The Spaceship Problem Re-Examined
This paper re-examines the spaceship problem, i.e. the design of the optimal population under the environmental constraint of a fixed area available for life, by focusing on the dilemma between adding new beings and extending the life of existing beings. For that purpose, we characterize, under the assumption that individual lifetime welfare depends positively on the length of life but negatively on population density, the preference ordering of a utilitarian planner over lifetime-equal histories, i.e. pairs of initial population size and survival conditions yielding an equal number of life periods. It is shown that a Benthamite planner is not necessarily indifferent between lifetime-equal histories, and that a Millian utilitarian planner prefers lifetime-equal histories yielding the smallest population with the longest life. The solutions under Critical-level and Number-dampened utilitarianisms are also shown to differ significantly.
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International Economic Review,
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