Question 1: Short questions (25 points in total)

Please write no more than one hand-written page (maximum) when answering each of these questions.

a. Consider a household living for two periods. Let ?" and ?" denote consumption and income, respectively, in period ? = 1,2. The interest rate is zero and the discount factor is one. The household faces the following maximisation problem:

subject to

max ?(?1, ?2) = ??(?1) + ??(?2), ,-,,.

?1 + ?2 = ?1 + ?2.

Suppose that ?1 = 2 and ?2 = 2. Solve for the optimal levels of ?1 and ?2. (5 points)

1. Use the national income identity to derive an expression showing how aggregate saving and investment are related in a small open economy. (5 points)
2. Consider a country with a debt-to-GDP ratio of 60 percent. The GDP growth rate is 2 percent and the interest rate is 6 percent. What must be true about the primary budget balance in order for government debt to be sustainable? Motivate your answer. (5 points)
3. Do commercial banks affect the money supply in the economy? Why/who not? Derive an expression that motivates your answer. (5 points)
4. 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 inflation rate in country A versus that in country B? Explain the central mechanism behind this result. (5 points)

Question 1: Short questions (25 points in total) Please write no more than one hand-written page (maximum) when answering each of these questions. a. Consider a household living for two periods. Let c and y, 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, (2) = In(c1) + In(c2), C1.C2 subject to C1 + C2 = V1 + yz. Suppose that y1 = 2 and y2 = 2. Solve for the optimal levels of c, and c2. (5 points) b. Use the national income identity to derive an expression showing how aggregate saving and investment are related in a small open economy. (5 points) c. Consider a country with a debt-to-GDP ratio of 60 percent. The GDP growth rate is 2 percent and the interest rate is 6 percent. What must be true about the primary budget balance in order for government debt to be sustainable? Motivate your answer. (5 points) d. Do commercial banks affect the money supply in the economy? Why/who not? Derive an expression that motivates your answer. (5 points) e. 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 inflation rate in country A versus that in country B? Explain the central mechanism behind this result. (5 points)