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 al Suppose a = 2. If John can freely borrow and lend at 5% interest rate what would be his optimal consumption in both periods? 1

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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 al
Suppose a = 2. If John can freely borrow and lend at 5% interest rate what
would be his optimal consumption in both periods?
1
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 bl
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?
Transcribed Image Text: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 al Suppose a = 2. If John can freely borrow and lend at 5% interest rate what would be his optimal consumption in both periods? 1 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 bl 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?
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