Only (g), (h),(i)

Alice and Bob live in a two-person two-good exchange economy. Their utility functions are UA(x1, x2 ) = (24) 3x4 UB(XP , x2 ) = 1x2 Their endowments are WA = (4, 4), WB = (8, 4) Note that I have not asked for any diagrams below, but you may find it useful to draw them. Show your work for all parts. (a) Find the equation for the set of all interior points on the contract curve. Please simplify it to express x2 as a function of act. (b) What two equations would determine the worst core outcome for Alice? You need not solve them, but please make sure both equations are in terms of of and x2. () What two equations would determine the best core outcome for Alice? You need not solve them, but please make sure both equations are in terms of of and x2 (d) Suppose the Walrasian auctioneer announces prices for both goods, with p1 = 1, i.e. Good 1 is the "numeraire." Find each player's gross demands for Good 1 in terms of p2. (e) Find p2 such that the markets clear. What is the resulting competitive allocation, i.e. how much of each good do Alice and Bob wind up with? The next part references part (3e), but you should still be able to answer it even if you didn't solve (3e). (f) From the Fundamental Welfare Theorem, we know that the allocation you found in part (3e) is in the core. How would you check this directly, i.e. what calculations would you perform? For the remaining parts, we switch Bob's utility function to UB(21 , 2-2) = (21 + xB) 37 but leave Alice's the same. (g) Find the equation for the set of all interior points on the contract curve, and simplify it to express x2 as a function of a f. (h) Find the market-clearing prices and competitive allocation. (i) One of Alice and Bob is no better off at the competitive allocation than at their endowment; which one? Only an answer is required. Even if you got stuck on the previous part, try to guess