1. Agents live for two periods and seek to maximise lifetime welfare, given by W = ((121)1'\" + 3(c2)1'')/(1 a) where c, is consumption in period i and ,8 and a are parameters, with 0 0. They are subject to the budget constraint (:1 + c2/(1 + r) = 121 + 3:1 :1 + (y2 - t2)/(1 +r) where 171 is initial wealth, r is the interest rate, I; is a lump sum tax paid in period f and y, is income in period if. a. How does this framework help to explain the evidence that in a ' given period the wealthy have a higher savings rate but that the aggregate savings rate doesn't tend to increase over time as the average income rises? b. Show analytically the effect of changing the timing of taxes