Abstract
A projection method is proposed for infinite-horizon economic growth problems. Exponentially discounted orthogonal Laguerre polynomials are used as the basis functions for the parameterization of the solution. The convergence of the method is studied numerically for integrable cases in the Ramsey model. It is shown that the best convergence of the method is achieved if the parameter in the exponent is chosen to be equal to the negative eigenvalue of the linearization matrix of the Hamiltonian system around a steady state at infinity. In the considered examples, the projection method leads to a system of equations with a small number of unknowns, in contrast to the methods using finite difference approximation.
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Notes
In the paper [9], the inequality with the opposite sign is required to satisfy the balanced growth condition. In this case, there is no steady state \(k_{ss}\), and capital grows to infinity.
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Translated from Trudy Instituta Matematiki i Mekhaniki UrO RAN, Vol. 28, No. 3, pp. 17 - 29, 2022 https://doi.org/10.21538/0134-4889-2022-28-3-17-29.
Translated by E. Vasil’eva
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Arystanbekov, B.M., Melnikov, N.B. Projection Method for Infinite-Horizon Economic Growth Problems. Proc. Steklov Inst. Math. 319 (Suppl 1), S54–S65 (2022). https://doi.org/10.1134/S0081543822060062
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DOI: https://doi.org/10.1134/S0081543822060062