Marge and Homer Simpson are stranded on an empty island. They brought nothing with them,
but found 10 units of good 1 and 10 units of good 2; they do not expect to Önd or make anything
else. You may skip either part b or part c.
(a) (10) Find all Pareto optimal allocations if Marge has utility u(x1; x2) = ln x1 + ln x2; while
Homer has utility u(x1; x2) = ln x1 + x2 (note, these utility functions di§er on good 2).
(b) (12) Now suppose that instead of the utility functions in (a), MargeÃs utility is u(x1; x2) =
minfx1; x2g while HomerÃs is u(x1; x2) = x1.
i. Explain why it is Pareto optimal to give Marge (4,6) and Homer (6,4), but not if the
bundles are reversed (Marge with (6,4) and Homer with (4,6)).
ii. Generalizing (i), can you Önd all Pareto optimal allocations?