The Economic Growth Model With Demographic Factors And Individual Choices

Population structure has undergone great changes in recent decades.With the improvement of living and medical standards,the mortality rate is declining and life expectancy is lengthening.The increase in child-rearing costs,coupled with longer life expectancy,has led people to reduce the number of children they have had and to in-crease the savings rate for consumption in old age,thus the fertility rate is declining.The dual effects of lower mortality and lower fertility lead to a decline in population growth and population aging.With the aggravation of aging,great changes have tak-en place in social organization and economic structure,which have even affected the domination of government budget.These changes have raised people's awareness of maintaining a sustainable economic growth,and how these changes will affect individu-al choices and economic growth has long been an issue of concern to economists.In this thesis,four models are established,from the point view of mathematics,we study the influence of some factors that lead to the change of population structure on individual behavior and economic growth.Firstly,we establish a continuous OLG model with the actual survival law.By solving the model,we find that the individual optimal consumption and asset paths are related to the actual survival law.Considering total production process,we obtain the balanced growth path by a static comparative analysis and study the existence of the equilibrium growth rate.Specifically,there exists a trivial balanced growth rate which is equal to the interest rate.Moreover,we provide the condition for existence and uiqueness of the non-trivial balanced growth rate and show that an increase in the population growth rate has a positive impact on the nol-trivial balanced growth rate,but the effect of population growth rate on per capita growth rate is negative(by simulation).Secondly,we establish an economic growth model with endogenous fertility rate.Suppose individuals utility include.s two aspets of their self-consumption and the en-joyment of raising children,raising children need some cost.In our model,we mainly analyze the dynamics of per capita consumption and per capita capital and the char-acteristics of equilibrium points in open and closed economies,and discuss the effects of the degree of enjoyment from raising children,proportion of children's consumption and mortality rate on the effective steady-state per capita consumption and capital in both economies.Thirdly,we establish an overlapping generations growth model with family altru-ism and endogenous fertility,in which public expenditures are spent on pensions and public education.Firstly,we study the effect of population aging and the public educa-tion investment on the fertility.It is shown that fertility is declining as the population aging and there exists an inverted-U shape with the increase in public education invest-ment.In addition,we focus on the study of the relationship between population aging and economic growth and discussing how governments can use the allocation of public expenditures on pensions and public education as an alternative policy instrument to increase economic growth.Lastly,we build a discrete generation overlap model with Cobb-Douglas production technology and endogenous life,in which taxes are divided into pension and health expenditures survival probability is determined by medical expenditure and level of medical service.We first discuss the existence of economic equilibrium and whether there exist multiple stable states.After that,t.he influence of the change of medical service level and production technology on te economic dynamics is studied.Finally,we discuss the effect of the proportion of health expenditure(reducing pension)on steady per capita capital at the fixed tax rate.The results show that the level of medical service and the production technology are two important factors that affect the economic dynamics.The change of the medical service level and the production technology make the economy appear multiple stable balance and poverty trap.The increase in medical services and production technology is large enough to lift poorer economies permanently out of the poverty trap and eventually to a higher equilibrium.In addition,increasing health care spending and reducing pensions can also contribute to a steady increase in per capita capital.