Japan has been experiencing significant changes in its demographics. This study examines the effects of public care services and in doing so, aims to show that it is possible to improve overall welfare level by substituting family care with public care services, particularly when family care and public care services are interchangeable. In addition, we show that instead of reducing family care to zero, further expanding public care services can help achieve welfare optimization.
Japan has been experiencing dramatic changes in its demographics owing to multiple factors. While its elderly population has been increasing because of extended average life expectancy, birth rate has been declining with the growing rate of unmarried individuals and tendencies of late marriages and child birth. Thus, managing the increase in elderly population has become a serious concern. According to the Ministry of Health, Labour and Welfare (2013) [
Mizushima (2009) [
In addition to these studies, some studies investigated the effects of subsidies for elderly care on economic growth and social welfare. Tabata (2005) [
In this paper, we examine the case of individuals who may require care in their old age and assume that the elderly receive either informal care provided by family members or formal care funded by the public sector. Further, assuming a substitutable relationship between the two forms of caretaking, the extent to which informal and formal care should be provided is analyzed2.
We consider a closed overlapping-generations model. In this model, individuals live in two periods. All individuals have the same probability,
Suppose that the government levies a lump-sum tax
where
We assume that the parent’s utility depends on the amount of informal care he/she receives from his/her children
where
where
Individuals born in period t care about their parents, and their parents’ utility
where
As for the children, their altruism is limited to helping their parents in the case of dependency4. Thus, their utility is as follows:
where
Mizushima (2009) [
Taking
The optimal condition for children with parents in need of care is as follows:
Given the substitutable relationship between family and public care, any change in the amount of family care is negatively associated with a change in publicly provided care. Therefore, disposable income increases with an increase in labor hours, and thus, the consumption level also increases. Family care provision takes a positive value when (A1) holds:
This also means that public care services are provided within the boundary
An increase in the provision of public care services, which induces a lower marginal utility of family care, decreases the incentives to work and encourages reduced family care provision.
Here,
public care services can result in suppressed consumption in the form of a tax burden. By contrast, for individuals with parents in need of care, public care services can be a substituted for family care, resulting in a greater consumption capacity. In this case, if the scale of public care services is within the boundary of (A1), the tax burden on individuals with healthy parents is not excessive and therefore, the consumption of individuals with healthy parents is greater than that of individuals with parents in need of care.
A welfare level in the steady state with public care services is represented by
follows:
where
Proposition: Improved welfare is possible by providing all care for unhealthy parents through public long-term care services.
Proof: According to Equation (4),
comes
Public care services can influence welfare through the effects of insecurity about health in one’s old age, parents’ health condition, and variations in consumption depending on parents’ health status. Regardless of the condition of one’s parents, knowing the health condition in one’s old age is not possible. Hence, public care services function as a preventive measure against such insecurities, thus contributing toward a higher quality of life. If parents are in need of care, public care services can also improve overall welfare by increasing the total amount of care available and the consumption level of their children. By contrast, if the parents are healthy, the tax burden could lower the consumption level, thus diminishing the overall positive benefits of welfare services. In this case, provided the scale of public care services is not excessive, the negative effect of lower consumption by individuals with healthy parents can be minimized, leading to an improved overall welfare level.
Corollary: Instead of reducing the level of family care to zero, further expanding public care services can help achieve welfare optimization.
The scale of public care services, which induces family care to be zero, is derived to maximize parent’s utility and one’s consumption, given the uncertainty of future health. On the other hand, the optimal level of public care services, which maximizes welfare in the steady state, internalizes uncertainty regarding future health status. Because public care services can provide insurance against future health concerns, the internalization of an uncertainty positively affects welfare through an increase in utility.
Thus, given the positive effects regarding future health insecurities, which was not considered for the maximization of individuals’ an welfare, expanding the scale of public care services can result in the overall improvement of societal welfare, even if it entails further tax collection.
In this paper, our aim was to analyze that to what extent should the public care services provide for parents in need of care. To examine this, we assume that all individuals have the same probability of becoming dependent at the beginning of the second period. Then, we showed that when family care and public care services were interchangeable, it was possible to improve welfare by providing all care for unhealthy parents through public long-term care services. We also showed that instead of reducing family care to zero, further expanding public care services could help achieve welfare optimization, even if it entailed further tax collection.
I would like to thank Tetsuya Nakajima, and Yusuke Hirota for their valuable comments on this paper. I am also grateful to anonymous referee for his/her helpful comments and suggestions.
YukoMihara, (2015) Relationship between Family Care and Public Care Services for the Elderly. Modern Economy,06,948-953. doi: 10.4236/me.2015.69089