. (1+1 =2 points) Find utility functions given each of the following indifference curves [express k as a function of x,y, 2, as applicable] km; _ xafo'yfd b. y = 0541-3 40;2 k) 0.5x . (1+1 = 2 points) CES Utility " 5 a. Show that the CES function a? + [3% is homothetic. b. Show that homotheticity holds in the cases where (5' = 1 (perfect substitutes), and 6 = 0 (CobbDouglas). ELZ . (2+2 = 4 points) a. A young connoisseur has $600 to spend to build a small wine cellar. She enjoys two vintages in particular: a 2001 French Bordeaux (3') at $40 per bottle and a less expensive 2005 California varietal wine (6) priced at $8. If her utility is given by U (e) = f2! 3613, then how much of each wine would she purchase? b. When she arrived at the wine store, she discovered that the price of the French Bordeaux had fallen to $20 a bottle. If the price of the California wine remains stable at $8 per bottle, how much of each wine should she purchase to maximize utility under these altered conditions? Is she better off in part (b) or part (a)