Utilitarian tradeoff between population growth and income growth

Utilitarian social welfare functions were devised for a world with a fixed population. With endogenous population, Edgeworth conjectured that the Benthamite principle of maximizing total utility (classical utilitarianism) would lead to a larger population size and a lower standard of living than the Millian principle of maximizing per capita utility (average utilitarianism). One objection to the Benthamite criterion was that its application to a world with finite resources often implied large population size in conjunction with an ‘embarrassingly low’ average standard of living. In a static environment with altruistic parents, this may not be warranted. In a growth situation, this criticism is even less likely to be supported. This paper extends the comparison of classical and average utilitarianism from a static to a dynamic and endogenously growing economy. Using a stylised endogenous growth framework, it confirms that the Benthamite population growth rate exceeds the Millian growth rate. In terms of the rate of growth of per capita income, the reverse is true. Having the standard of living often increasing under the Benthamite criterion, our results thereby depart significantly from ‘the repugnant conclusion’ levelled against classical utilitarianism.