Theoretical studies generally show that as a financing pattern of endowment insurance, the funded system is superior to the payasyougo system from the perspective of capital per capita. This article analyzes whether the funded system is completely superior to the payasyougo system from the perspective of welfare economics with exogenous and endogenous fertilities. The theoretical model shows that: under a certain combination of parameters, either with exogenous fertility or endogenous fertility, there exists a contribution rate of pension that the social welfare under payasyougo system is higher than that under funded system. The numerical simulation shows that: the contribution rate of pension can make the social welfare under the payasyougo system higher. And in the case of exogenous fertility (which is in line with Chinas fertility policy), the social welfare is the highest when the contribution rate of payasyougo pension is around 12%; in the case of endogenous fertility (which is in line with developed countries fertility policy), the social welfare is the highest when the contribution rate of payasyougo pension is around 6%. The former value is similar to the existing research conclusions that Chinas contribution rate of payasyougo pension should be reduced to around 15%, and the latter value is similar to the current contribution rate of payasyougo pension in developed countries such as the United States (6.2%) and Japan (7.7%). The robustness test shows that: the conclusions of the numerical simulation remain as long as the parameter assignment is within a reasonable range. This paper provides theoretical support for the reduction of Chinas contribution rate of payasyougo pension.