The“core Walrasian equilibrium is in core Proof: let (x, p) be the Walrasian equilibrium with initial endowment wi If not there is some coalition s and some feasible allocation x,, such that all agents i in S strictly prefer Xi to X,,and∑x=∑ But Walrasian equilibrium implies x>p∑ w, for px>The “core” • Walrasian equilibrium is in core. – Proof: let (x,p) be the Walrasian equilibrium with initial endowment wi . – If not , there is some coalition S and some feasible allocation x’, such that all agents i in S strictly prefer to , and – But Walrasian equilibrium implies i x i  x i i i S i S w     x = for i i i i S i S w w   p x p px p      