Consider a two types of agent three-period model of consumption/savings decision, with household 1 lifetime utility given by

U = In(cq) + Biln(c2) + Bhin(c3), where B1 = 0.98 and with household 2 lifetime utility given by U = In(cq) + Baln(c2) + BZIn(c3), where B2 = 0.95 . The household 1 earns exogenous income y, = 0 in the first period, y2 = 11 in the second period and y3 = 12 in the third period, the household 2 earns exogenous income y7 = 10 in the first period, y2 = 11 in the second period and y? = 0 in the third period and can borrow and save at the real interest rate r1 between the first and second periods and r2 between the second and third periods. Assume that there are no taxes. (a) (10 points) Define an equilibrium. (b) (30 points) Compute the interest rates of equilibrium