Suppose that there is a small open economy named C in this world. Households in country...

 

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Suppose that there is a small open economy named C in this world. Households in country C are risk averse with a period utility function of u(c₁) - In(c) and a time discount factor < 1. The world interest rate r₁ is given in the international financial markets. Bo <0. The interest rate on Bo is ro. The income profile for this country is given by (Y₁ and Y₂). Time also runs for two periods: t=1,2. 1. (10 points): Suppose that there is a negative temporary income shock such that Y₁ decreases to Y₁ - AY with no change in Y2. Note that AY > 0. (a) Show that in this setup, the current account at period 1 CA₁ co-moves with Y₁ in the same direction. (That is, CA₁ decreases). (b) How does CA₂ change ? 2. (20 points): Suppose that the economy can face the following two different temporary income profiles. The first case is (Y₁ + AY*, Y₂), and the second case (Y₁, Y2+ AY**). That is, in the first case, the positive income shock hits the economy only in the first period, whereas in the second case, the positive income shock hits the economy only in the second period. 1) Suppose that the equilibrium C₁ and C₂ in the first case are the same as those in the second case. Find a relationship between AY* and AY** which equalizes the two consumption profiles. 2) Suppose that the two equilibrium consumption profiles are identical (i.e., the same condition as 1)). Compare CA₁ for the two cases. That is, which case (first or second) has a larger CA₁? What is the intuition behind this result? Suppose that there is a small open economy named C in this world. Households in country C are risk averse with a period utility function of u(c₁) - In(c) and a time discount factor < 1. The world interest rate r₁ is given in the international financial markets. Bo <0. The interest rate on Bo is ro. The income profile for this country is given by (Y₁ and Y₂). Time also runs for two periods: t=1,2. 1. (10 points): Suppose that there is a negative temporary income shock such that Y₁ decreases to Y₁ - AY with no change in Y2. Note that AY > 0. (a) Show that in this setup, the current account at period 1 CA₁ co-moves with Y₁ in the same direction. (That is, CA₁ decreases). (b) How does CA₂ change ? 2. (20 points): Suppose that the economy can face the following two different temporary income profiles. The first case is (Y₁ + AY*, Y₂), and the second case (Y₁, Y2+ AY**). That is, in the first case, the positive income shock hits the economy only in the first period, whereas in the second case, the positive income shock hits the economy only in the second period. 1) Suppose that the equilibrium C₁ and C₂ in the first case are the same as those in the second case. Find a relationship between AY* and AY** which equalizes the two consumption profiles. 2) Suppose that the two equilibrium consumption profiles are identical (i.e., the same condition as 1)). Compare CA₁ for the two cases. That is, which case (first or second) has a larger CA₁? What is the intuition behind this result?

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1a If Y1 decreases then consumption C1 must decrease as well to satisfy the budget constraint Since ... View the full answer