On Supply-Constrained Equilibria

Introduction In the microeconomic literature on equilibrium under price rigidities and quantity rationing, starting with the work of Bénassy (1975), Drèze (1975) and Younès (1975), it has been customary to impose as part of the definition of equilibrium that a given numeraire commodity should not be rationed. This practice has two distinct motivations. On the one hand, it guarantees that at least one commodity is not rationed, thereby ruling out the trivial equilibrium enforced by rationing to zero the supply of all commodities or, alternatively, their demand. On the other hand, this practice provides a more realistic treatment of money as a numeraire, since quantity constraints on net trades of money are very rarely observed. This second motivation, unlike the first, requires that the never-constrained commodity be chosen a priori . For the remaining commodities, rationing may affect either supply or demand but not both sides of a same market simultaneously. This requirement of ‘orderly rationing’ (Hahn, 1978) seems generally accepted, at least to study systematic imbalance as distinct from frictional imbalance. It is supported by casual observations as well as theoretical arguments; see Malinvaud and Younès (1977b) and Grandmont et al . (1978). For a commodity with a predetermined price, the rationing may affect either side of the market. For a commodity with downward (resp. upward) price rigidity, rationing is limited to supply (resp. demand).