A competitive growth model with endogenous fertility

Abstract

This paper investigates the interaction between endogenous fertility behavior and the distribution of income and wealth arnong farnilies in a competitive market economy. We construct a growth model in which altruistic dynasties are heterogeneous in their initial stocks of physical capital. Dynasties make choices of farnily size along with decisions about consumption and intergenerational transfers. We show that if the rate of time preference is increasing in the number of children and preferences over nurnber of children satisfy a norrnality assumption, all steady states are characterized by equality of capital stocks and consumption arnong families. We also provide sufficient conditions for uniqueness of the steady state. In order to illustrate these results, we present an example in which preferences over number of children are logarithrnic and the technology is Cobb-Douglas. For this combination of preferences and technology, there exists a unique egalitarian steady state. Moreover, the economy converges to this steady state in only one generation .