Consider an endowment model with two periods, t = 1, 2. The world consists of two...

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Consider an endowment model with two periods, t = 1, 2. The world consists of two countries, Home and Foreign. Output in the home country at dates 1 and 2 equals Y₁ and Y₂ respectively. and output levels in the foreign country are given by Y₁ and ₂. Representative households in both countries have preferences given by U(C₁, C₂) In(C₁) + Bln(C₂) where C₁ and C₂ denote consumption in period 1 and 2 respectively, and 3 € (0,1) is a discount factor. Variables and parameters belonging to the foreign country are denoted by a hat. (E.g. C₁ and C₂ denote consumption levels in the foreign country). The countries can borrow and lend to each other at (gross) interest rate 1 + r. (a) [3 marks] Write down Home's intertemporal budget constraint. (b) [7 marks] Write down the Euler equation characterizing Home's optimal consumption over the two periods. (c) [7 marks] Show that Home's date 1 savings (remember that date 1 savings S₁ = Y₁ - C₁(r)) equal 1 S₁ 1+ 3 (1 + 3)(1+r) (d) [10 marks] Write down the condition for market clearing on the world level. Compute the world interest rate r. (e) [8 marks] Suppose now the two countries live in autarky, i.e. they do not trade with each other. Derive the autarky interest rates in Home and Foreign, rA and FA. (f) [5 marks] Explain intuitively why the world interest rate must lie between the two autarky rates. [No formal derivation needed.] (g) [10 marks] Show that the country with an autarky interest rate below the world interest rater will run a trade surplus in period 1, while the country with an autarky rate above r will run a trade deficit. Consider an endowment model with two periods, t = 1, 2. The world consists of two countries, Home and Foreign. Output in the home country at dates 1 and 2 equals Y₁ and Y₂ respectively. and output levels in the foreign country are given by Y₁ and ₂. Representative households in both countries have preferences given by U(C₁, C₂) In(C₁) + Bln(C₂) where C₁ and C₂ denote consumption in period 1 and 2 respectively, and 3 € (0,1) is a discount factor. Variables and parameters belonging to the foreign country are denoted by a hat. (E.g. C₁ and C₂ denote consumption levels in the foreign country). The countries can borrow and lend to each other at (gross) interest rate 1 + r. (a) [3 marks] Write down Home's intertemporal budget constraint. (b) [7 marks] Write down the Euler equation characterizing Home's optimal consumption over the two periods. (c) [7 marks] Show that Home's date 1 savings (remember that date 1 savings S₁ = Y₁ - C₁(r)) equal 1 S₁ 1+ 3 (1 + 3)(1+r) (d) [10 marks] Write down the condition for market clearing on the world level. Compute the world interest rate r. (e) [8 marks] Suppose now the two countries live in autarky, i.e. they do not trade with each other. Derive the autarky interest rates in Home and Foreign, rA and FA. (f) [5 marks] Explain intuitively why the world interest rate must lie between the two autarky rates. [No formal derivation needed.] (g) [10 marks] Show that the country with an autarky interest rate below the world interest rater will run a trade surplus in period 1, while the country with an autarky rate above r will run a trade deficit.

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e In autarky each country does not trade with the rest of the world which means their interest rates ... View the full answer