The Pareto optimal provision of a public good in a society occurs when the sum of the marginal valuations of the public good (taken across all individuals) is equal to the marginal cost of providing that public good. These marginal valuations are, formally, marginal rates of substitution relative to some reference private good, and the marginal cost is a marginal rate of transformation that describes how much of that private good it costs to produce an incremental unit of the public good.) This contrasts to the Pareto optimality condition of private goods, which equates each consumer's valuation of the private good to its marginal cost of production.