How life expectancy affects welfare in a Diamond-type overlapping generations model

The effect of life expectancy, especially endogenous life expectancy driven by health investment, on social welfare has major implications for the formulation of healthy investment policies. Using an overlapping generation model within a general equilibrium framework, this paper constructs a new model for a balanced path that includes an uncertain lifetime to simulate the effect of exogenous and endogenous life expectancy on social welfare and economics. It is found that exogenous longevity increase does not necessarily increase welfare. Under certain conditions, the lifetime utility function is an inverted U-shape, not a monotonic increase. In terms of endogenous longevity improvements, the conditions for a positive effect on welfare and economic are more stringent, and there even exists that endogenous life expectancy with the lowest level is greatest effective welfare utility. Numerical simulations show that China's current economic effect and welfare effect of life expectancy are still on the rising stage, and allow some room for life expectancy improvement. However, the welfare utility of endogenous life expectancy driven by the health investment in China is poor, so the effect of positive externality and negative welfare must be considered when defining health investment policy. The improvement of total factor productivity is the key to address the problems of positive externality and negative welfare influence.