3-period consumption-savings problem (30%). This question extends the 2period model we discussed in class to 3periods. Agents live for 3periods and maximize their discounted intertemporal utility subject to their resource constraint. max[ln(c1)+;31n(63) +331n(c3)] s.t. c, +kr+1 g (l +r)k,, 0 0 given. (a) Write down the Lagrangian for this optimization problem and solve for the optimal Cl, 63, 63, k3, kg, and k4. (7 marks) (b) Write the problem in recursive form and solve for the optimal c1, 3, 3, k3, kg, and k4. (10 marks) (c) Compare your answers from part (b) with part (a), are they the same? (7 marks) (d) Suppose EU + r) : 1, what are the optimal consumption levels in periods 1, 2, and 3? (6 marks)