Problem Suppose that investors' preferences for consumption at time t are represented by the habit formation" utility function: u(Q) = (4-4-1)1-4-1 1-Y In other words, investors value their current consumption relative to their past consumption, i.e., they form a consumption habit. It is common to write the "habit formation utility function as U(Ct, 5,) = ($)1-1-1 1-Y where se = 4-4-1 is the surplus consumption ratio. Suppose that the subjective discount factor is B = 1. Questions: a. Compute the time-t + 1 stochastic discount factor in this economy and express it in terms of the product of consumption and the surplus consumption ratio at times t and t +1, i.e., mt+1(CtSt, Ct+1St+1). b. Suppose that ct-1 = 3.5 and c4 = 4. Also, suppose that at time t + 1, consumption is uncertain and can take two values, which are equally likely: c*1 = 4.5 and #1 = 7.5. Finally, suppose that the coefficient of risk aversion is y = 2. Compute the surplus consumption ratio at time t and in states B and G at time t + 1. Compute the time-t + 1 stochastic discount factor in states B and G. c. Find the time-t price p. of stock X that pays 0 in state B and 1 in state G, and ceases to exist at time t + 1. Again, you may assume that the two states are equally likely to occur. d. Find the time-t price p of stock Y that pays 1 in state B and 0 in state G, and ceases to exist at time t + 1. Again, you may assume that the two states are equally likely to occur. Comment on similarities/differences of your answers to c. and d (two sentences should be enough). Problem Suppose that investors' preferences for consumption at time t are represented by the habit formation" utility function: u(Q) = (4-4-1)1-4-1 1-Y In other words, investors value their current consumption relative to their past consumption, i.e., they form a consumption habit. It is common to write the "habit formation utility function as U(Ct, 5,) = ($)1-1-1 1-Y where se = 4-4-1 is the surplus consumption ratio. Suppose that the subjective discount factor is B = 1. Questions: a. Compute the time-t + 1 stochastic discount factor in this economy and express it in terms of the product of consumption and the surplus consumption ratio at times t and t +1, i.e., mt+1(CtSt, Ct+1St+1). b. Suppose that ct-1 = 3.5 and c4 = 4. Also, suppose that at time t + 1, consumption is uncertain and can take two values, which are equally likely: c*1 = 4.5 and #1 = 7.5. Finally, suppose that the coefficient of risk aversion is y = 2. Compute the surplus consumption ratio at time t and in states B and G at time t + 1. Compute the time-t + 1 stochastic discount factor in states B and G. c. Find the time-t price p. of stock X that pays 0 in state B and 1 in state G, and ceases to exist at time t + 1. Again, you may assume that the two states are equally likely to occur. d. Find the time-t price p of stock Y that pays 1 in state B and 0 in state G, and ceases to exist at time t + 1. Again, you may assume that the two states are equally likely to occur. Comment on similarities/differences of your answers to c. and d (two sentences should be enough)