Quantity Constrained General Equilibrium

Abstract

In a standard general equilibrium model it is assumed that there are no price restrictions and that prices adjust infinitely fast to their equilibrium values.In case of price restrictions a general equilibrium may not exist and rationing on net demands or supplies is needed to clear the markets.In the mid 1970s it was shown that in case of upper and lower bound restrictions on the prices there exists a quantity constrained equilibrium at which not both demand and supply of a good are rationed simultaneously and there is rationing on the net supply or net demand of a good only if the price of that good is on its lower or upper bound, respectively.For an arbitrary set of admissible prices it was recently proposed to let the rationing schemes be determined by the components of a vector being a direction in which the prices are restricted to move.When the set of restricted prices is convex and compact, it was shown that there exists a connected set of such quantity constrained equilibria, containing two trivial no-trade equilibria without trade opportunities.In this paper we refine the concept of quantity constrained equilibrium and propose a specific quantity constrained equilibrium which may serve as a general equilibrium in case of price restrictions.At this equilibrium demand rationing and supply rationing are in balance with each other, so that trade opportunities are maximal and therefore trivial no-trade and other equilibria with less trade opportunities are excluded.Moreover, in equilibrium only relative prices matter. Any homogenous transformation or normalization of the set of admissible prices yields the same set of quantity constrained general equilibria up to scaling of the price vectors.

Keywords: exchange economy, price restrictions, general equilibrium, rationing

JEL Classification: C62, C63, C68, D51