An economy consists of two individuals, Sempronius and Jacobus, each with logarithmic utility. There are two equally likely states of nature. Sempronius has an endowment of 10 ducats worth of consumption in both states. Jacobus has an endowment of a contingent claim for 15 ducats worth of consumption in state 1, but only 5 ducats worth of consumption in state 2. Jacobus offers Sempronius the following trade: Jacobus will give Sempronius 3 ducats worth of consumption in the event that state 1 occurs in exchange for a promise from Sempronius to provide Jacobus with 2 ducats worth of consumption in the event that state 2 occurs (a) Are both individuals made better off by the proposed trade? (b) Is the final contingent-consumption allocation resulting from this trade Pareto efficient? (c) Describe the set of all Pareto-efficient allocations in this economy. (d) How would your answer to part (c) change if the probability of state 1 was p 0.4, instead of 0.5?
