The demand distribution is employed as a novel and powerful basis for analyzing monopoly provision of price-excludable public goods (and could be used to analyze other market structures or, in some circumstances, private goods provision). For (uniform) per-unit, all-or-none, two-part, and multipart pricing, we identify: Characteristics of revenue functions, relative profitability, and operational procedures for selecting price-output levels. Under all these strategies, rationing of some consumers by output is required, and a positive price-output relationship may arise. In general the revenue ranking of pricing strategies is sensitive to the distribution of demand and, though multipart pricing can be expected to be revenue dominant, uniform per-unit pricing emerges as a surprisingly robust strategy even before operational complexity is fully taken into account.

Geoffrey Brennan, Cliff Walsh; Private Markets in (Excludable) Public Goods: A Reexamination*, The Quarterly Journal of Economics, Volume 100, Issue 3, 1 A

The demand distribution is employed as a novel and powerful basis for analyzing monopoly provision of price-excludable public goods (and could be used to analyze other market structures or, in some circumstances, private goods provision). For (uniform) per-unit, all-or-none, two-part, and multipart pricing, we identify: Characteristics of revenue functions, relative profitability, and operational procedures for selecting price-output levels. Under all these strategies, rationing of some consumers by output is required, and a positive price-output relationship may arise. In general the revenue ranking of pricing strategies is sensitive to the distribution of demand and, though multipart pricing can be expected to be revenue dominant, uniform per-unit pricing emerges as a surprisingly robust strategy even before operational complexity is fully taken into account.