Quantity constrained equilibria

In a standard general equilibrium model it is assumed that there are no price restictionsand that prices adjust infinitely fast to their equilibrium values. In this paper the set ofadmissible prices is allowed to be an arbitrary convex set. For such an arbitrary set it cannotbe guaranteed that there exists a constrained equilibrium satisfying the usual condition that aprice will be on its upper or lower bound in case of rationing. Therefore we introduce a moregeneral equilibrium concept, called Quantity Constrained Equilibrium (QCE). At such an equilibriumthe levels of supply and demand rationing are completely determined by the components of adirection in which the price system cannot be moved further without leaving the set of admissibleprices. When the set is compact, we show the existence of a connected set of QCEs, containing twotrivial no-trade equilibria. Moreover, the set contains for every commodity a generalized Drèzeequilibrium, being a QCE at which this commodity is not being rationed, and also a generalizedsupply-constrained equilibrium without demand rationing. We apply this main result to severalspecial cases, including the case of an unbounded set of admissible prices.