1. Nathan's life time utility is c1 + 0.98 c2. His income stream are y1 = 40, 000 and y2 = 30, 000. Nathan's boss offers him the option of shifting x units of income from next year to this year. If Nathan takes this option, his income next year is reduced by x units and his income this year is increased by x units.

(a) (2 points) If the real interest rate is 0%, would Nathan take this option? Why and why not?

(b) (4 points) Suppose that r = 0%. Before Nathan takes the offer, what is his optimal consumption allocation? How much does he save?

(c) (2 points) Use a diagram to show how this shift in income will affect Nathan's consumption choice and saving. Explain your graph.

(d) (2 points) If the real interest rate is 2%, would Nathan take this option? Why and why not?

2. (10 points) Kathy's life time utility is ln (c1) + 0.9 ln (c2). Her income stream are y1 = 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 3000 C1 + = (3000 - 400) + 1 + 6% 1 + 6%\f