The shape of a preference function when one individual's utility depends not only upon his own rate of consumption, but also upon his neighbor's rate of consumption — second party preferences, 2. — Definitions of avaricious, altruistic, and egalitarian sentiment, 4. — Division of a fixed supply of commodities between two individuals, 6. — The maximum mazimorum of satisfaction when any move from an equilibrium position leaves all parties worse off, 12. — Some implications for welfare policies and programs, 15.