Utilitarianism and social discounting with countably many generations

We extend Harsanyi's (1955) utilitarianism theorem to an infinite-horizon multi-generation setting: Under some additional assumptions, the Pareto condition is equivalent to utilitarian aggregation and the utilitarian weights are unique. We analyze the properties of utilitarian weights, such as the limiting behavior of utilitarian weights for distant future generations, and the comparative statics of utilitarian weights as the social discount factor or the social risk attitude changes. Among other findings, we show that a higher social discount rate is associated with a more unequal assignment of utilitarian weights across generations.