Question 2 (20 points)

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.

Question 2 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?

Question 2 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?

Question 2 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?

Question 2 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?

need help in all THANKS

Question 2 (20 points) 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. Question 2 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? Question 2 Part a2 Suppose a=2. Now, John can lend at 5% interest rate, but can't borrow at all. What would be his optimal consumption in both periods? Question 2 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? Question 2 Part b2 Suppose a=0.5. Now, John can lend at 5% interest rate, but can't borrow. What would be his optimal consumption in both periods