In a standard general equilibrium model it is assumed that there are no price restictions and that prices adjust infinitely fast to their equilibrium values. In this paper the set of admissible prices is allowed to be an arbitrary convex set. For such an arbitrary set it cannot be guaranteed that there exists a constrained equilibrium satisfying the usual condition that a price will be on its upper or lower bound in case of rationing. Therefore we introduce a more general equilibrium concept, called Quantity Constrained Equilibrium (QCE). At such an equilibrium the levels of supply and demand rationing are completely determined by the components of a direction in which the price system cannot be moved further without leaving the set of admissible prices. When the set is compact, we show the existence of a connected set of QCEs, containing two trivial no-trade equilibria. Moreover, the set contains for every commodity a generalized Drèze equilibrium, being a QCE at which this commodity is not being rationed, and also a generalized supply-constrained equilibrium without demand rationing. We apply this main result to several special cases, including the case of an unbounded set of admissible prices.
The text is part of a series Tinbergen Institute Discussion Papers Number 01-116/1
Classification:
C62 - Existence and Stability Conditions of Equilibrium ; C63 - Computational Techniques ; C68 - Computable General Equilibrium Models ; D51 - Exchange and Production Economies
