Characterizations of long-run producer optima and the short-runapproach to long-run market equilibrium: a general theory withapplications to peak-load pricing
AbstractThis is a new formal framework for the theory of competitive equilibrium and its applications.Our "short-run approach" means the calculation of long-run producer optimaand general equilibria from the short-run solutions to the producer's profit maximizationprogramme and its dual. The marginal interpretation of the dual solution means that itcan be used to value the capital and other fixed inputs, whose levels are then adjustedaccordingly (where possible). But short-run profit can be a nondifferentiable function ofthe fixed quantities, and the short-run cost is nondifferentiable whenever there is a rigidcapacity constraint. Nondifferentiability of the optimal value requires the introductionof nonsmooth calculus into equilibrium analysis, and subdifferential generalizations ofsmooth-calculus results of microeconomics are given, including the key Wong-Viner EnvelopeTheorem. This resolves long-standing discrepancies between "textbook theory"and industrial experience. The other tool employed to characterise long-run produceroptima is a primal-dual pair of programmes. Both marginalist and programming characterizationsof producer optima are given in a taxonomy of seventeen equivalent systemsof conditions. When the technology is described by production sets, the most usefulsystem for the short-run approach is that using the short-run profit programme andits dual. This programme pair is employed to set up a formal framework for long-rungeneral-equilibrium pricing of a range of commodities with joint costs of production.This gives a practical method that finds the short-run general equilibrium en route tothe long-run equilibrium, exploiting the operating policies and plant valuations that mustbe determined anyway. These critical short-run solutions have relatively simple formsthat can greatly ease the fixed-point problem of solving for equilibrium, as is shownon an electricity pricing example. Applicable criteria are given for the existence of theshort-run solutions and for the absence of a duality gap. The general analysis is speltout for technologies with conditionally fixed coefficients, a concept extending that of thefixed-coefficients production function to the case of multiple outputs. The short-run approachis applied to the peak-load pricing of electricity generated by thermal, hydro andpumped-storage plants. This gives, for the first time, a sound method of valuing thefixed assets-in this case, river flows and the sites suitable for reservoirs.
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Bibliographic InfoPaper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Theoretical Economics Paper Series with number /2005/490.
Date of creation: May 2005
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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp
general equilibrium; fixed-input valuation; nondifferentiable joint costs; Wong-Viner Envelope Theorem; public utility pricing;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
- D46 - Microeconomics - - Market Structure and Pricing - - - Value Theory
- D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models
- L94 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Electric Utilities
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-02-26 (All new papers)
- NEP-ENE-2006-02-26 (Energy Economics)
- NEP-MIC-2006-02-26 (Microeconomics)
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