This question asks you to explore when it is possible for a sophisticate to use an illiquid asset to implement her period-1 desired consumption path. Consider a 3-period saving-consumption example in which the person has {3,6 discounting and a concave instantaneous utility function. First consider the case in which the person can borrow and save at an interest rate of 'r = 0%, and suppose further that her lifetime wealth is W = $5200. For this case, the following facts are true: The person's period-1 desired behavior is c: = $2000 0; = $1600 (:3 = $1600. The person's actual behavior is of = $2050 cg = $1750 cg? = $1400. Note: I have NOT given you enough information to solve for these values, because I have not told you what 5 and 6 are and I have not told you what the instantaneous utility function is. But these values are all that's needed to answer the questions below. Now consider the following case. The person cannot borrow, and she has two options for saving. First, she can put her money in the bank and earn an interest rate r = 0%, in which case she will have full access to the money next period. Second, she can invest in an illiquid asset and earn an interest rate of if = 0%. If she invests in the illiquid asset in period 1, then she cannot get any access to these funds until period 3. For each of the income ows below, is it possible to use the illiquid asset to implement period-1 desired behavior? If so, describe the full details of period1 behavior (how much do you consume, how much do you put in the bank, and how much do you invest in the illiquid asset). If not, discuss what the person's actual consumption path is likely to look like. (a) Yl = $2800, Yg = $1200, and Y3 = $1200. (b) Y1 = $2250, Y2 = $1925, and Y3 = $1025. (c) Y1 = $2250, Yg = $1625, and YE, = $1325. ((1) Y1 = $2250, Y2 = $1325, and Y3 = $1625. Note: For each part, your answer should clearly state the person's actual consumption paththat is, her c1, her (:2, and her C3as well as the amount .33 put in the bank in period 1, and the amount 2 put in the illiquid asset in period 1. For some of these, it might be that you cannot provide an exact answer; in that case, your answer should be a range in which the object would liee.g., :3 E (50, 100)