Problem B1. (12 points). Consumer Theory: Consumer's choice and compensation. Happy Goluki likes tea (good 1) and cookies (good 2). Her preferences are represented by the utility function U(q1,q2) = (q1)1/3+ (qz)1/3, where q1 is the number of cups of tea and q; is the number of cookies. Goluki is given I = $108 that she is allowed to spend as she wishes on tea and cookies. 6) b) d) Calculate Goluki's optimal bundle if the price of tea is p1=$4 and the price of cookies is p2=$1. Call this bundle A and show it on a diagram (put tea on the horizontal axis). Suppose that the price of tea increases to $9 (I know, I can't believe it either, but Melbourne does have some very fancy tea places) and the price of cookies stays the same. Calculate Goluki's new optimal bundle of tea and cookies (call it bundle B). Show it on a diagram om part a). Calculate the income required so that Goluki can obtain the same utility as from the original bundle (from part a) but at the new prices. Calculate this new bundle, call it bundle C and show it on the diagram from part a). What is the total effect, income effect and substitution effect (on tea) of an increase in price of tea from $4 to $9? Show them on a diagram from part a). Goluki's parents are willing to compensate her for an increase in prices. They consider two different options, described below in e) and f). 6) g) If they want to make her as well-off as she was before the price increase, how much extra money would they have to give her? This amount is called the compensating variation. What bundle will she consume? Goluki's parents can give her enough money, so that she can afford the same combination of tea and cookies, as in part a), at the new prices. Find her new optimal bundle (call it F) in that case and show it on the same diagram as in part (1). Is Goluki better off with bundle F or with the bundle chosen in part e)? Should Goluki's parents give her extra money as in part e) or in part f), if their aim is to compensate her for price increase? Briey explain