Application of the Hamiltonian System in Deriving Solution to Dynamic System of the Sectoral Labour Market

Abstract

The paper describes the application of the Hamiltonian System in deriving a solution to the dynamic system of the sectoral labour market. The aim is to determine the best control that would allow maximum sector participation in a three-sector labour market. The three sectors of the labour market are the goods-producing sector, the service-providing sector, and the agriculture sector. The sectoral labour market is formulated as an optimal control problem whose solution is sought using the Hamiltonian system by following the necessary conditions for optimality in the Hamiltonian System of Pontryagin’s Maximum Principle. The paper considered that the optimal control would be the measure of labour market efforts to produce the general worker’s population, and any split would mean there is production of active sector productive workers. The sector with the highest optimal allocation of effort, defined as the control within a fixed time, is identified as the best-performing sector. Service-providing sector, in this case, presented the best control. The obtained optimal control parameter is later applied to the experimental data to check on the effect of the control on the sectoral labour market participation rate. The results of the problem indicated that the application of the control had a significant effect on the sectoral labour market participation rate as compared to when there was no control. The sector with the highest annual growth rate measured as the sectoral participation rate was identified as the goods-producing sector