(g) Find the equation for the set of all interior points on the contract curve, and simplify it to express x2A as a function of x1A.(h) Find the market-clearing prices and competitive allocation.(i) One of Alice and Bob is no better off at the competitive allocation than their endowment; which one? only an answer is required.

are lice and Bob live in a two-person two-good exchange economy. Their utility functions UA(x1, x2 ) = (21)3x2 UB(xP, x2) = xx2 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 af. (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 ever if you didn't solve (3e) (f) From the Fundamental Welfare Theorem, we know that the allocation you foun in part (3e) is in the core. How would you check this directly, i.e. what calculation would you perform? For the remaining parts, we switch Bob's utility function to UB (21 , 202 ) = (21+ 202 ) but leave Alice's the same. g Find the equation for the set of all interior points on the contract curve, simplify it to express x2 as a function of x4. Find the market-clearing prices and competitive allocation. One of Alice and Bob is no better off at the competitive allocation than at endowment; which one? Only an answer is required. Even if you got stuck on previous part, try to guess