(Question 1)

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 u1 and u2, respectively. (a) Define the function v : R2 - R by v(21, X2) = min ful (21, x2), u2(21, 202) } . Is the preference ordering represented by the utility function v convex? (b) Define the function w : R2 - R by w (1, 2) = u1 (1, 2) + u2(21, 202). Is the preference ordering represented by the utility function w convex?Anna's preference ordering is represented by the utility function 1 ! 1n (V 2593;122:3232) where :51 denotes her consumption of good 1 and 3:2 denotes her consumption of good 2. Compute Anna's demand functions 3:1(m, $31,332), 33207;, p1, p2). \"(3713372) =