1. Consider a twoperiod model where a household chooses consumption Cr and CH1 , and saving SF , given the endowment Y! and Y\" and interest rate r to maximize following 1 U=u(C.)+Bu(C. \"(CF26W\"), BE(O=1),a >0. lifetime utility +1) with (a) Show that the utility function "((3) features a positive marginal utility and a diminishing marginal utility. (b) Write down the household problem for nding the optimal C1\" and CH1 . Derive the rstorder conditions. (c) Then solve for C' as a function of Y" Y!\" ,r (and, of course, the parameters). Using the result and the lifetime budget constraint, verify that C3 = CH1 if [3 (1 + r) = 1