A two-sector economic growth model with optimal labor and capital allocation

In this paper, a two-sector growth model with optimal labor force and capital allocation is given. By treating the quantities of the labor force and capital in the consumption production sector as the control variables in the model, we obtain a two-dimension dynamical system from solving the household utility maximum problem. It is proved that the system has a unique nonzero equilibrium which is a saddle, so there exists an optimal labor force and capital allocation process in the economic growth. The capital accumulation and consumption production strictly increase along the growth path. At the end of this paper, a numerical computation is given to present the allocation process of capital and labor.