Arbitrary small indivisibilities may play an important role when the strong survival assumption does not hold. A hierarchic price is a finite ordered family of price vectors <InlineEquation ID="Equ1"> <EquationSource Format="TEX"><![CDATA[$\{p_1,\ldots ,p_k\}$]]></EquationSource> </InlineEquation>. It extends the notion of exchange values proposed by Gay [15]. These price notions were introduced in order to...</equationsource></inlineequation>

Without a survival assumption, a Walras equilibrium may fail to exist. Only the existence of a quasi-equilibrium can be proven. Several notions of irreducibility were proposed in order to allow a weakening of the survival assumption. We introduce an irreducibility condition which generalizes...

We study an economy where all goods entering preferences or production processes are indivisible. Fiat money not entering consumers' preferences is an additional perfectly divisible parameter. We establish a First and Second Welfare Theorem and a core equivalence result for the rationing...