4. (25 points) Assume the the economy of Econoland is populated by a single representative consumer. The consumer has cares about present consumption (C) and future consumption (Cf) according to log ( C ) + Blog ( C's ) . (1) where log represents the natural logarithm. The consumer enters the present with wealth A, income Y and pays taxes T. In the present, the consumer chooses how much to consume, C, and how much to save for the future, A, out of her total wealth plus after-tax income C + A = Y-T+ A, (2) knowing that in the future she will be receiving an income Y and pay taxes T . Thus, future con- sumption will be given by of = (1 + r) Af + If - If , (3) where r is the real interest rate. The consumer chooses C, CJ, and A to maximize her well being (1). (a) Write down the consumer's budget constraint in present value form. (b) What is the representative consumer's desired consumption, CD, as a function of r, Y, Yf,T, If and B ? Now assume that the Government enters with some initial debt D and must pay for current government expenditures G by raising taxes T and issuing new debt DJ so D + G = T + DS . In the future the government will have to raise taxes T to pay for future Government expenditures Gf plus the debt issued at the end of the previous period withwith interest (1 + r) DJ so ( 1 + r ) D f + Gf = If (c) Write down the budget constraint of the government in present value form, i.e. give an expression relating initial government debt D, the present value of taxes T + 1, If, and the present value of government expenditures G + 1. Gf. (d) Assume that Y = 30, Yf = 40, G = 10, Gf = 15, B = .5 and r = .3. If all of government debt, D = 30, is held by the consumer of Econoland so A = D, what will be the desired consumption, CD, of the consumer? (e) If the Government instead had an incoming debt of D = 50, still held entirely by the consumer of Econoland ( A = D), what will be the desired consumption C' of the consumer? Does the level of Government Debt effect the consumption decisions of the agent? Now assume that only half the debt of Econoland is held by the consumer, so A = D/2 and the remainder held by foreign investors. Repeat parts (d) and (e) under this assumption. Does the level of Government Debt matter now