x*>x*(p)for叫lp1<1 Continuity gives you the existence of a price where consumers are indifferent Consider, the sequence x**(p1 -nand the sequence x*, where x**(pI-m)2x* for all n, continuity implies that x**(p12x Likewise consider the sequences x**(pI+n)and x, where x**(PI+D<x* for all n, So x**(p1)<x* which together imply that x**(PI)Nx* Thus each person has a price at which he is indifferent between consuming commodity one and not doing so In this case, individual demand is always downward sloping -no income effects orx  xp1  for all p1   p1. Continuity gives you the existence of a price where consumers are indifferent. Consider, the sequence xp1  1 n  and the sequence x, where xp1  1 n   x for all n, continuity implies that xp1  x . Likewise consider the sequences xp1  1 n  and x, where xp1  1 n   x for all n, so xp1  x which together imply that xp1   x. Thus each person has a price at which he is indifferent between consuming commodity one and not doing so. In this case, individual demand is always downward sloping– no income effects or