Vanishing Indivisibilities in Linear Exchange Economies.

A hierarchic price is a finite ordered family of price vectors {p1,...,pk}. It extends the notion of exchange values proposed by Gay (1978). These price notions were introduced in order to establish the existence of a competitive equilibrium without the strong survival assumption. It is well known that without such an assumption a standard Walras equilibrium need not exist. We prove in the framework of linear exchange economies that a hierarchic price may be seen as a standard price of an economy with small indivisibilities.