2. (10 points) Kathy's life time utility is In ci + 0.9 In C2. Her income stream are y = Y2 3000. The real interest rate is 6%. (a) (3 points) Compute Kathy's optimal consumption allocation and saving. (b) (3 points) Suppose that Kathy has to pay a lump-sum tax of 400, but only in the first period. Her budget constraint is given below: C2 Ci + 1+ 6% 3000 (3000 400) + 1+6% Compute Kathy's optimal consumption allocation and saving in this case. (c) (4 points) Suppose that Kathy has to pay a lump-sum tax of 200 in both periods. Her budget constraint becomes the following: C2 (3000 200) (3000 200) + - Cyt 1+ 6% 1 + 6% Compute Kathy's optimal consumption allocation and saving in this case. (d) (1 point) Compare the difference between part (b) and (a) with that between part (c) and (a). In particular, compute the marginal propensity to consume in the first period in each comparison. What do you find