Essays on quantitative economic theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Aachen
Shaker
2006
|
| Series: | Berichte aus der Volkswirtschaft
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 236 S. graph. Darst. 21 cm, 387 gr. |
| ISBN: | 3832247483 |
Staff View
MARC
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| 100 | 1 | |a Bethmann, Dirk |d 1972- |e Verfasser |0 (DE-588)124068006 |4 aut | |
| 245 | 1 | 0 | |a Essays on quantitative economic theory |c Dirk Bethmann |
| 264 | 1 | |a Aachen |b Shaker |c 2006 | |
| 300 | |a XX, 236 S. |b graph. Darst. |c 21 cm, 387 gr. | ||
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| 490 | 0 | |a Berichte aus der Volkswirtschaft | |
| 502 | |a Zugl.: Berlin, Humboldt-Univ., Diss., 2005 | ||
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Record in the Search Index
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| adam_text | Contents
Dedication iii
Preface xiii
List of Figures xv
List of Tables xvii
Notation xviii
1 Introduction and Overview 1
1.1 Introduction 1
1.2 Chapter 2: The Robinson Crusoe economy 3
1.3 Chapter 3: Closed form solutions and macroeconomic models . 4
1.4 Chapter 4: Transitional dynamics in endogenous growth models 7
1.5 Chapter 5: Open loop solutions in dynamic games 12
1.6 Chapter 6: Paternal uncertainty and child investments 16
v
v| Contents
2 The Robinson Crusoe Economy 19
2.1 Introduction 19
2.2 The model 22
2.2.1 The preferences 23
2.2.2 The schooling sector 23
2.2.3 The goods sector 24
2.3 Robinson Crusoe s dynamic optimization problem 25
2.4 Two candidates for the value function 27
2.5 Homogeneity and the introduction of state like and control like
variables 31
2.6 The phase diagrams for the Robinson Crusoe economy 34
2.7 Logarithmic preferences and the value function like function . . 36
2.8 Discrete versus continuous time modeling 37
2.9 Conclusion 40
3 The Closed Form Solution to a Stochastic Version of the Uzawa
Lucas Endogenous Growth Model 43
3.1 Introduction 44
3.2 The model 45
3.2.1 The household 45
3.2.2 The schooling sector 47
3.2.3 The goods sector 47
Contents vii
3.2.4 The state sector in the decentralized economy .... 48
3.3 The centralized solution of the model 49
3.4 The decentralized solution of the model 52
3.4.1 The representative agent s optimization problem . . 52
3.4.2 The representative agent s optimal decisions .... 55
3.4.3 The government s optimal policy 56
3.5 Stability properties and time series implications of the solutions 57
3.6 Summary and concluding remarks 60
4 A Simple Method to Study the Transitional Dynamics in En¬
dogenous Growth Models (with Markus ReiS) 61
4.1 Introduction 62
4.2 The Uzawa Lucas model 63
4.3 The general idea 65
4.4 The centralized economy 69
4.4.1 The social planner s optimization problem 70
4.4.2 Determining the centralized solution 74
4.5 The decentralized economy 76
4.5.1 The symmetric equilibrium 77
4.5.2 The representative agent s optimization problem . . 78
4.5.3 Determining the decentralized solution 82
4.6 U shaped output growth rates 85
viii Contents
4.7 Discussion of the numerical results 88
4.8 Conclusion 93
5 The Open Loop Solution of the Uzawa Lucas Model of Endoge¬
nous Growth with N Agents 95
5.1 Introduction 96
5.2 The model 98
5.3 The N player game 100
5.4 The open loop solution 102
5.4.1 The Hamilton Jacobi Bellman equation 102
5.4.2 The symmetric Nash equilibrium 106
5.4.3 A brief discussion of feedback equilibria 109
5.5 Numerical results Ill
5.6 Conclusion 118
6 Paternal Uncertainty and the Economics of Mating, Parental
Investment in Children, and Marriage 121
6.1 Introduction 122
6.2 The Model 125
6.2.1 Preferences, Endowments, and Reproductive Tech¬
nology 125
6.2.2 Parental Investment and Child Quality 128
6.2.3 Optimal Strategies and Mating Market 129
Contents ix
6.3 Results 132
6.3.1 Mating Costs, Number of Partners, and Paternal
Uncertainty 133
6.3.2 (Parental) Investment in Child Quality 134
6.3.3 Welfare 136
6.4 Marriage 138
6.4.1 Marriage as an Institution 138
6.4.2 Accounting for Changes in Marriage Patterns .... 139
6.5 Conclusion 143
7 Summary and Concluding Remarks 145
Appendices 149
A The Robinson Crusoe Economy 153
A.I Sufficiency of Crusoe s first order necessary conditions under
V(k,h) and W(k,h) 154
A.2 Evolution of the capital stocks under W(k, ft) 155
A.3 Violation of the transversality conditions under W(k, ft) 156
A.4 Specification of the common fixed point Xs, of V(k, ft) and W(k, ft)157
B The Closed Form Solution to a Stochastic Version oftheUzawa
Lucas Endogenous Growth Model 159
B.I Finding the value function by iteration 159
x Contents
B.2 The centralized economy 164
B.3 The decentralized economy 168
C A Simple Method to Study the Transitional Dynamics in En¬
dogenous Growth Models 173
C.I W(k, h) is an upper bound for the true value function V(k, h) ¦ 173
C.2 Proposition 4.1 174
C.3 W(k, h) is an upper bound for the true value function V(k, h) . 174
C.4 Output growth and its rate of change in the centralized case . . 175
C.5 Output growth and its rate of change in the decentralized case . 175
C.6 The initial value problems for u(x) 176
D The Open Loop Solution of the Uzawa Lucas Model of Endoge¬
nous Growth with N Agents 177
D.I The initial value g (z*8) 177
D.2 The initial value problems for u(x) 178
D.3 Human capital allocation 178
E Paternal Uncertainty and the Economics of Mating, Parental
Investment in Children, and Marriage 179
E.I The social optimum 179
E.2 The S method 180
F Mathematics Codes 183
Contents xi
F.I Mathematica Code: A Simple Method to Study the Transitional
Dynamics in Endogenous Growth Models 183
F.2 Mathematica Code: The open loop solution to the Uzawa Lucas
Model of Endogenous Growth 207
F.3 Mathematica Code: Paternal Uncertainty and the Economics of
Mating, Parental Investment in Children, and Marriage 219
Bibliography 223
Index 23S
|
| adam_txt |
Contents
Dedication iii
Preface xiii
List of Figures xv
List of Tables xvii
Notation xviii
1 Introduction and Overview 1
1.1 Introduction 1
1.2 Chapter 2: The Robinson Crusoe economy 3
1.3 Chapter 3: Closed form solutions and macroeconomic models . 4
1.4 Chapter 4: Transitional dynamics in endogenous growth models 7
1.5 Chapter 5: Open loop solutions in dynamic games 12
1.6 Chapter 6: Paternal uncertainty and child investments 16
v
v| Contents
2 The Robinson Crusoe Economy 19
2.1 Introduction 19
2.2 The model 22
2.2.1 The preferences 23
2.2.2 The schooling sector 23
2.2.3 The goods sector 24
2.3 Robinson Crusoe's dynamic optimization problem 25
2.4 Two candidates for the value function 27
2.5 Homogeneity and the introduction of state like and control like
variables 31
2.6 The phase diagrams for the Robinson Crusoe economy 34
2.7 Logarithmic preferences and the value function like function . . 36
2.8 Discrete versus continuous time modeling 37
2.9 Conclusion 40
3 The Closed Form Solution to a Stochastic Version of the Uzawa
Lucas Endogenous Growth Model 43
3.1 Introduction 44
3.2 The model 45
3.2.1 The household 45
3.2.2 The schooling sector 47
3.2.3 The goods sector 47
Contents vii
3.2.4 The state sector in the decentralized economy . 48
3.3 The centralized solution of the model 49
3.4 The decentralized solution of the model 52
3.4.1 The representative agent's optimization problem . . 52
3.4.2 The representative agent's optimal decisions . 55
3.4.3 The government's optimal policy 56
3.5 Stability properties and time series implications of the solutions 57
3.6 Summary and concluding remarks 60
4 A Simple Method to Study the Transitional Dynamics in En¬
dogenous Growth Models (with Markus ReiS) 61
4.1 Introduction 62
4.2 The Uzawa Lucas model 63
4.3 The general idea 65
4.4 The centralized economy 69
4.4.1 The social planner's optimization problem 70
4.4.2 Determining the centralized solution 74
4.5 The decentralized economy 76
4.5.1 The symmetric equilibrium 77
4.5.2 The representative agent's optimization problem . . 78
4.5.3 Determining the decentralized solution 82
4.6 U shaped output growth rates 85
viii Contents
4.7 Discussion of the numerical results 88
4.8 Conclusion 93
5 The Open Loop Solution of the Uzawa Lucas Model of Endoge¬
nous Growth with N Agents 95
5.1 Introduction 96
5.2 The model 98
5.3 The N player game 100
5.4 The open loop solution 102
5.4.1 The Hamilton Jacobi Bellman equation 102
5.4.2 The symmetric Nash equilibrium 106
5.4.3 A brief discussion of feedback equilibria 109
5.5 Numerical results Ill
5.6 Conclusion 118
6 Paternal Uncertainty and the Economics of Mating, Parental
Investment in Children, and Marriage 121
6.1 Introduction 122
6.2 The Model 125
6.2.1 Preferences, Endowments, and Reproductive Tech¬
nology 125
6.2.2 Parental Investment and Child Quality 128
6.2.3 Optimal Strategies and Mating Market 129
Contents ix
6.3 Results 132
6.3.1 Mating Costs, Number of Partners, and Paternal
Uncertainty 133
6.3.2 (Parental) Investment in Child Quality 134
6.3.3 Welfare 136
6.4 Marriage 138
6.4.1 Marriage as an Institution 138
6.4.2 Accounting for Changes in Marriage Patterns . 139
6.5 Conclusion 143
7 Summary and Concluding Remarks 145
Appendices 149
A The Robinson Crusoe Economy 153
A.I Sufficiency of Crusoe's first order necessary conditions under
V(k,h) and W(k,h) 154
A.2 Evolution of the capital stocks under W(k, ft) 155
A.3 Violation of the transversality conditions under W(k, ft) 156
A.4 Specification of the common fixed point Xs, of V(k, ft) and W(k, ft)157
B The Closed Form Solution to a Stochastic Version oftheUzawa
Lucas Endogenous Growth Model 159
B.I Finding the value function by iteration 159
x Contents
B.2 The centralized economy 164
B.3 The decentralized economy 168
C A Simple Method to Study the Transitional Dynamics in En¬
dogenous Growth Models 173
C.I W(k, h) is an upper bound for the true value function V(k, h) ¦ 173
C.2 Proposition 4.1 174
C.3 W(k, h) is an upper bound for the true value function V(k, h) . 174
C.4 Output growth and its rate of change in the centralized case . . 175
C.5 Output growth and its rate of change in the decentralized case . 175
C.6 The initial value problems for u(x) 176
D The Open Loop Solution of the Uzawa Lucas Model of Endoge¬
nous Growth with N Agents 177
D.I The initial value g'(z*8) 177
D.2 The initial value problems for u(x) 178
D.3 Human capital allocation 178
E Paternal Uncertainty and the Economics of Mating, Parental
Investment in Children, and Marriage 179
E.I The social optimum 179
E.2 The S method 180
F Mathematics Codes 183
Contents xi
F.I Mathematica Code: A Simple Method to Study the Transitional
Dynamics in Endogenous Growth Models 183
F.2 Mathematica Code: The open loop solution to the Uzawa Lucas
Model of Endogenous Growth 207
F.3 Mathematica Code: Paternal Uncertainty and the Economics of
Mating, Parental Investment in Children, and Marriage 219
Bibliography 223
Index 23S |
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| id | DE-604.BV021563698 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:35:37Z |
| indexdate | 2024-07-09T20:38:43Z |
| institution | BVB |
| isbn | 3832247483 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014779603 |
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| owner_facet | DE-12 DE-M382 DE-11 DE-188 |
| physical | XX, 236 S. graph. Darst. 21 cm, 387 gr. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Shaker |
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| series2 | Berichte aus der Volkswirtschaft |
| spelling | Bethmann, Dirk 1972- Verfasser (DE-588)124068006 aut Essays on quantitative economic theory Dirk Bethmann Aachen Shaker 2006 XX, 236 S. graph. Darst. 21 cm, 387 gr. txt rdacontent n rdamedia nc rdacarrier Berichte aus der Volkswirtschaft Zugl.: Berlin, Humboldt-Univ., Diss., 2005 Endogenes Wirtschaftswachstum (DE-588)4378670-4 gnd rswk-swf Wachstumstheorie (DE-588)4128160-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Wachstumstheorie (DE-588)4128160-3 s Endogenes Wirtschaftswachstum (DE-588)4378670-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014779603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bethmann, Dirk 1972- Essays on quantitative economic theory Endogenes Wirtschaftswachstum (DE-588)4378670-4 gnd Wachstumstheorie (DE-588)4128160-3 gnd |
| subject_GND | (DE-588)4378670-4 (DE-588)4128160-3 (DE-588)4113937-9 |
| title | Essays on quantitative economic theory |
| title_auth | Essays on quantitative economic theory |
| title_exact_search | Essays on quantitative economic theory |
| title_exact_search_txtP | Essays on quantitative economic theory |
| title_full | Essays on quantitative economic theory Dirk Bethmann |
| title_fullStr | Essays on quantitative economic theory Dirk Bethmann |
| title_full_unstemmed | Essays on quantitative economic theory Dirk Bethmann |
| title_short | Essays on quantitative economic theory |
| title_sort | essays on quantitative economic theory |
| topic | Endogenes Wirtschaftswachstum (DE-588)4378670-4 gnd Wachstumstheorie (DE-588)4128160-3 gnd |
| topic_facet | Endogenes Wirtschaftswachstum Wachstumstheorie Hochschulschrift |
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