2024 – Homework 7 Economics W3213 Intermediate Macroeconomics 1 Mankiw page 523 524 Problems and Applications 2 and 3 2 Consider

Economics W3213

 

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 ln C1 + ln C2

 

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 S p 1 ).

(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 < rb = 0.25). Assume, as we did originally, that T1 = T2 = 2. Compute the optimal levels of consumption and savings. Compare your answer to the ones you gave for items (b) and (c) above and provide an intuitive explanation of your findings.

(f) Continue to assume that rs = 0.125 < rb = 0.25 and consider the government’s tax cut of 2 in period 1 coupled with a tax increase of 2.5 in period 2. Calculate the optimal levels of consumption and savings in period 1. Compare your answer with the one you gave for item (d) above. What is the intuition behind the different effects on consumption and savings, if any, that you obtain in the economies with and without financial frictions. Comment about the effectiveness of tax-driven stimulus policies in economies with financial frictions. Compare the welfare consequences of the tax cut in the economy with and in the economy without financial frictions.