In the received model of the voluntary provision of a pure public good, the usual practice is to proceed from assumptions about the group characteristics to inferences about an implied outcome. The approach advocated in this paper reverses the traditional direction. Assuming a Nash equilibrium, we ask how to characterize the diverse set of group characteristics which will support it. Approaching the problem from this angle we define three crucial characteristics of a group-equilibrium: consumer's “free rider inducing supply,” “zero contribution-inducing wealth” and “voluntary surplus tribute” which is the amount by which a person's actual income exceeds his/her “zero-contribution inducing wealth.” Defining these indicators we show how they form the foundation of a complete mapping between the distribution of individual characteristics of a group, and equilibrium public good supply. Certain questions such as the interaction between size of the group and heterogeneity of incomes and tastes not yet adequately addressed are shown to yield easily to this approach.