Which condition strictly differentiates the Samuelson Condition for the optimal provision of pure public goods from private goods efficiency?

For a private good, each consumer consumes a separate quantity. The efficiency condition is that every individual’s MRS must equal the MRT, so that MRS(1) = MRS(2) = ... = MRT. This is option (B). Option (E) is the same condition in a competitive market, where each MRS and the MRT equal the price ratio. For a pure public good, every individual consumes the same quantity. One additional unit therefore benefits all the individuals together, and the social marginal benefit is the sum of the individual marginal valuations. Efficiency requires this sum to be equal to the marginal cost of producing the public good in terms of the private good: Sum of MRS(i) = MRT It is the only valid condition in the list that sums MRS across individuals. Option (C) is not a valid statement, because the MRT is a single technological rate and is not summed across individuals. In option (D), the personal (Lindahl) prices generally differ across consumers, since each is based on the individual’s own valuation. They only need to add up to MC. Hence the correct option is (A).