Abstract
Parfit’s Repugnant Conclusion stipulates that under total utilitarianism, it might be optimal to choose increasing population size while consumption per capita goes to zero. We evaluate this claim within a canonical AK model with endogenous population size and a reduced form relationship between demographic and economic growth. First we characterize the optimal solution paths for any capital dilution function. Second, we prove that while the Repugnant Conclusion can never occur for realistic values of intertemporal substitution in the traditional linear dilution model, it does occur when population growth is linked to economic growth via an inverted U-shaped relationship.
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Notes
The theorem does not include the case σ = 1. To simplify the exposition, we exclude this special case, which can be also treated with the dynamic programming approach used in this paper but requires a different proof.
It should be noted that both conditions ρ “large enough” or “A low enough” are always compatible with the value-function boundedness condition 6.
It is worth pointing out here that the mechanism behind this particular result, namely behind the fact that optimal population rate is a decreasing function of the intertemporal altruism parameter γ, is identical to the one in Palivos and Yip: the case for which we get the latter property corresponds exactly to the case where instantaneous utility is negative.
One can check that such general conditions, while mathematically trivial to obtain, are not very useful economically speaking.
Considering the more general parameterization, μ(n) = αn + β, with β > 0 measuring the non-demographic depreciation rate of capital, will not alter the main results listed below.
For example, one can study the implications of using the so-called dynamic average utilitarianism as invoked in Arrow et al. (2004), that’s a social welfare function of the form \(\frac{\int_0^{+\infty} e^{-\rho t} \frac{ c^{1-\sigma}(t)}{1-\sigma} N(t) {\,\mathrm{d}} t}{\int_0^{+\infty} e^{-\rho t} N(t) {\,\mathrm{d}} t}\).
References
Arrow K, Dasgupta P, Goulder L, Daly G et al (2004) Are We Consuming Too Much?. J Econ Perspect 18(3):147–172
Arrow K, Bensoussan A, Feng Q, Sethi S (2010) The Genuine Savings Criterion and the Value of Population in an Economy with Endogenous Fertility Rate. In: Boucekkine R, Hritonenko N, Yatsenko Y (eds) Optimal control of age-structured populations in economy, demography, and the environment. Taylor and Francis, London
Bardi M, Capuzzo Dolcetta I (1997) Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Springer, Berlin
Blanchet D (1988) Age structure and capital dilution effects in neo-classical growth models. J Popul Econ 1(3):183–194
Boucekkine R, de la Croix D and Licandro O (2002) Human vintage capital, demographic trends and endogenous growth. J Econ Theory 104(2):340–375
Bucci A (2008) Population growth in a model of economic growth with human capital accumulation and horizontal R&D. J Macroecon 30(3):1124–1147
Edgeworth F (1925) Papers relating to political economy, vol III. Macmillan, London
Henry D (1981) Geometric theory of semilinear parabolic equations. Lecture notes in mathematics 840. Springer, Berlin
Kelley A, Schmidt RM (1995) Aggregate population and economic growth correlations: the role of the components of demographic changes. Demography 32(4):543–555
Kelley A (1988) Economic consequences of population change in the third world. J Econ Lit 26(4):1685–1728
Parfit D (1984) Reasons and persons. Oxford University Press, Oxford
Nerlove M, Razin A, Sadka E (1985) Population size: individual choice and social optima. Q J Econ 100(2):321–334
Palivos T, Yip CK (1993) Optimal population size and endogenous growth. Econ Lett 41(1):107–110
Razin A, Yuen CW (1995) Utilitarian tradeoff between population growth and income growth. J Popul Econ 8(1):81–87
Strulik H (2005) The role of human capital and population growth in r&d-based models of economic growth. Rev Int Econ 13(1):129–145
Acknowledgements
This paper has benefitted from useful feedback from two anonymous referees and an editor of this journal, David de la Croix, Gustav Feichtinger, Fausto Gozzi, Axel Gosseries, Vladimir Veliov and participants in the 2009 Viennese Vintage Workshop and the 2010 Lisbon Euro conference. The authors acknowledges financial support from the French Speaking Community of Belgium though an ARC grant 09/14-018 on Sustainability.
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Boucekkine, R., Fabbri, G. Assessing Parfit’s Repugnant Conclusion within a canonical endogenous growth set-up. J Popul Econ 26, 751–767 (2013). https://doi.org/10.1007/s00148-011-0384-6
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DOI: https://doi.org/10.1007/s00148-011-0384-6