Consider a two types of agent three-period model of consumption/savings decisions, with household lifetime utility given by

M = ln(c%) +Blln(c) + fln(c), where ,61 = 0.98 and with household 2 lifetime utility given by u = Mei) +2ln(c';') + glne), where 52 = 0.95 . The household 1 earns exogenous income : = 0 in the rst period, 14% = 11 in the second period and y; = 12 in the third period, the household 2 earns exogenous income y? = 10 in the rst period, y3 = 11 in the second period and 1/5? = 0 in the third period and can borrow and save at the real interest rate 71 between the first and second periods and 7'2 between the second and third periods. Assume that there are no taxes