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Hi, I have this exercise. I’m having problems trying to understand question C.Can someone give an insight please!!
 
 
Consider an open economy called Greca. Assume there are two periods, where Grecans consume C1 in period 1 and C2 in period 2. Y1 denotes income in period 1 and Y2 denotes income in period 2. Suppose that Y1 = Y2 = 100 and suppose that consumer preferences among Grecans are
given by the following:
U (C1, C2) = ln(C1) + β*ln(C2)
where ln(C1) is the natural logarithm of C and β is the rate of time preference.
a. Write the intertemporal budget constraint facing Grecans.
b. Expressing C2 as a function of C1 and substituting into the consumer preferences above. Derive the optimal consumption allocation C1 and C2, each as a function of β and the interest rate, r (alternatively, you can solve the optimization problem using the Lagrangian).
c. What condition must be true on β and r for Grecans to choose to save some of their income in period 1? What condition must be true for Grecans to choose to borrow in period 1? What does this tell us more generally about the relationship between time preference, the interest rate, and borrowing behaviour?
d. From this point onward, assume that 1/β = 1.1. If the interest rate is 5%, find the optimal consumption allocation C1 and C2. Based on your answer to part c, does this consumption allocation and borrowing/saving choice make sense?
 
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