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

Krasovskii AA, Lebedev PD, & Tarasyev AM (2017). Bernoulli substitution in the Ramsey model: Optimal trajectories under control constraints. Computational Mathematics and Mathematical Physics 57 (5): 770-783. DOI:10.1134/S0965542517050050.

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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.

Item Type: Article
Additional Information: Published in Russian in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 5, pp. 768–782.
Uncontrolled Keywords: mathematical modeling, optimal growth problem, Pontryagin’s maximum principle, steady states
Research Programs: Ecosystems Services and Management (ESM)
Depositing User: Luke Kirwan
Date Deposited: 12 Jun 2017 08:24
Last Modified: 17 Oct 2017 09:19
URI: http://pure.iiasa.ac.at/14661

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