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Consider the following consumption decision problem. A consumer lives for two periods and receives income of...

Consider the following consumption decision problem. A consumer lives for two periods and receives income of y in each period. She chooses to consume c1 units of a good in period 1 and c2 units of the good in period 2. The price of the good is one. The consumer can borrow or invest at rate r. The consumer’s utility function is: U = ln(c1) + δ ln(c2), where δ > 0.

a. Derive the optimal consumption in each period?

b. How does optimal consumption in each period vary with the interest rate? Explain why.

c. Use your answer in part (a) to derive a condition that determines whether the consumer saves in the first period? Interpret this condition.

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