An economy's potential output is Q=51. It is certain this year, at t=1, but next year t=2 it can fall to Q-sigma = 51-40 or boom to Q+sigma = 51+40. NIIP0=0, r=0, and beta=1, so that everybody is perfectly patient. But there is still a reason for precautionary saving because of the uncertainty about the future. The savings will be done by lending abroad.

1. Write down the budget constraint in terms of output, consumption, and current account (remember that NIIP0=0 and r=0)

2. A logarithmically additive utility function is

U = lnC1 + lnC2

Write it down in terms of output and current account.

3. What is the optimal current account if the output in the second year is certain at Q=51?

Find the utility under perfect certainty, when next year's output is as certain as this year's output.

4. Now write down the utility function from the question above, but this time there is uncertainty in the second period. With a probability of 50% the output is 51-40 and with the probability of 50% it is 51+40. You can keep the current account as unknown.

5. Find the utility level in an autarkic (no-trade) economy under uncertainty.

6. Insert here a graph of the above utility being a function of C1+C2. Label clearly on the graph: low consumption, high consumption, expected consumption, utility of expected consumption (certainty), and expected utility (uncertainty).

7. This uncertainty problem solves to a current account of CA=12.58. Find the utility if the country runs this current account in the first period and receives it back in the second.