On Nonlinear Pricing

Nonlinear prices are commonly observed in market economies. This paper investigates nonlinear pricing under general conditions. It explores how nonlinear pricing can arise under nonconvexity. The arguments are presented in the context of an optimization problem, where a separating hypersurface provides information on pricing under general nonconvexity. The analysis applies to efficiency assessments, noting that Pareto efficiency can be expressed as the maximization of aggregate benefit. When nonconvexity requires a nonlinear separating hypersurface, this implies that nonlinear pricing becomes an integral part of efficiency analysis. This evaluation applies to nonmarket goods (e.g., the pricing of carbon emission) as well as market goods. We show how nonlinear pricing depends on the nature of nonconvexity. We discuss how associated price discrimination schemes can be implemented to support efficient allocations.