Dynamics of Capital-labour Model with Hattaf-Yousfi Functional Response
Driss Riad *
Department of Mathematics and Computer Science, Faculty of Sciences Ben M'sik, Hassan II University, P.O.Box 7955 Sidi Othman, Casablanca, Morocco.
Khalid Hattaf
Department of Mathematics and Computer Science, Faculty of Sciences Ben M'sik, Hassan II University, P.O.Box 7955 Sidi Othman, Casablanca, Morocco and Centre Regional des Metiers de l'Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco.
Noura Yousfi
Department of Mathematics and Computer Science, Faculty of Sciences Ben M'sik, Hassan II University, P.O.Box 7955 Sidi Othman, Casablanca, Morocco.
*Author to whom correspondence should be addressed.
Abstract
The labour force is a fundamental component of every modern economy. It is also called the workforce that is the total number of the people who are eligible to work, including the employed and unemployed people. The company supplies free jobs which number is proportional to the invested capital. In this work, we propose a mathematical model that describes the dynamics of free jobs and labour force. In the model, the rate by which the labour force is filling in free jobs is modeled by Hattaf-Yousfi functional response. Furthermore, we first show that the proposed model is mathematically and economically well-posed. Moreover, the dynamical behavior of the model is studied by determining the existence and stability of equilibria.
Keywords: Capital-labour model, free jobs, labour force, Hattaf-Yousfi functional response