(30 points) Consider an exchange economy with 2 consumers whose preferences and endowments are represented by: u+(x1, x2) = (x2)2 and e' = (5,0) u(x1, x2) = (2-1)} (x2)} and e2 = (5,15) (a) Characterize the set of all Pareto efficient allocations. (b) Find all Walrasian equilibria (please report both equilibrium price vector and allocation, you can restrict attention to p >> 0). Now assume there is, in addition to the consumers from above, a third consumer with 1(21, X2) = 3x1 + 2x, and e= (10,10). (c) At which prices is the endowment of the third consumer one of the bundles in her demand set? (d) Is the allocation = (!, , ) = ((0,7.5), (10, 7.5), (10,10)) in the core? (e) Is the allocation T (T1, 22,7%) = (1, 1), (9, 14), (10,10)) in the core