x*(p1)={x∈Bo(p1):x≥ y for all y∈Bo Where B0(D1)= {x∈x:x1=1and∑h2 pixi w-pi Ifx*>(1,0,0.0)then there exists a p,[,w] for all pi>pl,x*<x**(pi) and x*x*(pi) for all pI< p. If preferences are continuous then where x*Nx* (p1) Proof: It is obviously true that there exist some values of p1∈[0,w] in which x*<x**(p1) and some values for x*>x**(p1), at the least x*<x**(O)and x*>x*(v)xp1   x  B0p1 : x  y for all y  B0 where B0p1  x  X : x1  1 and i2 L pixi  w  p1 . If x  1, 0, 0. . . 0 then there exists a  p1 0,w for all p1   p1, x  xp1  and x  xp1  for all p1   p1. If preferences are continuous then where x  x  p1 . Proof: It is obviously true that there exist some values of p1 0,w in which x  xp1  and some values for x  xp1 , at the least x  x0 and x  xw