3. [10] Consider a two-period consumption model in which an individuals life- 11 time utility is u(c1, c2) = c12 c2 , where ct is the consumption in period t. The individual earns I1 = 1000 in period 1 and receives pension I2 = 500 in period 2. Suppose the individual can save or borrow at the net interest rate 10%(r = 0.1).Assume that prices in two periods are p1 = 2 and p2 = 4, respectively.

(a) [5] Find the individuals optimal consumption level in each period.

(b) [5] Suppose now the price in period 2 increases to p2 = 8, and the govern- ment wants to adjust the pension to I2 so that the individual is equally well off as before the price change. Find I2.