Closed‐form solutions of two‐sector Romer model of endogenous growth using partial Hamiltonian approach

Abstract

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 on control and state variables. The growth rates of all economic variables are evaluated, and their long-run behavior is predicted. KEYWORDSfactor tax incidence, first integrals, gauge function, partial Hamiltonian, Pontryagin's principle MSC CLASSIFICATION34H05; 49K15

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