Correspondence
120
11.7
Conclusion
123
11.8
Notes and Comments
123
Chapter
12
Equilibrium with Constant Returns
124
12.1
Introduction
124
12.2
Decreasing and Constant Returns: General Case
124
12.3
Constant Returns: Reduced Form
125
12.4
Equilibria of the Model
M
126
52.
S
The Equilibrium Manifold Approach
126
12.6
The Equilibrium Manifold for the Model
ЛГ
127
12.7
The Natural Projection
133
12.8
Regular and Critical Equilibria
134
12.9
Degrees of the Natural Projection
137
12.10
Regular and Singular Economies
138
12.11
Uniqueness of Equilibrium over
π
(Ђ
139
12.12
The Natural Projection as a Finite Covering of the Set of Regular
Economies
141
12.13
Values of the Natural Projection Degrees
143
12.14
Conclusion
144
12.15
Notes and Comments
144
Postscript
145
Appendix A
Notation
149
A.I Points, Vectors, Inner Product
149
A.2 Gradient
149
A3
Second-Order Derivatives and the Hessian Matrix of a Smooth
Function
150
Appendix
В
Point-set Topology
151
B.I Proper Maps
151
Appendix
С
Smooth Manifolds
152
C.I The Implicit Function Theorem
152
C.2 Smooth Manifolds and Submanifolds
152
C.3 Smooth Mappings, immersions, and Submersions
153
Contents · ix
Appendix
D
Singularities of Smooth Maps
155
D.I Critical and Regular Points
155
D.2 Singular and Regular Values
155
D.3 Sard s Theorem
156
DA The Regular Value Theorem
156
D.5 The Case where dim X
=
dim
Y
156
D.6 Coverings
157
D.7 Surjectivity of Maps with Non-Zero Modulo
2
Degree
157
Appendix
E
Convexity
159
E.I Convex and Strictly Convex Sets
159
E.2 Quasi-concave Functions
159
E.3 Smooth Quasi-concavity and Second-Order Derivatives
162
E.4 Bordered Hessian of a Smoothly Quasi-concave Function
164
E.5 Recession Cone of a Convex Set
165
Appendix
F
Miscellany
166
F.I Dimension of Semi-algebraic Sets
166
References
167
Index
171
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:39:51Z |
| institution | BVB |
| isbn | 9780691146799 0691146799 |
| language | English |
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| physical | XII, 175 S. graph. Darst. |
| publishDate | 2011 |
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| publisher | Princeton Univ. Press |
| record_format | marc |
| spelling | Balasko, Yves Verfasser (DE-588)170150984 aut General equilibrium theory of value Yves Balasko Princeton, NJ [u.a.] Princeton Univ. Press 2011 XII, 175 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Gleichgewichtstheorie (DE-588)4071876-1 gnd rswk-swf Gleichgewichtstheorie (DE-588)4071876-1 s b DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020328897&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Balasko, Yves General equilibrium theory of value Gleichgewichtstheorie (DE-588)4071876-1 gnd |
| subject_GND | (DE-588)4071876-1 |
| title | General equilibrium theory of value |
| title_auth | General equilibrium theory of value |
| title_exact_search | General equilibrium theory of value |
| title_full | General equilibrium theory of value Yves Balasko |
| title_fullStr | General equilibrium theory of value Yves Balasko |
| title_full_unstemmed | General equilibrium theory of value Yves Balasko |
| title_short | General equilibrium theory of value |
| title_sort | general equilibrium theory of value |
| topic | Gleichgewichtstheorie (DE-588)4071876-1 gnd |
| topic_facet | Gleichgewichtstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020328897&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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