uppose that two roommates, Andy and Bob, are trying to pick an apartment in Chicago along the red line. Locations can be chosen from the set of alternatives A = {x : x [0, 1]}.2 Andy and Bob both want to minimize their daily commute but they work at dierent locations: Andy at xA = 0.3, while Bob at xB = 0.6. Specically, their utility functions are uA(x) = (x xA)2 and uB(x) = (x xB)2. (1) What is the set of all Pareto ecient outcomes in A (assuming no money can be exchanged)? (2) Suppose from now on that Andy and Bob can also exchange money, and their utility of location x when they pay ti is ui(x) ti. (We assume budget balance, so that whatever one of them pays must be received by the other one.) What is the set of Pareto ecient allocations? (Hint: Use a theorem from the lecture)