Geodesic
Bernoulli substitution in the Ramsey model: Optimal trajectories under control constraints
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 5, pp. 768-782

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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. 
@article{ZVMMF_2017_57_5_a1,
     author = {A. A. Krasovskii and P. D. Lebedev and A. M. Tarasyev},
     title = {Bernoulli substitution in the {Ramsey} model: {Optimal} trajectories under control constraints},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {768--782},
     publisher = {mathdoc},
     volume = {57},
     number = {5},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_5_a1/}
}
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A. A. Krasovskii; P. D. Lebedev; A. M. Tarasyev. Bernoulli substitution in the Ramsey model: Optimal trajectories under control constraints. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 5, pp. 768-782. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_5_a1/