The Becker Fertility Model: Theory and Critique

This paper is an exploration of the theoretical properties of the Becker fertility model. I demonstrate that the comparative statics of the Becker fertility model with a general budget constraint and its corresponding expenditure model can be expressed in terms of the ordinary consumer expenditure function with a change of variable. When there are no fixed-costs of quality per child, the Becker fertility model is equivalent to the ordinary consumer model with restrictions on the form of the utility function. Solutions to the Becker fertility model are provided with the Cobb-Douglas, CES, and AIDS specifications under this assumption, Becker’s hypothesis that demand for quality per child increases with income is not valid under any Cobb-Douglas or CES specification, but can be tested with a valid estimation of the AIDS model. I also evaluate the role of fixed-costs of quality per child in Becker’s model and show that they introduce a third term into the Slutsky matrix, i.e. in addition to ordinary substitution and income effects, but that these effects are small when the average fixed costs of quality per child is small relative to the marginal cost of quality per child. When the Becker model is expressed in terms of children, quality, and other goods, children must be a substitute for either their quality or for other goods and either quality or other goods must be a luxury good.