Seoul National University Department of Economics Woong Yong Park ECON-212.502 - Macroeconomic Theory Homework #1 (Due at 5pm, March 18th) 1. Consider a household who lives for three periods: t = 1, 2, 3. The household seeks to maximize lifetime utility by allocating endowed income to consumption and saving as follows: max log (c1) + Blog (c2) + 2 log (c3), subject to C1 + $1 SW1 , (1) C2 + $2 S (1 + 7) $1, ( 2 ) C3 + $3 S (1 + r) $2, (3 ) C1 , C2, C3 2 0, (4) where c and s, are consumption and saving for period t = 1, 2, 3, r > 0 is the net interest rate on saving, and 0 0 in period 1. For now, assume that the household can freely save or borrow at r (st