Bernoulli substitution in the Ramsey model: Optimal trajectories under control constraints
- Authors: Krasovskii A.A.1, Lebedev P.D.2, Tarasyev A.M.2,3
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Affiliations:
- International Institute for Applied Systems Analysis (IIASA)
- Institute of Mathematics and Mechanics, Ural Branch
- Ural Federal University
- Issue: Vol 57, No 5 (2017)
- Pages: 770-783
- Section: Article
- URL: https://journal-vniispk.ru/0965-5425/article/view/179126
- DOI: https://doi.org/10.1134/S0965542517050050
- ID: 179126
Cite item
Abstract
We consider a neoclassical (economic) growth model. A nonlinear Ramsey equation, modeling capital dynamics, in the case of Cobb-Douglas production function is reduced to the linear differential equation via a Bernoulli substitution. This considerably facilitates the search for a solution to the optimal growth problem with logarithmic preferences. The study deals with solving the corresponding infinite horizon optimal control problem. We consider a vector field of the Hamiltonian system in the Pontryagin maximum principle, taking into account control constraints. We prove the existence of two alternative steady states, depending on the constraints. A proposed algorithm for constructing growth trajectories combines methods of open-loop control and closed-loop regulatory control. For some levels of constraints and initial conditions, a closed-form solution is obtained. We also demonstrate the impact of technological change on the economic equilibrium dynamics. Results are supported by computer calculations.
About the authors
A. A. Krasovskii
International Institute for Applied Systems Analysis (IIASA)
Author for correspondence.
Email: krasov@iiasa.ac.at
Austria, Schlossplatz 1, Laxenburg, A-2361
P. D. Lebedev
Institute of Mathematics and Mechanics, Ural Branch
Email: krasov@iiasa.ac.at
Russian Federation, Yekaterinburg, 620990
A. M. Tarasyev
Institute of Mathematics and Mechanics, Ural Branch; Ural Federal University
Email: krasov@iiasa.ac.at
Russian Federation, Yekaterinburg, 620990; Yekaterinburg, 620002
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