Characterizations of Long-Run Producer Optimum

This gives characterizations of long-run producer optimum for a general convex technology. Each is either an optimization system or a differential system (i.e., a set of conditions put in terms of either the marginal optimal values or the optimal solutions to a primal-dual pair of programmes). One system is singled out because of its importance to applications. It is the Split SRP Optimization System, which serves as the preferred basis for the short-run approach because the technology of electricity generation is best described by production sets, and because short-run cost (SRC) minimization for each separate plant is easily split off as a subprogramme of short-run profit (SRP) maximization. The first differential system presented is the SRC/P Partial Differential System, which generalizes Boiteux’s original set of conditions. The L/SRC Partial Differential System has the same mathematical form but uses the LRC instead of the SRP. Equivalence of the two systems extends, to nondifferentiable costs, the Wong-Viner Envelope Theorem on equality of SRMC and LRMC. This is made possible by using the subdifferential as a generalized, multi-valued derivative, and by replacing input optimality with the stronger condition that the rental prices be equal to the profit-imputed values of the fixed inputs. The values must be based on increments to the operating profit (it is ineffective to try to value capacity increments by reductions in a nondifferentiable operating cost).