Modern macroeconomics with historical perspectives [electronic resource] / Shuetsu Takahashi, Mitsuyoshi Yanagihara, Kei Hosoya, Tsuyoshi Shinozaki, editors.

Intro
Contents
1 Declining Population Growth and the Serendipity Theorem
1.1 Introduction
1.2 The Basic Overlapping Generations Model and the Serendipity Theorem
1.3 Population Growth, Social Welfare, and Capital Accumulation
1.4 Cobb-Douglas Preference and CES Technology
1.5 Optimum Population Growth Rate
1.5.1 Maximization of Indirect Social Welfare Function
1.5.2 Optimum Population Rate
1.5.3 Negative Optimum Population Rates
1.5.4 Effects of Parameter Changes
1.6 Technological Innovation and Optimum Population Growth
1.7 Concluding Remarks

Appendix
Proof of dk?/dn < 0
Derivation of (1Equ321.32) and (1Equ331.33)
Proof of dk/dn < dk?/dn< dk/dn< 0 in Fig. 1.1a
Proof of dk?/dn < dk / dn < 0 < dk / dn in the Unstable Case
Proof of dk/dn < dk?/dn< d k/dn < 0 in Fig. 1.2a
References
2 Consumption of Leisure Goods, Leisure Time, and Inheritance of Tastes for Leisure in an Overlapping Generations Model
2.1 Introduction
2.2 The Model
2.2.1 Framework
2.2.2 An Individual
2.2.3 Firms
2.2.4 Equilibrium
2.3 Comparative Statics: Effects of Preference and Productivity

2.3.1 Effects of Preference for Leisure
2.3.2 Effects of Capital Intensity
2.4 Numerical Example
2.5 Conclusion
Appendix
Proof of Proposition 2
References
3 Overlapping Generations Model with Relative Preference for Children's Human Capital
3.1 Introduction
3.2 The Model
3.2.1 Individuals
3.2.2 Firms
3.2.3 Equilibrium
3.3 Social Optimum
3.4 Optimal Policy
3.5 Conclusion
Appendix
Derivation of the Socially Optimum Conditions for the Balanced Growth Path
Derivation of the Optimal Subsidy/Tax Rate

Derivation of the Interest Rate in the Case of To == 0
References
4 The Impact of Life Insurance on Human Capital Investment During the Steady Growth Period in Japan: Simulation Analysis in an Overlapping Generations Model with Endogenous Growth
4.1 Introduction
4.2 Model
4.2.1 Individuals
4.2.2 Firms
4.2.3 Government
4.2.4 Equilibrium
4.3 Parameter Settings
4.4 Simulation Results
4.5 Conclusion
References
5 The Effects of Patience in a Growth Model with Infrastructure and a Related Externality
5.1 Introduction
5.2 The Model

5.2.1 The Case of Increasing Marginal Impatience
5.2.2 The Case of Decreasing Marginal Impatience
5.3 Unique Equilibrium Situation
5.3.1 The Benchmark Case
5.3.2 Verification of Numerical Results
5.4 Equilibrium Dynamics
5.5 Concluding Remarks
Appendix
Supplementary Figures
References
6 Intergenerational Inequalities and Policy Options for Achieving Generational Balance in Japan
6.1 Introduction
6.2 The Methodology of Generational Accounting
6.2.1 The Model
6.2.1.1 The Fiscal Burden Facing Future Generation
6.2.1.2 Indicator of Generational Imbalance