The“core Shrinking core: there is a unique market equilibrium x' from initial endowment w if y is not the equilibrium, there is some replication r, such that y is not in the r-core Proof: since y is not the equilibrium, there is another allocation g improve upon A(or B)at least. That means see the 8=8w+(1-a)y for some 8>0 Let a=T/V(T and V are integers)The “core” • Shrinking core: there is a unique market equilibrium x * from initial endowment w. if y is not the equilibrium, there is some replication r, such that y is not in the r-core. Proof: since y is not the equilibrium, there is another allocation g improve upon A(or B) at least. That means see the fig. – Let (T and V are integers) (1 ) for some 0 A A g w y = + −      =T V/