Implicit in the seminal contribution of Barro-Becker [1], the lack of persistence of inequality in the presence of endogenous fertility is one of the most striking features of the models à la Barro-Becker. In this pedagogical note, we show how to uncover and interpret the latter property using standard optimization in contrast to the dynamic programming under homogeneity usually invoked in this literature.
Bosi, S., Boucekkine, R., & Seegmuller, T. (2011). The Dynamics of Wealth Inequality under Endogenous Fertility: A Remark on the Barro-Becker Model with Heterogenous Endowments. Theoretical Economics Letters, 1(1), 3-7. https://doi.org/10.4236/tel.2011.11002 (Original work published 2011)