Research On The Endowment Insurance And Fertility Rate Under The Dual Utility Model

With the policy of "two children" fully liberalized,the implementation of "one child" policy for more than 30 years is now fully relaxed.The adjustment of reproductive policy is mainly to alleviate the increasingly serious low fertility risk and aging phenomenon.How will the "two children" policy and the old-age insurance affect with each other?Based on the theory of generation overlap and endogenous growth model,this paper uses the optimization idea to study the relationship between the "two children" policy and the old-age insurance,to analyze the relationship of the fertility rate and enterprise contribution rate,pension and retirement age.Firstly,In the traditional generation overlap model,the variable income,consumption,savings and parenting cost of representative consumers are taken as the research objects.The new variable of parenting(consumption)is added in the utility function to make the traditional generation overlap model be extended to the first type of pension model.Fertility rate and the enterprise contribution rate of the solution are finally derived through the model derived.The relationship between the fertility rate and the enterprise contribution rate is positively correlated,while the relationship between fertility and pension seems to be more complex by in-depth analysis.Secondly,the first type of pension model is extended to the second type of pension model,in which the retirement age and life expectancy parameter are added.The analysis shows that there is a negative correlation between fertility and retirement age.Under the background of satisfying market equilibrium and social welfare maximization,the optimal enterprise contribution rate is going to be solved.Finally,it will be proved by numerical simulation and the relevant policy advice will be given.