I. Would any individual use money to finance his/her consumption as old? Why or why not? What will be the value of at? Write down an individuals life-time budget constraint. [ Marks 5]
II. Derive first order conditions characterizing the optimal choices of capital investment and money holding and interpret them. [Marks 10]
III. Write down the goods market clearing condition. Using the goods market clearing condition along with budget constraints and first order conditions, derive the optimal amount of capital investment. [Marks 10]
Question 3: (Illiquidity) Consider an Overlapping Generation (OLG) model with individuals living for three periods. In any period t, Nt young individuals are born. Population grows at a constant rate n with N4 nNt-1, Vt > 1. Let C1,t, C2,t+1, and C3,t+2 be the consumption of an individual born in time t in his/her first, second, and third period of life respectively. Each individual receives y units of a perishable good as endowment when young. Middle-aged and old do not receive any endowment. Let the utility function of an individual born at time t be CI,t + c2,4+1 +0%,++2 Each individual also possesses a technology which converts one unit of good saved as capital in the first period in X units of goods in the third period with X > n?. The money supply grows at a constant rate, z > 1, i.e., Mt = zMt-1. The newly created money is distributed among middle-aged individuals equally in each period by the government as lump-sum transfer. Let at be the real value of transfer made to a middle-aged individual at time t. Suppose that exchanges on credit is not possible. In answering the question, you can assume that the real rate of return on money, Ut+1 Ut Question 3: (Illiquidity) Consider an Overlapping Generation (OLG) model with individuals living for three periods. In any period t, Nt young individuals are born. Population grows at a constant rate n with N4 nNt-1, Vt > 1. Let C1,t, C2,t+1, and C3,t+2 be the consumption of an individual born in time t in his/her first, second, and third period of life respectively. Each individual receives y units of a perishable good as endowment when young. Middle-aged and old do not receive any endowment. Let the utility function of an individual born at time t be CI,t + c2,4+1 +0%,++2 Each individual also possesses a technology which converts one unit of good saved as capital in the first period in X units of goods in the third period with X > n?. The money supply grows at a constant rate, z > 1, i.e., Mt = zMt-1. The newly created money is distributed among middle-aged individuals equally in each period by the government as lump-sum transfer. Let at be the real value of transfer made to a middle-aged individual at time t. Suppose that exchanges on credit is not possible. In answering the question, you can assume that the real rate of return on money, Ut+1 Ut
