Introduction and contents In this paper, we study an exchange economy where allocation of resources is guided by a price mechanism, but prices are subject to inequality constraints. An equilibrium is obtained by introducing quantity constraints on the net trades of those commodities for which the price constraints are binding. The set of admissible quantity constraints is defined in a way which avoids trivial equilibria. Two kinds of price rigidities are considered in turn, namely constraints on nominal prices in an economy with a numeraire (Sections 4 and 5) and constraints on relative or real prices in an economy without a numeraire (Section 6). The two kinds are then considered simultaneously (Section 7). In each case, we find that inequality constraints on net trades may be substituted for price adjustments, one-to-one, as devices to equate supply and demand. (Clearly, this is a statement about feasibility, not about efficiency.) Some background remarks on price rigidities and quantity rationing (Section 2) precede the description of the model (Section 3). The results are so organized that the basic technique of proof is introduced first on a simple problem (constraints on all nominal prices); the technique is then extended in two directions (constraints on some but not all nominal prices, constraints on all real prices); these extensions are combined in a final theorem, of which the first three are special cases (constraints on some nominal and/or some real prices).
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