2. Tim has preferences over consumption in period 1 and 2 of the form 1/4 3/4 . The price of consumption is $1 in both periods. He has $6,000 in u(x ,x,) = 2x] X2 the bank now and is trying to decide between two different investment opportunities, A and B. MU,=1/2x x2 *and MU,=3/2x1 x. A: invest $5,000 in period 1 and receive $12,000 in period 2. B: invest $1,000 in period 1 and receive $3,000 in period 2. a. If Tim can borrow and lend at a rate of interest of 50 percent, which investment opportunity will he choose? (Assume that Tim cannot invest more than $5000 if he chooses A, or $1000 if he chooses B.) Show your analysis. b. Given your answer in (a), how much will he consume in each period