Consider an individual who lives for T periods, the first R of which he spends working. Income in those first R periods

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Consider An Individual Who Lives For T Periods The First R Of Which He Spends Working Income In Those First R Periods 1 (287.17 KiB) Viewed 42 times

Consider an individual who lives for T periods, the first R of which he spends working. Income in those first R periods is given by Yt, and income in periods R+ 1 through T is zero. The individual has a discount factor of B and can save and borrow at the real interest rate r. The individual's optimal behavior is dictated by the standard Euler equation (you don't need to derive it). = = (1+r+)-1 (a) (5 points) Assume that B = 1, r = 0, R = 30, T = 45, and yt = 25 for 1sts R. Calculate the individual's consumption in cach period. You don't need to derive the lifetime budget constraint, just remember that ET-1 (1+4)2-1 = { (b) (5 points) Based on your findings in part (a), draw a diagram that shows the paths for consumption, income, and assets over the individual's lifetime. Be sure to label it carefully. (c) (10 points) How would this individual change his consumption following a one-time increase in income? What would his response be if the increase in income was permanent? Explain the similarities and/or differences between the two cases. (d) (12 points) Would your answer in part 2c change if individuals were borrowing constrained? (e) (10 points) Assume that B(1+r) = 1, r = 0.2, R = 45, T = 55, and yt = 25 for 1sts R. Calculate the individual's consumption in each period. Remember that the formula for the sum a geometric sequence is 1 +5 +52 + ... +87-1 = {{-1st-1 = T = = = T 1-ST = = 1-8.