1. Consider the following constrained two-period optimization problem: max u(c1, c2) = - exp(-701) - Bexp(-702) (1) 1 subject to: C + (2) where y > 0 is the coefficient of absolute risk aversion (CARA), BE (0, 1) is the discount factor, (c1, c2) is the optimal bundle of consumption in periods 1 and 2, I is the given total income during the two periods, R is the gross interest rate. (a) Set up the Lagrangian function for the above optimization problem, and derive the first order conditions. (b) Solve for the optimal consumption bundle (cj, c; ) and the lagrange multiplier A for the budget constraint in terms of the given model parameters (B, 7, R. I) .2. Consider the following lifetime optimal consumption-saving problem T max Est In ct (3) subject to R (at - at ) , t = 0, . . ., T (4) 00 = Q (0), ar+1 20, (5) where f is the consumer's rate of time preference (8