John has the following utility function U(c1,c2) = min{c1 + ac2,c2}, where c1 and c2 are his consumption in periods 1 and 2, respectively and a is some positive constant. Suppose John has $100 income in period 1 and $105 income in period 2. Prices in both periods are $1.

Part a1: Suppose a = 2. If John can freely borrow and lend at 5% interest rate what would be his optimal consumption in both periods?

Part a2: Suppose a = 2. Now, John can lend at 5% interest rate, but cant borrow at all. What would be his optimal consumption in both periods?

Part b1: Suppose a = 0.5. If John can freely borrow and lend at 5% interest rate what would be his optimal consumption in both periods?

Part b2: Suppose a = 0.5. Now, John can lend at 5% interest rate, but cant borrow. What would be his optimal consumption in both periods?