The existence of walrasian equilibrium fz:s4-1→>鸦 is a continuous function witch satisfied Walras' law, pz(p)=0, then there exist some p in s-l such that z(p)<0 Construct a unit simplex: P, K k s={pinW:∑ P1= k-1 Defined 8.S> 8, (p) p,+max(0, z, (p)) 1+ j-max(0, =, (p)The existence of Walrasian equilibrium • If is a continuous function witch satisfied Walras’ law, , then there exist some in such that . – Construct a unit simplex: – Defined 1 : k k z s − →  p p z( ) 0 =  p k 1 s − z( ) 0  p  1 i i K j j p p p = =  1 1 { in : 1 k k k i i s p − = =  = p  1 1 : k k g s s − − → 1 max(0, ( )) ( ) 1 max(0, ( ) i i i K j j p z g z = + = + p p p