Optimal consumption with irreversible investment in the context of the Ramsey model

The Ramsey model is widely used in macroeconomic studies, but only few studies consider the irreversibility of investment which is an important aspect of real-life investment. In this paper, we consider a Ramsey model with irreversible investment. While the main focus of the current literature is on a qualitative discussion of such problems, our paper provides a framework for quantitative analysis of the transition path. Finding the optimal transition path in a Ramsey model with irreversible investment requires solving a multistage optimal control problem with two kinds of stages. These stages are called 'free' and 'blocked' intervals in the literature, with zero gross investment in the blocked interval and positive gross investment in the free interval. We show that the optimality conditions for such a problem imply the continuity of the control variable along the transition path, which is an important feature in finding the switching moments between free and blocked intervals. We use this feature and the backward integration method for a quantitative analysis of the transition path.