The Dynamics of Wealth Inequality under Endogenous Fertility: A Remark on the Barro-Becker Model with Heterogenous Endowments

Stefano Bosi, Raouf Boucekkine, Thomas Seegmuller

CNRS and GREQAM, Paris, France.
IRES and CORE, Catholic University of Louvain, Louvain-La-Neuve, Belgium;GREQAM, Aix-Marseille University, Marseille, France.
THEMA and University of Cergy-Pontoise, Cergy, France.

DOI: 10.4236/tel.[phone]                

Abstract

Implicit in the seminal contribution of Barro-Becker [1], the lack of persistence of inequality in the pre- sence 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.

Keywords

Endogenous Fertility, Heterogeneous Households, Optimal Growth

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	F. Alvarez, “Social Mobility: The Barro-Becker Children Meet the Laitner-Loury Dynasties,” Review of Economic Dynamics, Vol. 2, No. 1, 1999, pp. 65-103. doi:10.1006/redy.1998.0052
[2]	R. J. Barro and G. S. Becker, “Fertility Choice in a Model of Economic Growth,” Econometrica, Vol. 57, No. 2, 1989, pp. 481-501. doi:10.2307/1912563
[3]	G. S. Becker and R. J. Barro, “A Reformulation of the Economic Theory of Fertility,” Quarterly Journal of Eco- nomics, Vol. 103, No. 1, 1988, pp. 1-25. doi:10.2307/1882640
[4]	G. S. Becker and R. J. Barro “A Reformulation of the Economic Theory of Fertility,” The Quarterly Journal of Economics, Vol. 103, No. 1, 1988, pp. 1-25. doi:10.2307/1882640
[5]	S. Bosi and T. Seegmuller, “Mortality Differential and Growth: What Do We Learn from the Barro-Becker Mo- del?” Mathematical Popula-tion Studies, Forthcoming, 2010.
[6]	F. Caselli and J. Ventura, “A Representative Consumer Theory of Distri-bution,” American Economic Review, Vol. 90, No. 4, 2000, pp. 909-926. doi:10.1257/aer.90.4.909
[7]	S. Chatterjee, “Transitional Dynamics and the Distribution of Wealth in a Neoclassical Growth Model,” Journal of Public Economics, Vol. 54, No. 1, 1994, pp. 97-119. doi:10.1016/0047-2727(94)90072-8
[8]	C. Gar-cia-Pe?alosa and S. J. Turnovsky, “The Dynamics of Wealth Inequality in a Simple Ramsey Model: A Note on the Role of Production Flexibility,” Macroeconomic Dy-namics, Vol. 13, No. 2, 2009, pp. 250-262. doi:10.1017/S1365100508070508