An Economic Growth Model With Exogenous Or Endogenous Fertility

We develop a finite demographic macroeconomic model with endogenous or exoge-nous fertility that features age-dependent mortality at individual level,thus individuals are heterogeneous.Rational agents maximizes his lifetime utility under his budget con-straint.Firms maximize their profits,hire labor and rent capital until their marginal products equal their factor prices.We use the model to investigate the consequences of decline in fertility rate,rise in retirement age and rise in tax rate of pension at aggregate level.We prove the.existence of the BGP growth rate of our model and our framework incorporates a simple PAYG pension system and assumes a perfect annuity market,To make our analysis more realistic,we add empirical contents to the model,prove.the cases analyzed in the article are realistic.In the model with endogenous fertility,fertil-ity rate is determined by weight of happiness toward having children and proportion of expenditure.of each child to his parent’s own consumption.We show that a decrease infertility rate caused by a decrease in the weight of happiness toward having children or an increase in the proportion of expenditure of each child to his parent’s own consump-tion has a negative effect on the long-run economic growth rate.Surprisingly,we found that both an increase in the retirement age and an increase in the tax ra.te of pension dampen the long-run economic prosperity.