Walrasian equilibrium as limit of a competitive equilibrium without divisible goods

Abstract

We study economies where all commodities are indivisible at the individual level, but perfectly divisible at the aggregate level of the economy. Under the survival assumption, we show that a competitive outcome in the discrete economy, called rationing equilibrium, converges to a Walras equilibrium of the limit economy when the level of indivisibility becomes small. If the survival assumption does not hold at the limit economy, then the rationing equilibrium converges to a hierarchic equilibrium