Optimal population size and endogenous growth

"Many applications in economics require the selection of an objective function which enables the comparison of allocations involving different population sizes. The two most commonly used criteria are the Benthamite and the Millian welfare functions, also known as classical and average utilitarianism, respectively. The former maximizes total utility of the society and thus represents individuals, while the latter maximizes average utility and so represents generations. Edgeworth (1925) was the first to conjecture, that the Benthamite principle leads to a larger population size and a lower standard of living.... The purpose of this paper is to examine Edgeworth's conjecture in an endogenous growth framework in which there are interactions between output and population growth rates. It is shown that, under conditions that ensure an optimum, the Benthamite criterion leads to smaller population and higher output growth rates than the Millian."