4. (16 points) Consider the two-period model. The consumer's preferences over current and future consumption (c and c ) are: U (c,c') = In(c) + In(c) subject to C c+ =y - t + y -t' = we. 1 +r 1 +r The consumer's budget parameters are given by y = 150, t = 20, y = 144, t = 24, T = 0.2, where y and y are current and future income, t and t' are current and future lump-sum taxes, a is housing wealth in the first period and r is the real interest rate. (a) Find lifetime wealth, we. (b) Find the optimal levels of current consumption (c), future consumption (c ) and saving (y - t - c). (c) Confirm that the allocation you found in part (b) is in fact optimal, by completing the following table. U (C, C ) = C In (c) + In (c ) 105 114 115 116 125