Arbitrary small indivisibilities

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 establish the existence of a generalized competitive equilibrium without the strong survival assumption. We show that a hierarchic price models phenomena related to small indivisibilities which the standard approach may not capture. More precisely, we prove in the framework of linear exchange economies that a hierarchic price may be seen as a standard price of an economy with arbitrary small indivisibilities. Copyright Springer-Verlag Berlin Heidelberg 2003