We extend to multiple private commodities the seminal model by Bergstrom et al. (J Public Econ 29:25–49, 1986) on the private provision of public goods. Considering the relative value of the aggregate donations, we define a notion of equilibrium and show its existence. We analyze the effects of resource redistributions on the equilibrium outcome, identifying conditions that guarantee neutrality. We study some further properties of the contribution equilibrium, and provide a strategic market game approach, defining a sequence of non-cooperative games whose equilibria converge to an equilibrium of the economy.