Suppose that two individuals A and B meet and undertake a joint project in which the returns are 1,000 with probability 0.5, and 2,000 otherwise. They are negotiating an agreement regarding the division of the returns. That is they decide on a division rule before the project comes to fruition and they know what the outcome is. An example is: if the outcome is 1,000, then A pays 20 to B, and B gets 1,200. If it is 2,000, then they split it 1,000–1,000. Prove that if A is risk-averse and B is risk-neutral, then any efficient division rule will give the same amount to A irrespective of project outcome and B will bear all the risk. (The division rule is efficient in the sense that no other rule exists in which both parties enjoy higher ex ante expected utility.)