Income modeling and balancing: a rigorous treatment of distribution patterns
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2015
|
| Schriftenreihe: | Lecture notes in economics and mathematical systems
679 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XXI, 174 S. graph. Darst. |
| ISBN: | 9783319132235 |
Internformat
MARC
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| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2015 | |
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Datensatz im Suchindex
| _version_ | 1804153044166770688 |
|---|---|
| adam_text | Contents
Part I
Lorenz
Curves, Orders and Redistribution
1
Introduction
.................................................................. 3
2
The Generalized Inverse of Distribution Functions
...................... 9
2.1
A Gentle Derivation of the Generalized Inverse
.................... 9
2.2
Properties of the Generalized Inverse Distribution Function
......... 12
2.3
Generalized Inverse and Order Relations
.............................. 17
2.4
Approximations
......................................................... 18
2.5
Generalized Inverse and Computations
................................ 22
2.5.1
Generalized Inverses from Generalized Inverses
.............. 22
2.5.2
Generalized Inverse of the Generalized Inverse
............... 23
2.5.3
Generalized Inverse and Expectation Values
.................. 26
References
..................................................................... 28
3 Lorenz
Densities and
Lorenz
Curves
...................................... 29
3.1
Introduction of
Lorenz
Densities and
Lorenz
Curves
................. 29
3.2
Some Properties of
Lorenz
Densities and
Lorenz
Curves
............. 34
3.3
Approximations
......................................................... 37
3.3.1
Approximations Based on Distribution Functions
............ 37
3.3.2
Related Approximations
........................................ 41
3.4
Characterizations of
Lorenz
Densities and
Lorenz
Curves
........... 41
3.5 Lorenz
Curves for all Distributions
.................................... 44
3.6 Lorenz
Curves from
Lorenz
Curves
.................................... 48
3.6.1 Lorenz
Curves from Two or More
Lorenz
Curves
............ 48
3.6.2 Lorenz
Curves from One
Lorenz
Curve
....................... 48
3.7 Lorenz
Curves for Finite and Infinite Variance Distributions
......... 49
3.8
The
Gini
Index and Other Inequality Indices
.......................... 50
3.8.1
Gini
Index
....................................................... 50
3.8.2
Other Inequality Indices
........................................ 52
3.9 Lorenz
Curves in Higher Dimensions
.................................. 53
References
..................................................................... 53
xvii
xviii Contents
4 Lorenz
Curves
and Partial Orders
......................................... 55
4.1
Partial Orders for
Lorenz
Curves
....................................... 55
4.2 Lorenz
Order and Majorization
........................................ 57
4.3 Lorenz
Order and Integral Orders
...................................... 62
4.3.1 Lorenz
Curves and Orders
...................................... 62
4.3.2 Lorenz
Densities and the Increasing Convex Order
........... 68
4.4
Utility Functions and
Lorenz
Curves
................................... 69
4.4.1
A Representation Formula
..................................... 69
4.4.2
Modifications of the Representation
........................... 74
4.4.3
Utility of Consumption
......................................... 75
References
..................................................................... 81
5
Transfer and Distribution Approximation
................................ 83
5.1
Convergence in Distribution
............................................ 83
5.2
Extension of Pigou-Dalton Transfers
.................................. 85
5.3
Towards Strengthening Convergence in Distribution
.................. 89
5.4
A Probabilistic Version of Pigou-Dalton Transfers
................... 91
5.5
Taxation and Transfer
................................................... 92
5.6
Further Order Relation
.................................................. 94
References
..................................................................... 94
6
Societal Utility and the Atkinson Theorem
............................... 95
6.1
Pigou-Dalton Transfers: Revisited
..................................... 96
6.2
Pigou-Dalton Transfers and Distribution Approximations
............ 98
6.3
Economic Interpretation
................................................ 99
References
..................................................................... 100
Part II
Lorenz
Curves and Models
7
Pareto Distribution, Self-similarity and Empirics
........................ 103
7.1
Self-similarity of
Lorenz
Curves
....................................... 106
7.1.1
Pure Self-similarity
............................................. 107
7.1.2
Gini
Self-similarity
............................................. 109
7.1.3
Median Self-similarity
..........................................
Ill
7.2 Lorenz
Duality
.......................................................... 116
7.2.1
Transformations
................................................. 116
7.2.2
Alternative Transformation
..................................... 118
7.3
Plato s Concept of Social Justice
....................................... 121
7.4
Empirics of Income Distributions
...................................... 122
7.4.1
Best Fit Values for Nations
..................................... 122
7.4.2
Mean Value and Median in Poverty Assessment
.............. 125
7.4.3
Conclusion: The General Picture
.............................. 126
References
..................................................................... 128
Contents
xix
8
Proportionality-Induced Distribution Laws
.............................. 129
8.1
Geometrical Interpretation
.............................................. 129
8.2
The Main Differential Equations of the Equity Calculus
............. 131
8.3
Closed Form Solutions
.................................................. 132
8.4
Empirics
................................................................. 134
8.5
Further Differential Equations of the Equity Calculus
................ 135
8.5.1
Fractured Exponents
............................................ 135
8.5.2
Proportionality Functions
...................................... 136
8.5.3
Slack Functions
................................................. 137
8.5.4
Averages over Other Income Ranges
.......................... 138
8.5.5
Limitations
...................................................... 140
8.6
System of Proportionality Laws
........................................ 140
References
..................................................................... 140
9
Preferences and Coalitions
.................................................. 141
9.1
Introduction
............................................................. 141
9.2
Model
.................................................................... 142
9.2.1
General Approach
.............................................. 142
9.2.2
Related Work
............................ ........................ 143
9.2.3
Formal Approach
............................................... 144
9.3
Redistribution
........................................................... 145
9.3.1
Concept
.......................................................... 145
9.3.2
Identifying Minimum Loss Coalition Partners
................ 147
9.3.3
Bifurcation
...................................................... 150
9.3.4
Situation After Compensation but Before
Complete Redistribution
........................................ 155
9.3.5
Situation After Complete Redistribution
...................... 157
9.3.6
Varying Majority Levels
........................................ 160
9.4
Other Income Distributions
............................................. 162
9.4.1
One-Parametric
Lorenz
Curves
................................ 162
9.4.2
Two-Parametric
Lorenz
Curves
................................ 166
9.4.3
Three-Parametric and Other
Lorenz
Curves
................... 168
9.5
Conclusion
.............................................................. 170
Appendix: Bifurcation Parameters for One-Parametric
Lorenz
Curves
—
General Case
........................................................ 170
References
..................................................................... 171
Index
............................................................................... 173
Lecture Notes in Economics and Mathematical Systems
Thomas Kampke
·
Franz Josef
Rademedier
Income Modeling and Balancing
A Rigorous Treatment of Distribution
torns
This book presents a rigorous treatment of the mathematical instruments available for
dealing with income distributions, in particular
Lorenz
curves and related methods.
The methods examined allow us to analyze, compare and modify such distributions
from an economic and social perspective. Ihough balanced income distributions are
key to peaceful coexistence within aid between nations, it is often difficult to identify
the right kind of balance needed» because there is an interesting interaction with
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Price of
Inequality* by Nobel laureate Joseph
Stigliti
is also touched on. Further» there is a dose
connection to the issue of democracy in the context of globalization. One highlight
of the book is its rigorous treatment of the so-called Atkinson theorem and some
extensions, which help to explain under which type of societal utility functions nations
tend to operate either in the direction of more balance or less balance. Finally» there
are some completely new insights into changing the balance pattern of societies and
the kind of coalitions between richer and poorer parts of society to organize political
support in democracies in either case.
Oxford University s Sir Tony Atkinson, well known for his so-called Atkinson theorem,
writes in his foreword to the book: [The authors] contribute directly to the recent
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are
going on in politics.
[...]
with this book the foundation of arguments
concerning a proper balance in income distribution in the sense of identifying an
l push from mathematics, which
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| any_adam_object | 1 |
| author | Kämpke, Thomas Radermacher, Franz J. 1950- |
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| building | Verbundindex |
| bvnumber | BV042393547 |
| classification_rvk | QC 200 QC 220 |
| ctrlnum | (OCoLC)904431953 (DE-599)BVBBV042393547 |
| discipline | Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV042393547 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:20:21Z |
| institution | BVB |
| isbn | 9783319132235 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027829381 |
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| physical | XXI, 174 S. graph. Darst. |
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| record_format | marc |
| series | Lecture notes in economics and mathematical systems |
| series2 | Lecture notes in economics and mathematical systems |
| spelling | Kämpke, Thomas Verfasser aut Income modeling and balancing a rigorous treatment of distribution patterns Thomas Kämpke ; Franz Josef Radermacher Berlin [u.a.] Springer 2015 XXI, 174 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in economics and mathematical systems 679 Volkswirtschaft (DE-588)4063885-6 gnd rswk-swf Einkommensverteilung (DE-588)4013898-7 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Wirtschaftsplanung (DE-588)4066491-0 gnd rswk-swf Lorenz-Kurve (DE-588)4194651-0 gnd rswk-swf Einkommensverteilung (DE-588)4013898-7 s Lorenz-Kurve (DE-588)4194651-0 s Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s DE-604 Volkswirtschaft (DE-588)4063885-6 s Mathematik (DE-588)4037944-9 s Wirtschaftsplanung (DE-588)4066491-0 s 1\p DE-604 Radermacher, Franz J. 1950- Verfasser (DE-588)120264218 aut Lecture notes in economics and mathematical systems 679 (DE-604)BV000000036 679 Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027829381&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027829381&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kämpke, Thomas Radermacher, Franz J. 1950- Income modeling and balancing a rigorous treatment of distribution patterns Lecture notes in economics and mathematical systems Volkswirtschaft (DE-588)4063885-6 gnd Einkommensverteilung (DE-588)4013898-7 gnd Mathematik (DE-588)4037944-9 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Wirtschaftsplanung (DE-588)4066491-0 gnd Lorenz-Kurve (DE-588)4194651-0 gnd |
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| title | Income modeling and balancing a rigorous treatment of distribution patterns |
| title_auth | Income modeling and balancing a rigorous treatment of distribution patterns |
| title_exact_search | Income modeling and balancing a rigorous treatment of distribution patterns |
| title_full | Income modeling and balancing a rigorous treatment of distribution patterns Thomas Kämpke ; Franz Josef Radermacher |
| title_fullStr | Income modeling and balancing a rigorous treatment of distribution patterns Thomas Kämpke ; Franz Josef Radermacher |
| title_full_unstemmed | Income modeling and balancing a rigorous treatment of distribution patterns Thomas Kämpke ; Franz Josef Radermacher |
| title_short | Income modeling and balancing |
| title_sort | income modeling and balancing a rigorous treatment of distribution patterns |
| title_sub | a rigorous treatment of distribution patterns |
| topic | Volkswirtschaft (DE-588)4063885-6 gnd Einkommensverteilung (DE-588)4013898-7 gnd Mathematik (DE-588)4037944-9 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Wirtschaftsplanung (DE-588)4066491-0 gnd Lorenz-Kurve (DE-588)4194651-0 gnd |
| topic_facet | Volkswirtschaft Einkommensverteilung Mathematik Wahrscheinlichkeitsverteilung Wirtschaftsplanung Lorenz-Kurve |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027829381&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027829381&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000036 |
| work_keys_str_mv | AT kampkethomas incomemodelingandbalancingarigoroustreatmentofdistributionpatterns AT radermacherfranzj incomemodelingandbalancingarigoroustreatmentofdistributionpatterns |