Tim has preferences over consumption in period 1 and 2 of the form. The price of consumption is $1 in both periods. He has $10,000 in the bank now and is trying to decide between two different investment opportunities, A and B.
A: invest $4,000 in period 1 and receive $8,000 in period 2.
B: invest $2,000 in period 1 and receive $5,000 in period 2.
If Tim can borrow and save at a rate of interest of 50 percent, which investment opportunity will he choose? (Assume that Tim cannot invest more than $4000 if he chooses A, or $2000 if he chooses B.) Show your analysis
Given your answer in (a), how much will he consume in each period?
Given your answer in (a), how much will he consume in each period if now his saving interest rate is 20% and the borrowing rate is still 50%? Show your analysis.