Ann chooses according to utility function: UA(XO, XH, XL) = Xo + XH - 1 x' +x1 - 1 x2 &0 H L And Beth chooses according to the utility function: UB(XO, XH, XL) = XO + XH - 1 x2 + 2x1 - 1 x2 *O H *O L where To represents consumption "today," Ty represents consumption "tomorrow" in event H, and IL represents consumption "tomorrow" in event L. Storage of the consumption good from today until tomorrow is not possible. Each person is endowed with 30 units of the good today; Ann will have 5 units tomorrow in state H and 25 units in state L; Beth will have 35 units in state H and 5 units in state L. (a) Determine the Pareto optimal allocations. (b) Determine the Arrow-Debreu equilibrium - i.c., the Arrow-Debreu prices and allocation. (c) Suppose there are two securities: a bond, each unit of which pays the holder 1 +r consumption units tomorrow whichever state occurs; and an insurance contract against state L, which pays the holder one consumption unit tomorrow if and only if state L occurs, and nothing if state H occurs. The interest rate r is determined in equilibrium. Use Arrow's security-pricing formula to determine the equilibrium interest rate r and the price p of each unit of the insurance contract. How many units of each security will each person buy or sell in equilibrium? (d) Suppose that the only market is a credit market (ic., a market for borrowing and lending). There are no markets in which one can insure oneself against either of tomorrow's two possible events. Explain why this will generally yield a market outcome that is not Pareto efficient