Department of Economics. University of Melbourne. Parkville Victoria 3052 Australia
ABSTRACT
This paper introduces, within a general equilibrium setting, an alternate theory of value that provides a value-based characterization of the most important notions of allocative equilibria even in cases wehre the (Walrasian) uniform price-based characherizations need not be applicable. The value is calculated in terms of the maximum revenue outcome of a discriminatory price auction for divisible goods.
Consumers participate in an auction that is closely related to the Treasury Bill Auction. Their bids have two components: a consumption seet and a price system. The aucioneer divides commodity bundles into consumable allocations that maximize revenue-we call the maximizing allocations auctioneer's allocations. Each consumer pays the price she bids. The resulting value function is called an auction price- which is not necessarily linear and in the single commodity setting its values coincide with the total revenues of the Treasury Bill Auction. By means of the auction prices we characterize Pareto optimality, Edgeworth and Walrasian equilibria as auctioneer's allocations of our Trasury Bill-like action.
Remarkably, we see aht the auction prices are more linear when greater divisibility of commodity bundles is allowed; something that seems to be common knowledge in the auction business. In fact, when we reach perfect divisbility, the auction prices become linear- and we are in the classical Arrow-Debreu-McKenzie world. Our approach treats both the standard Walrasian model with linear prices and our new model with auction prices. The analysis applies equally well to models with ordered and unordered preferences. The established theorems contain a smorgasboard of consequences, including the most important existence of equilibrium results in the literature.
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