The existence of walrasian equilibrium Brouwer's fixed-point theorem: continuous function f: s">",(s is a unit simplex) and there exist an x, that x=f(x) Scarf, 1973 when n=1; let g(x)=f(x)-J g(0)=f(0)-0≥0;g(1)=f(1)-1≤0 彐x,g(x)=0=f(x)-xThe existence of Walrasian equilibrium • Brouwer’s fixed-point theorem: continuous function , ( is a unit simplex) and there exist an x, that: • Scarf,1973. • when n=1;let g(x)=f(x)-x, : n n f s s → x x = f ( ) g f g f (0) (0) 0 0; (1) (1) 1 0 = −  = −   = = − x g x f x x , ( ) 0 ( ) n s