Uncertain horizon and stability. Analysis in an optimal growth model (Q1111449)

A one-sector neoclassical optimal growth model with uncertainty is considered. It is assumed that the production function f(x,w), where x is the input and \(w\in \{0,1\}\) is the state of the world, satisfies the usual neoclassical assumptions. The characterization of optimal programs by competitive prices is presented. It is proved that for any two optimal programs the conditional optimal capital stocks must be close to one another but not necessarily converge to the modified golden rule.