Answer to Question #1107 in Microeconomics for me

Question

Show that the indirect utility function V (p;w) is homogeneous of degree zero
and quasiconvex.

Answer 1

The homogeneousity& comes from the fact that if we multiply price and income by the same positive factor, the opportunity set (defined by the budget constraint) does not change, and therefore the choice made an the associated utility level will not change.
Quasi-convex: Formally it means that the sets {p: v(p,m) ! k} for any number k are convex. An implication is that if we draw the level curves of v(p,m) in the (p1,p2) space they will be convex toward the origin.