We have already proven that Marshallian demand is homogeneous of degree zero, this implies that indirect utility is homogeneous of degree zero Nonincreasing in p follows from the fact that if p falls you can always buy the old bundle and thus be no worse off Increasing in w uses that fact plus local non-satiation with an increase in w you can always buy the old bundle plus a little bit more of the good that you are not satiated with Continuity I leave up to youWe have already proven that Marshallian demand is homogeneous of degree zero, this implies that indirect utility is homogeneous of degree zero. Nonincreasing in p follows from the fact that if p falls you can always buy the old bundle, and thus be no worse off. Increasing in w uses that fact plus local non-satiation: with an increase in w you can always buy the old bundle plus a little bit more of the good that you are not satiated with. Continuity I leave up to you