An equation describing the set of Pareto-efficient allocations in an economy with a public good. In an economy with one public good, one private good, and H consumers, the Samuelson rule requires thatwhere
is the marginal rate of substitution for consumer h between the public good, G, and the private good, x, and MRTG, x is the marginal rate of transformation between G and x. The marginal rate of substitution should be interpreted as a measure of marginal benefit and the marginal rate of transformation as a measure of marginal cost. The marginal benefits are summed since an additional unit of the public good benefits all consumers.