Department of Economics Columbia University Homework 7 Economics W3213 Intermediate Macroeconomics 1. Mankiw, page 523-524, Problems and Applications 2 and 3. 2. Consider the consumption and saving decision of a two-period lived household with preferences described by the utility function lnC1 + lnC2 The household’s income in periods 1 and 2 are given by Y1 = 7 and Y2 = 10, respectively. The government levies lump-sum taxes in the amount of 2 in each period (that is, T1 = T2 = 2). Finally, the interest rate is 25 percent (or r = 0.25). (a) Calculate the present discounted value of the household’s lifetime disposable income. (b) Calculate the optimal level of consumption in period 1. (c) How much does the household save in period 1? (i.e., calculate Sp1). (d) Now assume that the government announces a tax cut of 2 in period 1 coupled with a future tax increase of 2.5 in period 2 (that is, T1 = -2 and T2 = 2.5). Calculate the optimal levels of consumption in periods 1 and 2 and the optimal level of private savings in period 1 that result after this announcement. Provide an intuitive explanation for your findings. (e) Now assume that, due to frictions in the financial market, the interest rate at which households save, denoted rs, is smaller than the interest rate at which households can borrow, denoted rb. Specifically, assume that rs is 12.5 percent, and that rb is 25 percent (i.e., rs = 0.125