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.
|Title of host publication||39TH INTERNATIONAL CONFERENCE ON MATHEMATICAL METHODS IN ECONOMICS (MME 2021)|
|Publisher||Czech University of Life Sciences Prague|
|Number of pages||6|
|Publication status||Published - 2021|
|Event||39th International Conference on Mathematical Methods in Economics (MME) - Prague, Czech Republic|
Duration: 8 Sept 2021 → 10 Sept 2021
|Conference||39th International Conference on Mathematical Methods in Economics (MME)|
|Abbreviated title||MME 2021|
|Period||8/09/21 → 10/09/21|
- p28 - "Socialist Systems and Transitional Economies: Natural Resources; Energy; Environment"
- Ramsey model
- Optimal control theory
- multistage optimal control problem
- Irreversibility of investment