Mathematical Model of Human Capital Dynamics

A mathematical description of household economic behavior is studied. On the one hand, households are consumers that seek to maximize the discounted utility function in an imperfect market of savings and consumer loans. On the other hand, households are workers in the labor market; they receive a wage and seek to enhance their skills to receive a higher wage. An increase in the level of worker’s skill is achieved via investment in human capital. In this paper, a mathematical model of the worker’s behavior in the labor market is represented in the form of an infinite-horizon optimal control problem. A solution existence theorem is proved, and necessary optimality conditions are obtained in the form of Pontryagin’s maximum principle. The model is identified using Russian statistical data for various social layers.