Reformulating marginal productivity theory by replacing productivity with respect to commodities with productivity with respect to persons and then defining perfectly competitive equilibrium as an allocation at which each person receives the marginal product of his/her contribution--called a no-surplus allocation--there emerges a competitive theory of price determination. Characterizations of no-surplus allocations are given in models with a nonatomic continuum of agents and an infinite-dimensional commodity space. Comparisons between the no-surplus and Walrasian equilibrium definitions of competitive equilibrium are made and some sufficient conditions are obtained for the existence of a no-surplus allocation.