Consider a household living for two periods. Let ct and 3/; denote consumption and income, respectively, in period t = 1,2. The interest rate is zero and the discount factor is one. The household faces the following maximisation problem: max U (c1, c2) = lnCcl) + 171(92): 1.92 subject to Cl +52 =3'1 +312- Suppose that y1 = 1 and y2 = 3. Solve for the optimal levels of Cl and C2. (5 points) Use the national income identity to derive an expression showing how aggregate saving and investment are related in a small open economy. (5 points) Consider a country with a debt-to-GDP ratio of 50 percent. The interest rate is 6 percent and the primary budget balance is 1 percent. What must be true about GDP growth in order for government debt to be sustainable? Motivate your answer mathematically. (5 points) Explain, intuitively, why it may be benecial to have central banks commit to a low ination rate. (5 points) Consider two small, open economies labeled A and B. Country A has higher productivity growth in the tradables sector than country B. What should we expect with regard to the ination rate in country A versus that in country B? Explain the central mechanism behind this result. (5 points)