Duality, separability, and functional structure: theory and economic applications
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
North-Holland
1978
|
| Series: | Dynamic economics: theory and applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 395 S. graph. Darst. |
| ISBN: | 0444002359 |
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| 245 | 1 | 0 | |a Duality, separability, and functional structure |b theory and economic applications |c Charles Blackorby ; Daniel Primont ; R. Robert Russell |
| 264 | 1 | |a New York u.a. |b North-Holland |c 1978 | |
| 300 | |a XIX, 395 S. |b graph. Darst. | ||
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| 490 | 0 | |a Dynamic economics: theory and applications | |
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| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Wirtschaft | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Editor s Preface
xiii
Preface
xv
Table of Theorems, Corollaries, and Lemmas
xvii
1.
Introduction
1
1.1
Brief Survey of the Literature
1
1.1.1
Separability
1
1.1.2
Functional Structure
1
1.1.3
Consumer Budgeting, Decentralization, and Price
Aggregation
2
1.1.4
Duality Theory and Separability
3
1.1.5
Nonsymmetric Structures
4
1.1.6
Applications of Separability
4
1.1.7
Testing for Separability
5
1.2
Outline of the Book
6
PART I DUALITY AND SEPARABILITY
11
2.
The Application of Duality Theory to Consumer Preferences
and Production Technologies
13
2.1
Consumer Preferences and Production Technologies
14
2.1.1
Preferences
14
2.1.2
Technologies
15
- 2.2
Marshallian Demand Functions and Indirect Utility
Functions
16
2.2.1
The Indirect Utility Function
16
2.2.2
Roy s Theorem and Its Dual
18
2.3
Hicksian Demand Functions, Cost Functions, and
Transformation Functions
24
2.3.1
The Cost Function
24
2.3.2
The Transformation Function
25
2.3.3
Duality and Cost and Transformation Functions
26
2.3.4
Hotelling s Theorem and Its Dual
34
2.4
Concluding Remarks
38
vii
viii CONTENTS
3.
Separability
41
3.1
The Definition of Separability
41
3.1.1
Notation
42
3.1.2
Separability Defined
43
3.1.3
Strict Separability Defined
46
3.1.4
Relationships between Separability and Strict
Separability
47
3.2
Alternative Definitions of Separability
52
3.3
Separability and Functional Structure
54
3.3.1
Basic Representation and Inheritance Theorems
for the Direct Utility (Production) Function
54
3.3.2
Separability in the Indirect Utility Function
66
3.3.3
Separability in the Cost Function
70
3.3.4
Separability in the Transformation Function
77
3.3.5
Inherited Properties of the Macro and Aggregator
Functions
78
3.4
Functional-Structure Equivalences
81
3.4.1
Equivalence of Separability of the Cost and
Transformation Functions
81
3.4.2
Homothetic Separability
86
3.4.3
The Homothetic-Separability Equivalence
Theorem
89
3.5
Concluding Remarks
100
PART II FUNCTIONAL STRUCTURE,
DECENTRALIZATION, AND
AGGREGATION
103
4.
Representation and Duality Theorems for Symmetrically
Structured Preferences and Technologies
105
4.1
Separable Structures
106
4.1.1
Notation
106
4.1.2
Representation Theorems
108
4.1.3
Conjugate Implicit (Strict) Separability
1И
4.2
Identification of Separable Sectors
114
4.3
Homothetic Separability
120
4.3.1
Separability in the Extended Partition
121
4.3.2
Homothetic Separability and Duality
123
4.3.3
Overall Homotheticity and Duality
125
CONTENTS ix
4.4
Complete
Separability
126
4.4.1
The Fundamental Theorem of Gorman
127
4.4.2
Representation Theorems
135
4.5
Homotheticity, Complete Separability, and Duality
150
4.5.1
Homothetic Separability and Complete
Homothetic Separability Contrasted
150
4.5.2
Representation Theorems
152
4.5.3
Duality Results
157
4.6
Additivity in the Binary Partition
159
4.6.1
Sono
Independence of a Single Variable
159
4.6.2
Independence of a Set of Variables
161
4.7
Multiplicative Representations
165
4.7.1
Strict Independence
165
4.7.2
A Strict-Independence Overlapping Theorem
168
4.8
Concluding Remarks
170
5.
Symmetric Budgeting, Decentralization, and Aggregation
173
5.1
Definitions of Decentralizability and Price and Quantity
Aggregation
175
5.1.1
Preliminaries
175
5.1.2
Decentralizability
177
5.1.3
Price Aggregation
179
5.1.4
Quantity Aggregation
180
5.2
Conditional Utility Functions
182
5.3
Decentralization
188
5.3.1
Strong Decentralizability
188
532.
Weak Decentralizability
191
5.3.3
Felicitous Decentralizability
192
5.4
Price Aggregation
193
5.4.1
The Generalized Gorman Polar Form
193
5.4.2
A Preliminary Lemma
194
5.4.3
Necessary and Sufficient Conditions for Price
Aggregation
196
5.4.4
Necessary and Sufficient Conditions for Additive
Price Aggregation
206
5.4.5
Examples
208
5.5
Quantity Aggregation
210
5.6
Conclusion
214
χ
CONTENTS
6.
Nonsymmetrically Structured Preferences and Technologies
217
6.1
Complete Nonsymmetric Separability (Complete
Recursivity)
218
6.1.1
Nonsymmetric Notation
219
6.1.2
Definitions and Representations
220
6.1.3
Conjugate Recursive Duality
227
6.2
Homothetic Complete Recursivity
228
6.2.1
Homothetically Completely Recursive
Representations
228
6.2.2
Homothetic-Complete-Recursivity Equivalences
232
6.3
Overall Homotheticity and Complete Recursivity
233
6.4
Nonsymmetric Separability (Recursivity)
237
6.5
Completely Recursive Aggregation and Decentralization
244
6.5.1
Introductory Comments
244
6.5.2
Recursive Decentralization
245
6.5.3
Recursive Algorithms
248
6.5.4
Recursive Price and Quantity Aggregation
250
6.6
Recursivity, Decentralization, and Aggregation
253
6.6.1
Direct Recursivity
253
6.6.2
Indirect Homothetic Recursivity
258
6.6.3
Recursive Indirect Utility Functions
259
PART III APPLICATIONS OF SEPARABILITY
AND FUNCTIONAL STRUCTURE
261
7.
Elasticities of Substitution and Neutral Technological Change
263
7.1
The Allen Partial Elasticities of Substitution:
Equality Restrictions and Separability
264
7.1.1
Definition of the Allen Elasticity
264
7.1.2
Separability and Equality Restrictions
265
7.1.3
Complete Separability and the Strong Equality
Restrictions
267
7.1.4
Recursivity and Nonsymmetric Equality
Restrictions
269
7Л.5
Concluding Remarks
271
7.2
Hicks Neutral Technological Change
272
7.2.1
Three Concepts of Hicks Neutrality
272
7.2.2
Equivalence Theorems
274
CONTENTS xi
8.
Separability and the Econometric Estimation
of Demand Systems
277
8.1
Separability as a Maintained Hypothesis
277
8.1.1
Estimation of Conditional Demand Systems
277
8.1.2
The S-Branch Utility Function
280
8.1.3
A More General Specification of the Gorman
Polar Form
284
8.1.4
Estimation and Aggregation
285
8.1.5
Demand-System Estimation and the Work-Leisure
Choice
287
8.1.6
Value-Added Production Functions and Input
Demand
288
8.1.7
intertemporal
Optimization and Current Demand
Systems
289
8.2
Testing for Functional Structure
290
8.2.1
Flexible Functional Forms
290
8.2.2
Testing for Separability
297
8.3
The Separability-Inflexibility of Flexible Functional
Forms
300
8.3.1
The Generalized Quadratic
300
8.3.2
The
Translog 308
8.3.3
The Generalized Quadratic Mean of Order
ρ
310
8.3.4
The Generalized Cobb-Douglas Form
312
8.3.5
The Mean of Order
ρ
315
8.3.6
Concluding Remarks
316
9.
Indices and
Subindices
of the Cost of Living
and the Standard of Living
317
9.1
The Theory of the Cost-of-Living Index
318
9.2
A Theory of the Standard-of-Living Index
321
9.3
Cost-of-Living
Subindices
324
9.3.1
Conditional Cost Functions
325
9.3.2
Partial Cost Functions
327
9.3.3
Implicitly Separable Cost Functions
328
9.3.4
Homothetic Separability and Cost-of-Living
Subindices
333
9.4
Standard-of-Living
Subindices
333
9.5
Aggregable
Subindices
335
xii CONTENTS
10. Intertemporal
Consistency and Intergenerational Conflict
341
10.1
Naive Planning and
Intertemporal
Consistency
341
10.1.1
The
Intertemporal
Society
342
10.1.2
Necessary and Sufficient Conditions for
Intertemporal
Consistency
344
10.2
Sophisticated Planning
350
10.2.1
The Sophisticated Society
350
10.2.2
The Existence of a Sophisticated Optimum
353
Appendix: Duality Theorems and Proofs
357
References
381
Index
393
|
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| indexdate | 2024-07-09T15:38:28Z |
| institution | BVB |
| isbn | 0444002359 |
| language | English |
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| series2 | Dynamic economics: theory and applications |
| spelling | Blackorby, Charles 1937- Verfasser (DE-588)128590564 aut Duality, separability, and functional structure theory and economic applications Charles Blackorby ; Daniel Primont ; R. Robert Russell New York u.a. North-Holland 1978 XIX, 395 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dynamic economics: theory and applications Mathématiques économiques Économie politique - Modèles mathématiques Mathematisches Modell Wirtschaft Economics Mathematical models Economics, Mathematical Ökonometrie (DE-588)4132280-0 gnd rswk-swf Ökonometrie (DE-588)4132280-0 s DE-604 Primont, Daniel A. Verfasser (DE-588)170071774 aut Russell, R. Robert Verfasser (DE-588)170185656 aut Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001297482&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blackorby, Charles 1937- Primont, Daniel A. Russell, R. Robert Duality, separability, and functional structure theory and economic applications Mathématiques économiques Économie politique - Modèles mathématiques Mathematisches Modell Wirtschaft Economics Mathematical models Economics, Mathematical Ökonometrie (DE-588)4132280-0 gnd |
| subject_GND | (DE-588)4132280-0 |
| title | Duality, separability, and functional structure theory and economic applications |
| title_auth | Duality, separability, and functional structure theory and economic applications |
| title_exact_search | Duality, separability, and functional structure theory and economic applications |
| title_full | Duality, separability, and functional structure theory and economic applications Charles Blackorby ; Daniel Primont ; R. Robert Russell |
| title_fullStr | Duality, separability, and functional structure theory and economic applications Charles Blackorby ; Daniel Primont ; R. Robert Russell |
| title_full_unstemmed | Duality, separability, and functional structure theory and economic applications Charles Blackorby ; Daniel Primont ; R. Robert Russell |
| title_short | Duality, separability, and functional structure |
| title_sort | duality separability and functional structure theory and economic applications |
| title_sub | theory and economic applications |
| topic | Mathématiques économiques Économie politique - Modèles mathématiques Mathematisches Modell Wirtschaft Economics Mathematical models Economics, Mathematical Ökonometrie (DE-588)4132280-0 gnd |
| topic_facet | Mathématiques économiques Économie politique - Modèles mathématiques Mathematisches Modell Wirtschaft Economics Mathematical models Economics, Mathematical Ökonometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001297482&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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