Consider an economy with two consumers, A and B; one commodity, m; and two possible states of nature, 1 and 2, which are equally likely to occur.
In state 1, A is endowed with three units of m and Bis endowed with one unit.
In state 2, A is endowed with one unit and B is endowed with two. The agents have identical von Neumann - Morgenstern preferences with the Bernoulli utility function u(m) = √m.
a. Draw an Edgeworth box depicting the feasible allocations of state 1 consumption of m and state 2 consumption.
b. Identify the ex ante Pareto efficient allocations 1.
c. Suppose each agent were offered the opportunity to purchase insurance by an outside provider at an actuarially fair premium, how much would each agent buy and how much m would they consume in each state?
d. Alternatively, suppose no such insurance were available but the agents might "self-insure," that is, trade in contingent claims. Which feasible trades might they agree to?
e. Finally, suppose they were to trade at market determined prices. Contrast each agent's consumption and level of well-being at the market outcome versus the outcome with outside insurance. Explain the difference.