This paper describes the application of maximum Hamiltonian of Pontryagin’s Maximum Principle in determining the best sectoral labour market performance of a market split into three sectors namely; goods producing, service providing and agriculture sectors. The sectoral labour market performance is modeled as a time-independent optimal control problem where the optimal control is determined using the maximum Hamiltonian. The solution is sought using the property of the Hamiltonian that transforms the problem from time-independent to time-dependent problem. The transformation makes use of a switching function and takes note of the time when the control changes from one extreme value to the next. That is, when the labour market efforts switch from producing general worker population to the active sector participants, the sector with more switches within the duration of study indicates more chances of producing more sector participants. The study found that good producing sector had no switch time, service providing sector had three switches while agriculture sector had two switch times within the study period of ten years. Therefore, among the three sectors, the service providing sector had the best performance.

labour market, sectoral labour market performance, labour market participation, maximum Hamiltonian, labour market efforts, optimal control, switching time, switching function.

Received: November 20, 2023; Revised: January 25, 2024; Accepted: February 3, 2024; Published: April 20, 2024

How to cite this article: Mary Mukuhi Mwangi, Moses Mwangi Manene, Pokhariyal Ganesh Prasad and Davis Bundi Ntwiga, Application of maximum Hamiltonian of Pontryagin’s Maximum Principle to sectoral labour market performance, Far East Journal of Applied Mathematics 117(1) (2024), 101-113. http://dx.doi.org/10.17654/0972096024005

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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