This paper considered 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 elementary mathematical technique we established a stochastic analogue 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.
Key words: Convergence, Optimal Control, Steady State, Economic Growth, Discrete Time, Stochastic Analogue.
|
