Existence of Competitive Equilibrium with a System of Complete Prices
In classical equilibrium analysis it is assumed that consumers may purchase a given amount of good in any fraction he (she) wishes from any of a fixed number of firms. Sometimes, as with ski-lifts, at any one time it is only possible for consumers to purchase from one firm. An equilibrium price system is a complete price system. In this paper, a complete price system is a system of prices that varies between firms even though the product each firm sells may be identical. In addition as any consumer switches the firm that he (she) purchases from the price faced by all consumers may change and it is sometimes necessary to impose lump sum transfers between consumers and between firms and between consumers and firms. Congestion is allowed. Even if there are no non-convexities associated with the choice of firm by consumers then lump sum transfers may be needed to ensure that first best allocations are supported. The presence of non-convexities and congestion ensures that proof of existence of equilibrium is difficult. A weak proof of existence is given.
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- Gerard Debreu, 1961. "New Concepts and Techniques for Equilibrium Analysis," Cowles Foundation Discussion Papers 129, Cowles Foundation for Research in Economics, Yale University.
- Barro, Robert J & Romer, Paul M, 1987. "Ski-Lift Pricing, with Applications to Labor and Other," American Economic Review, American Economic Association, vol. 77(5), pages 875-90, December.
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