3. Bart and Arnie each have income today of $12k per month. If the Democrats win the next election Bart's income will be $10K per month; if the Republicans win, his income will be $30K per month. Arnie's income will be $15K per month whichever party wins the election. Arnie's and Bart's preferences are described by the utility functions u (10, ID, IR) = 10 + 3VID + 2VIR and u (20, ID, IR) = 10 + 4VID + VIR, where To denotes the individual's monthly spending today, Ip denotes his monthly spending tomorrow if the Democrats win, and Ig denotes his monthly spending tomorrow if the Republicans win (all expressed in thousands of dollars - for example, Ig = 16 represents spending of $16K per month if the Republicans win). Note that Arnie's and Bart's marginal rates of substitution Are 3 MRSD MRSA MRS 2VID MRSR 2VIH (a) Determine the interior Parcto efficient allocation(s) by using the marginal conditions that characterize the Pareto allocations. (You needn't derive the marginal conditions from the Parcto definition or from the associated Pareto maximization problem.) (b) Determine the Arrow-Debreu allocation(s) and prices. When possible in the following parts, you can appeal to Arrow's securities pricing formula. (c) In the Arrow-Debreu "contingent claims" market structure, what is the (implicit) interest rate? (d) Suppose there are markets for two securities: one is a bond that pays $1K per month tomorrow independently of who wins the election; the other security pays $3K per month if the Democrats win and $2K per month if the Republicans win. Will both of these securities trade in equilibrium, or will one dominate the other so that only the dominant security trades? Explain. Determine the equilibrium prices of the securities, how much each person will hold of each security, and what each person's spending stream will be. What will be the interest rate? (e) Can either of the two utility functions u or u be represented as expected von Neumann- Morgenstern utility over the outcomes In and re? If so, show how; if not, show why not