A Reformulation of the Economic Theory of Fertility
When parents are altruistic toward children, the choices of fertility and consumption come from the maximization of a dynastic utility function. The maximization conditions imply first, an arbitrage condition for consumption across generations, and second, the equation of the benefit from an extra child to the net cost of rearing that child. These conditions imply that fertility in open economies depends positively on the world interest rate, on the degree of altruism, and on the growth of child-survival probabilities; and negatively on the rate of technical progress and the growth rate of social security. The growth of consumption across generations depends on changes in the net cost of rearing children, but not on interest rates or tirne preference. Even when we include life-cycle elements, we conclude that the growth of aggregate consumption per capita depends in the long run on the growth of consumption across generations. Thereby we show that real interest rates and growth rates of consumption per capita would be unrelated in the long run.