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Suppose that the real interest rate is constant over time and equal to 10%. Consider a two-period economy where coconuts are the only good. Further assume that the economy is endowed with 90 coconuts in period 1, and 121 coconuts in period 2.
1. Draw and label (on the same diagram) three intertemporal budget lines: one under the assumption that the economy begins with a net international investment position Bo*=0; another where the initial net international investment position is Bo*=-10; and one where the initial net international investment position is Bo*=10. Hint: the effect of a change in the initial international investment position is similar to the effect of a change in the first period endowment.
2. Based on the three intertemporal budget lines drawn for question 1, show that a utility-maximizing economy must have a trade surplus in at least one of the two periods when Bo*≤0, but could have trade deficits in both periods if Bo*>0. Hint: you need to draw the three budget lines along with possible indifference curves. It will be best if you draw three separate diagrams (one for each Bo*< 0, Bo*=0,and Bo*>0).
3. Suppose that Bo*= 0 and that U(C1,C2) = ln(C1) + ln(C2). Calculate the trade balance and current account for each period.
4. Suppose that disease strikes the economy. There is no effect on the current (period 1) harvest of coconuts, but households correctly anticipate that they will only be able to harvest 80 coconuts in the second period. Again assuming that Bo*= 0 and that U(C1,C2) = ln(C1) + ln(C2), how will this affect their trade balance and current account in each period? Calculate their numeric values and draw an appropriate diagram to illustrate this shock.
5. Rather than the disease in the previous question, suppose that scientists find a way to increase the number of coconuts by 10% in each period (so 99 coconuts in the first period, and 132 coconuts in the second period). Again assuming that Bo*= 0 and that U(C1,C2) = ln(C1) + ln(C2), how will this affect their trade balance and current account in each period? Calculate their numeric values and draw an appropriate diagram to illustrate this shock.
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