Optimal Growth – Optimal Control – Ramsey Saving: Dynamics of Optimal Intertemporal Consumption and Saving – The Solutions of Persistent Growth Models with Normative Capital Accumulation

We explore optimal saving solutions for the economic growth as generated endogenously by a Ramsey model. Sufficient conditions are presented for persistent economic growth within a standard Ramsey model. In phase diagrams of trajectories (solutions), the optimal trajectory (time path) is a separator. Below the separator, over-saving diminishes consumption, ultimately leading to a sub-optimal situation where all incomes are saved. On the other hand, above the separator under-saving suddenly collapses the economy as its productive capital vanishes to zero.The paper gives comprehensive quantitative applications for CIES preferences and CES technologies, together with parametric sensitivity analyses of the optimal solutions (time paths) for relevant observable variables - saving and growth rates.