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This chapter inquires into the optimal endogenous growth solutions generated by the dynamics of the basic Ramsey intertemporal saving-consumption model. General sufficient conditions are derived for the existence of unique optimal persistent growth solutions within Ramsey models. In phase diagrams, the optimal solution (time paths, trajectory) is a unique separator. The chapter gives comprehensive quantitative applications—using CES-VES production functions and HARA (Hyperbolic Absolute Risk Aversion) utility functions, together with parametric sensitivity analyses—of these optimal time paths for observable saving and growth rates. The original Ramsey (Econ J 38:543–559, 1928) optimal saving model with persistent growth is solved in closed form with constant (CEIS) and variable (VEIS) elasticity of intertemporal substitution with the latter to generate realistic historically observable evolutions of saving rates and economic growth rates.

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Ramsey Optimal Saving: Growth Models with Constant and Variable Elasticity of Intertemporal Substitution

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  • 发表日期：

    2025年

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  • Bjarne S. Jensen

摘要

This chapter inquires into the optimal endogenous growth solutions generated by the dynamics of the basic Ramsey intertemporal saving-consumption model. General sufficient conditions are derived for the existence of unique optimal persistent growth solutions within Ramsey models. In phase diagrams, the optimal solution (time paths, trajectory) is a unique separator. The chapter gives comprehensive quantitative applications—using CES-VES production functions and HARA (Hyperbolic Absolute Risk Aversion) utility functions, together with parametric sensitivity analyses—of these optimal time paths for observable saving and growth rates. The original Ramsey (Econ J 38:543–559, 1928) optimal saving model with persistent growth is solved in closed form with constant (CEIS) and variable (VEIS) elasticity of intertemporal substitution with the latter to generate realistic historically observable evolutions of saving rates and economic growth rates.