A Reformulation of the Economic Theory of Fertility

Abstract

An economic analysis of the linkages in fertility rates and capital accumulation across generations is developed considering the determination of fertility and capital accumulation in each generation when wage rates and interest rates are parameters to each family and to open economies. The model is based on the assumption that parents are altruistic toward their children. The utility of parents depends on their own consumption and on the utility of each child and the number of children. By relating the utility of children to their own consumption and to the utility of their children a dynastic utility function was obtained that depends on the consumption and number of descendants in all generations. The term reformulation was used because of the emphasis on dynastic utility model of altruism toward children and deriving the budget constraint and utility function of a dynastic family the model was applied to the Great Depression and World War II. The 1st-order conditions to maximize utility imply that fertility in any generation depends positively on the real interest rate and the degree of altruism and negatively on the rate of growth in per capita consumption from 1 generation to the next. Consumption of each descendant depends positively on the net cost of rearing a desdendant. Applying the model it is shown that the analysis is consistent with baby busts during the Depression and the war and with a baby boom after the war. The effects on fertility of child mortality subsidies to (or taxes on) children and social security and other transfer payments to adults were considered. The demand for surviving children rises during the transition to low child mortality but demand for survivors return to its prior level once mortality stabilizes at a low level. Fertility falls in response to declines in international real interest rates and increases in an economys rate of technological progress. Extending the analysis to include life-cycle variations in consumption earnings and utility fertility emerges as a function of expenditures on the subsistence and human capital of children but not of expenditures that simply raise the consumption of children. The path of aggregate consumption in demographic steady states does not depend on interest rates time preference or other determinants of life-cycle variations in consumption.