One day when Gilligan was diving in the lagoon he came across a gigantic oyster. Gilligan loved raw oysters so he pried the mollusk from the rocks and hastily came ashore. When he pried open the oyster he was surprised to find a huge gray pearl

Gilligan was thrilled at the sight of the large pearl and his immediate thought was to go and tell his friends about it. But then he reconsidered. To whom would he give the pearl? He thought it was pretty, but owning the pearl would not give him any satisfaction. When he thought about it, he realized that the Skipper, Mr. and Mrs. Howell, the Professor, Ginger and MaryAnn would all like to have the pearl. What should he do? He could not give the one pearl to all of his friends. Maybe he could find some more pearls. With this in mind he dove back into the lagoon and returned to the spot where he found the large oyster. Much to his surprise, barely hidden from view was a small colony of oysters. He pried each of them from the rocks and took them all ashore. Inside of each oyster he found a large pearl. Each pearl was as beautiful as the one that he had first discovered. When he had finished opening the oysters he counted his pearls. "One, two, three, four, five. That's it five pearls." But that's not enough. He did not need a pearl for himself, but he had six friends and only five pearls. Gilligan thought about this problem at least an hour. He finally stood and threw all five pearls back into the lagoon. "If everyone cannot have a pearl, then no one should have a pearl," he thought to himself as he watched the ripples from the pearls spread out across the lagoon. a. Define Pareto optimality. b. Was Gilligan's solution to his problem Pareto optimal? If so, explain why. If not, explain why not.

a.
An allocation is Pareto optimal if there is no other allocation that makes at least one person better off and harms no one.

b.
Assuming that the utility functions of the island dwellers are not interdependent, then Gilligan's solution is not Pareto optimal. It would be better to allocate the pearls to anyone than to throw them away. If the utility functions are interdependent, his solution might have been Pareto optimal.