7. (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 y - t' ct =y-t+ = we. 1tr 1tr The consumer's budget parameters are given by y = 150, t = 20, y = 144, t' = 24, r = 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) Set up the Lagrangian and 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 U (Ct, C ) = C O - In (c) + In (c) 105 the following table. 114 115 116 125