In economically developed countries, aging societies with fewer children are progressing. Increased longevity has necessitated postponement of the working retirement age. Our paper presents an examination of how subsidies for an elderly labor supply affect the elderly labor supply. Our paper presents derivation that this subsidy raises the elderly labor supply. Then, the wage rate of younger laborers can be increased because of complementarity between the younger labor supply and older labor supply. This effect is explained as an externality. By virtue of the externality effect, a subsidy to facilitate the elderly labor supply should be provided in support of social welfare.