Properties of the indirect utility function MWG Proposition 3. D. 3: Suppose that u(is a continuous utility function representing a locally non-satiated preference relation z defined on the consumption set R+. The indirect utility function v(p w)IS (a homogeneous of degree zero (b) strictly increasing in w and non-Increasing In p, (c)quasiconvex; that is, the set ip, w): v(p, w)<y is convex for any 2, and (d)continuous in p and wProperties of the indirect utility function. MWG Proposition 3.D.3: Suppose that u. is a continuous utility function representing a locally non-satiated preference relation  defined on the consumption set  L. The indirect utility function vp,w is: (a) homogeneous of degree zero, (b) strictly increasing in w and non-increasing in p, (c) quasiconvex; that is, the set p,w : vp,w  v is convex for any v, and (d) continuous in p and w