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Problem 1 (10 points) Let ~1 and

Problem 1 (10 points) Let and Z2 be two convex preference orderings over the space IR2 of consumption bundles. Assume that these preference orderings are represented by the utility functions ul and tL2, respectively. (a) Define the function v : IR2+ + IR by = min ul Cl,C2 , tL2 Cl,C2 V Cl,C2 Is the preference ordering represented by the utility function v convex? (b) Define the function w : + IR by = ul@l, C2) + U2@1, W Cl,C2 Is the preference ordering represented by the utility function w convex?