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 Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 5, Pages 768–782 (Mi zvmmf10569)

Bernoulli substitution in the Ramsey model: Optimal trajectories under control constraints

A. A. Krasovskiia, P. D. Lebedevb, A. M. Tarasyevbc

a International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria
b Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia
c Ural Federal University, Yekaterinburg, Russia

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.

Key words: mathematical modeling, optimal growth problem, Pontryagin's maximum principle, steady states.

 Funding Agency Grant Number Russian Science Foundation 15-11-10018

DOI: https://doi.org/10.7868/S0044466917050052

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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:5, 770–783

Bibliographic databases:

UDC: 519.626

Citation: A. A. Krasovskii, P. D. Lebedev, A. M. Tarasyev, “Bernoulli substitution in the Ramsey model: Optimal trajectories under control constraints”, Zh. Vychisl. Mat. Mat. Fiz., 57:5 (2017), 768–782; Comput. Math. Math. Phys., 57:5 (2017), 770–783

Citation in format AMSBIB
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