Consider a modified general equilibrium environment in which there are two possible states of the world, state 1 and state 2, which are equally likely ex-ante. There are two kinds of goods, a and b. There are two expected utility agents, Agent 1 and Agent 2, whose Bernoulli utilities depend on the state of the world, as well as their ultimate ownership levels of the various goods. In particular, the Bernoulli utility u1(, x1,a, x1,b) of Agent 1 is given by