Egalitarism under Population Change: The Role of Growth and Lifetime Span

We study the compatibility of the optimal population size concepts produced by different social welfare functions and egalitarism meant as "equal consumption for all individuals of all generations". Social welfare functions are parameterized by an altruism parameter generating the Benthamite and Millian criteria as polar cases. The economy considered is in continuous time and is populated by homogenous cohorts with a given life span. Production functions are linear in labor, (costly) procreation is the unique way to transfer resources forward in time. First, we show that egalitarism is optimal whatever the degree of altruism when life spans are infinite. That is egalitarism does not discriminate between the social welfare functions considered. However, when life spans are finite, egalitarism does not arise systematically as an optimal outcome. In particular, it depends on the degree of altruism, and also on the magnitude of the life span. In particular, to be enforced in a growing economy, that is when population growth is optimal in the long-run, this egalitarian rule can only hold when (i) the welfare function is Benthamite, (ii) and for a large enough life span. When altruism is impure, egalitarism is impossible in the context of a growing economy. Either in the Millian case, whatever the life span, or in the Benthamite/impure altruism cases, for small enough life spans, procreation is never optimal, leading to finite time extinction and maximal consumption for all existing individuals.