Sustainability in the Stochastic Ramsey Model

TL;DR

This paper examines the probability of maintaining constant consumption in a stochastic Ramsey model with random output-capital ratios, introducing Chebyshev inequality-based estimates and numerical analyses.

Contribution

It provides new probabilistic estimation methods for sustaining consumption in stochastic Ramsey models, expanding on existing results with Chebyshev inequalities and numerical calculations.

Findings

Chebyshev inequalities can estimate sustainability probabilities

Numerical results illustrate the effectiveness of the estimates

Probabilistic analysis enhances understanding of stochastic consumption sustainability

Abstract

In this paper we provide a self-contained exposition of the problem of sustaining a constant consumption level in a Ramsey model. Our focus is on the case in which the output capital-ratio is random. After a brief review of the known results on the probabilities of sustaining a target consumption from an initial stock, we present some new results on estimating the probabilities by using Chebyshev inequalities. Some numerical calculations for these estimates are also provided.