The optimum growth rate for population in the neoclassical overlapping generations model:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Frankfurt am Main [u.a.]
Lang
2007
|
| Series: | European university studies
Series 5, economics and management ; 3282 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XVI, 148 S. graph. Darst. 210 mm x 148 mm |
| ISBN: | 9783631573525 3631573529 |
Staff View
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| 245 | 1 | 0 | |a The optimum growth rate for population in the neoclassical overlapping generations model |c Wolfgang Kuhle |
| 264 | 1 | |a Frankfurt am Main [u.a.] |b Lang |c 2007 | |
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| 650 | 4 | |a Population - Modèles mathématiques | |
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Record in the Search Index
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| adam_text | Contents
1.
Introduction
1
1.1.
Historical Perspective
.................. 2
1.2.
Main Assumptions and Method of Analysis
.... 4
2.
The Optimum Growth Rate for Population in the Neo¬
classical Growth Model
7
2.1.
The Optimum Growth Rate for Population in the
Consumption-Loan Model
............... 8
2.1.1.
The Model
..................... 8
2.1.2.
The Social Optimum
.............. 9
2.1.3.
The Individual Utility Maximization
.... 12
2.1.4.
Financial Intermediation by the Government
14
2.1.5.
Provisional Result
................ 15
2.2.
The Optimum Growth Rate for Population in the
Neoclassical One-sector Growth Model
....... 16
2.2.1.
The Solow Growth Model
........... 16
2.2.2.
The First Golden Rule of Capital Accumu¬
lation
........................ 22
2.2.3.
The Disadvantages of High Rates of Popu¬
lation Growth
................... 24
2.2.4.
Provisional Result
................ 25
2.3.
The Optimum Growth Rate of Population in the
Diamond Neoclassical Growth Model
........ 25
2.3.1.
The Model
..................... 27
2.3.2.
The Social Optimum
.............. 28
xij
Contents
2.3.3.
The Second Order Sufficient Conditions
. . 32
2.3.4.
The Special Case of
CES
Utility and Pro¬
duction Functions
................ 35
2.3.5.
Attainability and Stability of the Social Op¬
timum: the Serendipity Theorem
...... 42
2.3.6.
The Optimum Growth Rate for Population
in
a Laissez Faire
Economy
.......... 46
2.3.7.
A Diagrammatic Discussion
.......... 58
2.4.
Summary
.......................... 66
3.
Extensions to the Problem of the Optimum Growth Rate
for Population in the Neoclassical Overlapping Genera¬
tions Model
70
3.1.
Child-dependency Costs
................ 71
3.2.
The Intergenerational Transfer Effect in a Model
with Child-dependency Costs and Continuous Time
71
3.2.1.
The Model
..................... 73
3.2.2.
The Welfare Implications of a Change in the
Growth Rate of Population
.......... 76
3.3.
The Serendipity Theorem and Child-dependency
Costs
............................ 78
3.3.1.
The Model
..................... 79
3.3.2.
The Social Optimum
.............. 80
3.3.3.
The
Laissez Faire
Economy
.......... 81
3.3.4.
A Second-Best Solution to the Problem of
Optimal
Population
..................... 82
Contents xiii
3.3.5. Optimum
Social
Security
............ 83
3.3.6.
Provisional Result
................ 85
3.4.
Government Debt
.................... 86
3.4.1.
The Model
..................... 88
3.4.2.
The Social Optimum
.............. 90
3.4.3.
The Competitive Economy with Government
Debt
........................ 91
3.4.4.
Attainability of the Social Optimum
..... 91
3.4.5.
The Optimum Growth Rate for Population
in a Competitive Economy
........... 92
3.4.6.
Debt and Welfare
................ 96
3.4.7.
Population and Welfare
............. 97
3.4.8.
Provisional Result
................ 101
3.5.
Summary
.......................... 102
4.
The Optimum Growth Rate for Population Derived from
the Economic Dependency Ratio
105
4.1.
The Dependency Approach
.............. 106
4.1.1.
The Model
..................... 107
4.1.2.
Further Aspects
................. 110
4.1.3.
Summary
..................... 112
5.
Conclusion
114
A The Bordered Hessian
121
В
Appendix
123
С
Oscillatory Stability
129
xiv Contents
D
The crucial r-n relation: Estimates
130
Б
Appendix
136
F
Pay-as-you-go Social Security and optimal population
138
G
Formal aspects to Diagram
16 140
References
141
In the course of the last century, birth rates in the
OECD
have fallen significantly.
This study is concerned with the long run factor price and welfare implications
of this decline in birth rates. The relevant models, i.e. the pure consumption
loan economy, the neoclassical one-sector growth model, variations of the
neoclassical overlapping generations model, and the economic dependency
approach are utilized to answer this question. The study features exact general
conditions for the existence of an interior optimum growth rate for population in
the neoclassical overlapping generations model and, hence, is closing a gap
in the preceding literature. Subsequent empirical testing suggests that these
conditions for the validity of the Serendipity Theorem are probably satisfied.
Wolfgang
Kuhle
studied economics at the
Freie Universität
Berlin from
2002
to
2006.
He was student assistant at the Chair for Economic Theory and teaching
assistant at the Department of Economics. Since
2007
he is working on his
dissertation at the macroeconomics unit of the Mannheim Research Institute
for the Economics of Aging
(MEA).
|
| adam_txt |
Contents
1.
Introduction
1
1.1.
Historical Perspective
. 2
1.2.
Main Assumptions and Method of Analysis
. 4
2.
The Optimum Growth Rate for Population in the Neo¬
classical Growth Model
7
2.1.
The Optimum Growth Rate for Population in the
Consumption-Loan Model
. 8
2.1.1.
The Model
. 8
2.1.2.
The Social Optimum
. 9
2.1.3.
The Individual Utility Maximization
. 12
2.1.4.
Financial Intermediation by the Government
14
2.1.5.
Provisional Result
. 15
2.2.
The Optimum Growth Rate for Population in the
Neoclassical One-sector Growth Model
. 16
2.2.1.
The Solow Growth Model
. 16
2.2.2.
The First Golden Rule of Capital Accumu¬
lation
. 22
2.2.3.
The Disadvantages of High Rates of Popu¬
lation Growth
. 24
2.2.4.
Provisional Result
. 25
2.3.
The Optimum Growth Rate of Population in the
Diamond Neoclassical Growth Model
. 25
2.3.1.
The Model
. 27
2.3.2.
The Social Optimum
. 28
xij
Contents
2.3.3.
The Second Order Sufficient Conditions
. . 32
2.3.4.
The Special Case of
CES
Utility and Pro¬
duction Functions
. 35
2.3.5.
Attainability and Stability of the Social Op¬
timum: the Serendipity Theorem
. 42
2.3.6.
The Optimum Growth Rate for Population
in
a Laissez Faire
Economy
. 46
2.3.7.
A Diagrammatic Discussion
. 58
2.4.
Summary
. 66
3.
Extensions to the Problem of the Optimum Growth Rate
for Population in the Neoclassical Overlapping Genera¬
tions Model
70
3.1.
Child-dependency Costs
. 71
3.2.
The Intergenerational Transfer Effect in a Model
with Child-dependency Costs and Continuous Time
71
3.2.1.
The Model
. 73
3.2.2.
The Welfare Implications of a Change in the
Growth Rate of Population
. 76
3.3.
The Serendipity Theorem and Child-dependency
Costs
. 78
3.3.1.
The Model
. 79
3.3.2.
The Social Optimum
. 80
3.3.3.
The
Laissez Faire
Economy
. 81
3.3.4.
A Second-Best Solution to the Problem of
Optimal
Population
. 82
Contents xiii
3.3.5. Optimum
Social
Security
. 83
3.3.6.
Provisional Result
. 85
3.4.
Government Debt
. 86
3.4.1.
The Model
. 88
3.4.2.
The Social Optimum
. 90
3.4.3.
The Competitive Economy with Government
Debt
. 91
3.4.4.
Attainability of the Social Optimum
. 91
3.4.5.
The Optimum Growth Rate for Population
in a Competitive Economy
. 92
3.4.6.
Debt and Welfare
. 96
3.4.7.
Population and Welfare
. 97
3.4.8.
Provisional Result
. 101
3.5.
Summary
. 102
4.
The Optimum Growth Rate for Population Derived from
the Economic Dependency Ratio
105
4.1.
The Dependency Approach
. 106
4.1.1.
The Model
. 107
4.1.2.
Further Aspects
. 110
4.1.3.
Summary
. 112
5.
Conclusion
114
A The Bordered Hessian
121
В
Appendix
123
С
Oscillatory Stability
129
xiv Contents
D
The crucial r-n relation: Estimates
130
Б
Appendix
136
F
Pay-as-you-go Social Security and optimal population
138
G
Formal aspects to Diagram
16 140
References
141
In the course of the last century, birth rates in the
OECD
have fallen significantly.
This study is concerned with the long run factor price and welfare implications
of this decline in birth rates. The relevant models, i.e. the pure consumption
loan economy, the neoclassical one-sector growth model, variations of the
neoclassical overlapping generations model, and the economic dependency
approach are utilized to answer this question. The study features exact general
conditions for the existence of an interior optimum growth rate for population in
the neoclassical overlapping generations model and, hence, is closing a gap
in the preceding literature. Subsequent empirical testing suggests that these
conditions for the validity of the Serendipity Theorem are probably satisfied.
Wolfgang
Kuhle
studied economics at the
Freie Universität
Berlin from
2002
to
2006.
He was student assistant at the Chair for Economic Theory and teaching
assistant at the Department of Economics. Since
2007
he is working on his
dissertation at the macroeconomics unit of the Mannheim Research Institute
for the Economics of Aging
(MEA). |
| any_adam_object | 1 |
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| series | European university studies |
| series2 | European university studies : Series 5, economics and management |
| spelling | Kuhle, Wolfgang Verfasser aut The optimum growth rate for population in the neoclassical overlapping generations model Wolfgang Kuhle Frankfurt am Main [u.a.] Lang 2007 XVI, 148 S. graph. Darst. 210 mm x 148 mm txt rdacontent n rdamedia nc rdacarrier European university studies : Series 5, economics and management 3282 Zugl.: Berlin, Univ., Diss., 2006 Population - Accroissement - Aspect économique Population - Accroissement - Modèles mathématiques Population - Aspect économique Population - Modèles mathématiques Mathematisches Modell Population Economic aspects Population Mathematical models Mehrgenerationenmodell (DE-588)4215762-6 gnd rswk-swf Neoklassisches Modell (DE-588)4115361-3 gnd rswk-swf Bevölkerungswachstum (DE-588)4129300-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Bevölkerungswachstum (DE-588)4129300-9 s Mehrgenerationenmodell (DE-588)4215762-6 s Neoklassisches Modell (DE-588)4115361-3 s DE-604 European university studies Series 5, economics and management ; 3282 (DE-604)BV000001798 3282 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016435610&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016435610&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Kuhle, Wolfgang The optimum growth rate for population in the neoclassical overlapping generations model European university studies Population - Accroissement - Aspect économique Population - Accroissement - Modèles mathématiques Population - Aspect économique Population - Modèles mathématiques Mathematisches Modell Population Economic aspects Population Mathematical models Mehrgenerationenmodell (DE-588)4215762-6 gnd Neoklassisches Modell (DE-588)4115361-3 gnd Bevölkerungswachstum (DE-588)4129300-9 gnd |
| subject_GND | (DE-588)4215762-6 (DE-588)4115361-3 (DE-588)4129300-9 (DE-588)4113937-9 |
| title | The optimum growth rate for population in the neoclassical overlapping generations model |
| title_auth | The optimum growth rate for population in the neoclassical overlapping generations model |
| title_exact_search | The optimum growth rate for population in the neoclassical overlapping generations model |
| title_exact_search_txtP | The optimum growth rate for population in the neoclassical overlapping generations model |
| title_full | The optimum growth rate for population in the neoclassical overlapping generations model Wolfgang Kuhle |
| title_fullStr | The optimum growth rate for population in the neoclassical overlapping generations model Wolfgang Kuhle |
| title_full_unstemmed | The optimum growth rate for population in the neoclassical overlapping generations model Wolfgang Kuhle |
| title_short | The optimum growth rate for population in the neoclassical overlapping generations model |
| title_sort | the optimum growth rate for population in the neoclassical overlapping generations model |
| topic | Population - Accroissement - Aspect économique Population - Accroissement - Modèles mathématiques Population - Aspect économique Population - Modèles mathématiques Mathematisches Modell Population Economic aspects Population Mathematical models Mehrgenerationenmodell (DE-588)4215762-6 gnd Neoklassisches Modell (DE-588)4115361-3 gnd Bevölkerungswachstum (DE-588)4129300-9 gnd |
| topic_facet | Population - Accroissement - Aspect économique Population - Accroissement - Modèles mathématiques Population - Aspect économique Population - Modèles mathématiques Mathematisches Modell Population Economic aspects Population Mathematical models Mehrgenerationenmodell Neoklassisches Modell Bevölkerungswachstum Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016435610&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=016435610&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001798 |
| work_keys_str_mv | AT kuhlewolfgang theoptimumgrowthrateforpopulationintheneoclassicaloverlappinggenerationsmodel |