Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/102118
Title: Bernoulli substitution in the Ramsey model: Optimal trajectories under control constraints
Authors: Krasovskii, A. A.
Lebedev, P. D.
Tarasyev, A. M.
Issue Date: 2017
Publisher: Maik Nauka-Interperiodica Publishing
Citation: Krasovskii A. A. Bernoulli substitution in the Ramsey model: Optimal trajectories under control constraints / A. A. Krasovskii, P. D. Lebedev, A. M. Tarasyev. — DOI 10.1134/S0965542517050050 // Computational Mathematics and Mathematical Physics. — 2017. — Vol. 57. — Iss. 5. — P. 770-783.
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. © 2017, Pleiades Publishing, Ltd.
Keywords: MATHEMATICAL MODELING
OPTIMAL GROWTH PROBLEM
PONTRYAGIN’S MAXIMUM PRINCIPLE
STEADY STATES
URI: http://hdl.handle.net/10995/102118
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85020676683
PURE ID: 1927004
ISSN: 9655425
DOI: 10.1134/S0965542517050050
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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