The final Chap. 10 develops in detail Richter’s Theorem (Richter, Preferences, Utility, and Demand, pp. 29–58. Harcourt Brace Jovanovich, New York, 1971) concerning the existence of nonstandard utility representations. It then introduces a nonstandard formulation of Gerard Debreu’s concept of a social system, proves the existence of equilibria for social systems, and concludes with an application of the concept to economic theory, specifically to the theory of pure exchange. It is shown in detail that equilibrium in pure exchange structures is a special case of equilibrium of a social system.