Xavier, Yolanda, and Zachary are considering whether to pool their funds to buy into a lottery. There is a 20% chance that they will win big and make $8 million dollars, a 40% chance that they will win second prize and make $2 million, and a 40% chance that they will lose and win nothing. The entrance fee to participate in this lottery is $2 million. The partners decide whether or not to play by majority vote. Assume that Xavier has utility function u(x) = x². The other two partners have utility function u(x) = x, where x is the total amount of money won in the lottery. Will the partners buy in?

Question

Quizplus · Accepted Answer

Xavier's expected utility from buying in is 0.2 * 8^2 + 0.4 * 2^2 + 0.4 * 0^2 - 2^2 = 3.2. His expected utility from not buying in is 0. Yolanda's and Zachary's expected utility from buying in is 0.2 * 8 + 0.4 * 2 + 0.4 * 0 - 2 = 2.4. Their expected utility from not buying in is 0. Therefore, Xavier will vote to buy in, and Yolanda and Zachary will also vote to buy in, so the partnership as a whole will buy in.

Xavier, Yolanda, and Zachary Are Considering Whether to Pool Their