2. Consider the long time horizon consumption/saving model from classes 12 and 13, specically the version where 6 = 1 / (1 + r) and T > 00. In answering the questions below, you can use the equations from lecture, but be sure to note which ones you are using (and show your work). (a) Suppose income is constant and equal to 1000, so 1000 = yo = y] = What does the agent consume in each period? (b) Let the interest rate be r = 0.05. Suppose in the initial period the government sends the agent 100. By how much does initial consumption (co) increase (round- ing to the nearest whole number)? (c) Again let T = 0.05, but now suppose the government sends the agent 100 in every period. By how much does initial consumption (co) increase? Long - time Horizon Consumption / saving model (2+ time periods) max E Btu ( CE ) - CE+ bet = yet ( Itr ) be t = 0 Do FbTy 1 = 0 Euler Equation : u = utility function U'(C+)= BW (CE+) ( 1+r) Ct = consumption butI = borrowing/ saving B = 1 - agents discount ye = income during period Its using Interest rate . u' (c . ) = u' ( cry, ) - means : Co = Q = (2 - " CP Like w/ 2+ periods : 2 periods, agents want smooth consumption w/ discounting thru int. rate Friedman's permanent income model cznyoth ye with constant consumption over large " MS Its (+r period of time