Alan has preferences over consumption in period 1 and 2 of the form u (x , x, )=2x,?+x2 1/2. The prices of consumption are pl and p2 respectively in period 1 and 2. He has $10,000 in the bank now and will receive another $10,000 in period 2. a. If pl=p2=1 and r=50%, how much Alan will consume in each period? b. If there is a 20% inflation or p2=1.2, what are the impact on Alan's consumptions? c. Now Alan finds out there are two different investment opportunities, A and B. A: invest $4,000 in period 1 and receive $8,000 in period 2. B: invest $1,000 in period 1 and receive $3,000 in period 2. If Alan can borrow and lend at a rate of interest of 50 percent, which investment opportunity will he choose? How much will he consume in each period now? How much Alan does Alan want to borrow? d. Given Alan's investment choice in c, what happens to Alan's consumption if the borrowing rate changed to 100%? e. Given Alan's investment choice in c, what happens to Alan's consumption if the bank set a borrowing limit for Alan at $5000