Tim has preferences over consumption in period 1 and 2 of the formu(c , c ) = 2c1^0.25c2^0.75.

The price of consumption is $1 in both periods. He has $6,000 in the bank now and is trying to decide between two different investment opportunities, A and B.

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.

1.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

2.Given your answer in (a), how much will he consume in each period?