This is the first of several chapters that analyze the structure of socially optimal solutions delivered by particular social welfare functions. It addresses the simple cases of utilitarian and maximin (Ralwsian) functions as preparation for the more lengthy analyses to follow. It describes the optimal solutions of both distribution problems, subject to a budget constraint and utility bounds, and notes that both problems are regionally decomposable due to the monotone separability of the social welfare functions. It concludes with a straightforward marginal analysis of stakeholder incentives to improve their efficiency of resource usage, while observing that a utilitarian criterion encourages competition, and a maximin criterion encourages cooperation.