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Closed‐form solutions of two‐sector Romer model of endogenous growth using partial Hamiltonian approach
Author(s) -
ul Haq Burhan,
Naeem Imran
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6303
Subject(s) - mathematics , hamiltonian (control theory) , ode , romer , control variable , endogenous growth theory , state variable , mathematical economics , mathematical optimization , human capital , economics , physics , thermodynamics , cartography , economic growth , geography , statistics
This article presents the closed‐form solutions of two‐sector human capital–based Romer growth model. The partial Hamiltonian approach is effectively applied to some growth models in order to compute the closed‐form solutions for economic variables involved in the model. Pontryagin's maximum principle provides the set of first‐order system of ODEs, which are regarded as an essential criteria for optimality. The partial Hamiltonian approach is utilized to construct three first integrals of the system using the current value Hamiltonian. With the aid of these first integrals, we computed two distinct exact solutions of Romer model under certain parametric restrictions. The closed‐form expressions for control, state, and costate variables are presented explicitly as a function of t . We have graphically illustrated the solution curves and observed the effect of human capital parameter α on control and state variables. The growth rates of all economic variables are evaluated, and their long‐run behavior is predicted.