The existence of walrasian equilibrium Assumption3: market clearing Desirability: z(p)>0 for p,=0 lemma: free goods: if p" is a walrasian equilibrium price, andz, (p)<o, then p*=0 lemma: Equivalent of demand and supply: all the commodities are desirable and p is a walrasian equilibrium prIce, then, ( p)=0The existence of Walrasian equilibrium • Assumption3: market clearing • Desirability: • lemma1: free goods: if p * is a walrasian equilibrium price, and ,then • lemma2: Equivalent of demand and supply: all the commodities are desirable and p * is a walrasian equilibrium price, then ( ) 0 for 0 i z p p  = ( ) 0 j z p   0 j p  = ( ) 0 j z p  =