A one sector model of economic growth with uncertain technology: An example of steady state analysis in a stochastic optimal control problem

Abstract

This paper considered the convergence of optimum levels of consumption and investment
to a steady state to the case where output or technical progress is a random variable.
The objective is the maximization of the expected value of the discounted sum of utilities
facing uncertain technology or technological progress and, furthermore, our analysis is
conducted in discrete time. Using the elementary mathematical technique, we estab-
lished a stochastic analog of convergence to a steady state—the modified golden rule.
The direction we took was to examine steady state or limiting behavior of the optimal
control and state variables. The stochastic process (14) converges to 0 or ∞ in probability.