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

Bjarne S. Jensen ()
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Bjarne S. Jensen: University of Southern Denmark (SDU)

Chapter Chapter 13 in The Elements and Dynamic Systems of Economic Growth and Trade Models, 2025, pp 325-409 from Springer

Abstract: Abstract 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.

Keywords: Optimal endogenous growth; Ramsey optimal saving-consumption model; Optimal persistent growth solutions; Separator; Ramsey (1928) affine dynamics; Constant/variable elasticity of intertemporal substitution (CEIS; VEIS) (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-52493-6_13

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DOI: 10.1007/978-3-031-52493-6_13

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