| Population in models of economic growth | |
| Introduction | p. 3 |
| Motivation and main question of this research | p. 3 |
| Organization of the research | p. 5 |
| The ageing population: Trends in Germany, United Kingdom and the USA | p. 6 |
| The size and the growth rate of population and economic growth | p. 13 |
| General literature on ageing population, declining population size and declining population growth rate | p. 13 |
| Population in economic growth theory with exogenous technological progress | p. 16 |
| Population in economic growth theory with endogenous technological progress | p. 19 |
| Models with scale effects | p. 20 |
| Models without scale effects | p. 25 |
| Scale effects and policy intervention to increase economic growth | p. 28 |
| Effects of a declining population in a model of economic growth | p. 31 |
| Introduction to a model of economic growth - The Solow (1956) model without technological progress | p. 32 |
| The real growth rate | p. 32 |
| The steady state | p. 37 |
| Transitional dynamics | p. 41 |
| Golden consumption | p. 42 |
| Speed of convergence | p. 44 |
| Conclusions on population and economic growth in the Solow model | p. 46 |
| The Solow (1956) model with technological progress | p. 48 |
| The real growth rate | p. 48 |
| The steady state | p. 50 |
| Transitional dynamics | p. 51 |
| Golden consumption | p. 52 |
| Speed of convergence | p. 54 |
| Conclusions on population and economic growth in the Solow model with technological progress | p. 55 |
| A model of economic growth with human capital - Mankiw, Romer and Weil (1992) | p. 57 |
| The real growth rate | p. 57 |
| The steady state | p. 58 |
| Transitional dynamics | p. 59 |
| Golden consumption | p. 60 |
| Speed of convergence | p. 61 |
| Conclusions on population and economic growth in the Mankiw, Romer, Weil model | p. 62 |
| A model of economic growth with human capital and age structure - Lindh and Malmberg (1999) | p. 62 |
| The real growth rate | p. 63 |
| The steady state | p. 63 |
| Transitional dynamics | p. 64 |
| Golden consumption | p. 65 |
| Speed of convergence | p. 65 |
| Conclusions on population and economic growth in the Lindh-Malmberg model | p. 66 |
| Effects of a declining population in a model of economic growth with endogenous human capital - Lucas (1988) | p. 67 |
| The problem of dynamic optimization and its solution | p. 67 |
| The problem of dynamic optimization with multiple control and state variables | p. 70 |
| A model of economic growth with human capital - Lucas (1988) | p. 72 |
| The real growth rate | p. 73 |
| The household | p. 74 |
| The Hamiltonian approach | p. 75 |
| The steady state | p. 79 |
| Conclusions on population and economic growth in the Lucas model | p. 81 |
| A note on the Lucas model | p. 82 |
| Conclusions of Part I | p. 89 |
| Models of economic growth with an ageing population | |
| Models of "Silver Growth" | p. 95 |
| Models with exogenous population | p. 97 |
| Model 1: The Solow (1956) model with an ageing population | p. 97 |
| The real growth rate | p. 98 |
| The steady state | p. 99 |
| Transitional dynamics | p. 102 |
| Silver consumption | p. 103 |
| Speed of convergence | p. 105 |
| Model 2: The Lucas (1988) model with an ageing population | p. 108 |
| The real growth rate | p. 108 |
| The steady state | p. 112 |
| Comparison of Model 2 and Lucas (1988) | p. 115 |
| Models with quasi-endogenous population | p. 119 |
| Model 3: The Lucas model with the new time allocation and quasi-endogenous population growth | p. 121 |
| The real growth rate | p. 123 |
| The steady state | p. 129 |
| Comparison of Model 3 and Lucas (1988) | p. 131 |
| A quantitative solution of Model 3 | p. 132 |
| Model 4: A model of silver growth with the new time allocation, quasi-endogenous population growth and an ageing population | p. 134 |
| The real growth rate | p. 136 |
| The steady state | p. 142 |
| Comparative statics | p. 145 |
| Comparison of Model 3 and Model 4 | p. 148 |
| Models with endogenous population | p. 151 |
| Model 5: The Lucas model with the new time allocation and endogenous population growth | p. 151 |
| The real growth rate | p. 154 |
| The steady state | p. 157 |
| Comparative statics and transitional dynamics | p. 160 |
| Model 6: A model of silver growth with the new time allocation, endogenous population growth and an ageing population | p. 163 |
| The real growth rate | p. 164 |
| The steady state | p. 168 |
| Comparative statics and transitional dynamics | p. 171 |
| Conclusions | p. 177 |
| Conclusions for economic growth theory | p. 178 |
| Conclusions for economic policy | p. 185 |
| Appendix | p. 189 |
| Derivations | p. 189 |
| Lucas (1988), section 4.2 | p. 189 |
| Model 4, section 8.2 | p. 190 |
| Model 5, section 9.1 | p. 190 |
| Model 6, section 9.2 | p. 191 |
| List of variables | p. 193 |
| References | p. 195 |
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