The Ramsey Model in Discrete Time and Decreasing Population Growth Rate
20 Pages Posted: 28 Mar 2014
Date Written: January 8, 2014
This paper extends the Ramsey-Cass-Koopmans growth model of optimal capital accumulation in discrete time by introducing a generic population growth law that satisfies the following properties: population is strictly increasing and bounded, and the population growth rate is decreasing to zero as time tends to infinity. We show that the optimization problem admits a unique solution that can be characterized by the Euler equation. A closed-form solution of the model is presented for the case of a Cobb-Douglas production function and a logarithmic utility function. In contrast to the original model, the solution is not always monotone.
Keywords: Ramsey economic growth model, discrete time, decreasing population growth rate, closed-form solution
JEL Classification: C62, O41
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