Maximum size of social security in a model of endogenous fertility

Social security tends to be unsustainable in nature. It reduces individuals'' demand for children as a measure to support their lifestyle during old age, which in turn undermines the financial basis of social security. Using a simple overlapping generations model with endogenous fertility and income transfer from children to parents, we discuss the maximum size of a pay-as-you-go social security program that can prevent a cumulative reduction of fertility and make a program sustainable. We also show that a child-care allowance raises the maximum size of the program and raises an individual''s lifetime utility.