Consider an economy composed of two people, Monday and Tuesday.
a) There are two possible allocations, and neither Monday nor Tuesday likes these allocations equally well. (That is, each of them believes that one of the allocations is better than the other. They don’t necessarily agree as to which allocation is better.) Can both allocations be Pareto optimal? If not, explain why not. If so, give an example.
b) Now imagine that there are five possible allocations. There are no two allocations that Monday likes equally well, and there are no two allocations that Tuesday likes equally well. Can all of the allocations be Pareto optimal? If not, explain why not. If so, give an example.
c) Finally, imagine that there 108 allocations. Is it possible that none of the allocations is Pareto optimal? If not, explain why not. If so, give an example.