Population Aging,Optimal Retirement Age In The Economic Growth Model

This paper constructs a model with three overlapping generations and exogenous fertility rate in which the old agents supply labor and has leisure preferences.The first part of the paper does not take the private education investment into account,it is shown that the economy in the model exists an optimal retirement age which depends on fertility rate,tax rate and the labor productivity of old to young.Moreover,this paper analyses the existence and type of the equailibrium.It is shown that when the human capital is constant returns to scale,there is not steady state,when the human capital is increasing returns to scale or decreasing returns to scale,the unique equilibrium exists and is saddle and stable node respectively.When human capital vary from decreasing returns to scale to increasing returns to scale,the model appears saddle-node bifurcation.The second part of the paper introduce the private education investment,it discusses the effective labor caipatal,private education investment and growth rate in the steady state.In the model,when the respective value of utility discount,degree of altruism towards children and tax rate corresponding to public education investment at different levels,their respective effect to the economic growth are different.