Problem 1 (10 points) Let ~1 and 2 be two convex preference orderings over the space R2 of consumption bundles. Assume that these preference orderings are represented by the utility functions uj and u2, respectively. (a) Define the function v : R2 - R by v(1, 2) = min {ul (x1, (2), U2(21, 22) } . Is the preference ordering represented by the utility function v convex? (b) Define the function w : R4 - R by w (1, 2) = ul (21, X2) + u2(21, 202). Is the preference ordering represented by the utility function w convex