Econ 336, International Economics: Finance, Spring 2023 Problem Set 3

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Problem Set 3

Econ 336, International Economics: Finance, Spring 2023

Due Date: Sunday, March 26th at 11:59pm ET

See course website for submission instructions

Exercise  1.   (From Schmitt-Groh´e, Uribe and Woodford 2022) Consider a two-period endowment economy. Assume that households’ preferences are described by the following

utility function

^C1 +  ^C2 ,

where C1  and C2  denote consumption in periods 1 and 2, respectively.  In each period, households are endowed with 10 units of goods.  Households pay lump-sum taxes T1  and T2 , in periods 1 and 2. Finally, households are born with no financial assets (B0(h)  = 0) and can borrow or lend in the international financial market at the world interest rate T*  = 0.1. The government starts period 1 with no outstanding assets or liabilities (B0(g)   = 0).  In period 1, the government collects lump-sum taxes T1  and consumes G1  = 1 unit of goods. In period 2, it collects lump-sum taxes T2  and consumes G2  = 1 unit of goods.  Like the household, the government has access to the world financial market.

1. Compute the equilibrium levels of consumption, the trade balance, and the current account in periods 1 and 2.

2. Suppose that T1  = 0. What is T2 ? What is private, government, and national saving in periods 1 and 2?

3. Suppose now that T1 increases from 0 to 1 while government purchases are unchanged in both periods. How does this tax hike affect the current account and the fiscal deficit in period 1? Briefly explain your result.

4. Suppose that in period 1 the government increases spending from 1 to 2 and keeps government spending in period 2 unchanged. What is the effect of this policy change on the current account in period 1? Explain.

5. Finally, suppose that there is a permanent increase in government purchases. Specif- ically, suppose that both G1  and G2  increase by 1. Find the response of the current account in period 1. Compare your result with that from the previous question and provide intuition.


Exercise  2.   (From Schmitt-Groh´e, Uribe and Woodford 2022) Consider a two-period, small open endowment economy.  Assume that households’ preferences are described by the utility function

lnC1 + lnC2 ,

where C1  and C2  denote consumption in periods 1 and 2, respectively.  Households are endowed with 10 units of goods in each period and pay proportional taxes on consumption. Let τ1  and τ2  denote the consumption tax rates in periods 1 and 2.  Finally, households are born with no financial assets (B0(h)   = 0) and can borrow or lend in the international financial market at the world interest rate T*  = 0.1. The government starts period 1 with no outstanding assets or liabilities (B0(g)  = 0). It taxes consumption at the same rate in both periods (τ1  = τ2 ) and consumes 1 unit of goods in each period. That is, G1  = G2  = 1, where G1  and G2  denote government consumption in periods 1 and 2.  Like the household, the government has access to the world financial market. In answering the following questions, show your work.

1. Compute the equilibrium tax rate and the equilibrium levels of consumption, the trade balance, private saving, the primary and secondary fiscal deficits, and the current account in periods 1 and 2.

2. Suppose now that the government implements a stimulus package consisting in re- ducing the tax rate by half in period 1, with government consumption unchanged in both periods.  Recalculate the equilibrium of all the variables listed in the previous question. Briefly explain your findings.

Exercise 3.  (From Feenstra and Taylor, “International Macroeconomics” 2014) Consider a Dutch investor with 1000 euros to place in a bank deposit in either the Netherlands or Great Britain.  The (one-year) interest rate on bank deposits is 2% in Britain and 4.04% in the Netherlands.  The (one-year) forward euro-pound exchange rate is 1.575 euros per pound and the spot rate is 1.5 euros per pound. Answer the following questions, using the exact equations for UIP and CIP as necessary.

(a) What is the euro-denominated return on Dutch deposits for this investor?

(b) What is the (riskless) euro-denominated return on British deposits for this investor using forward cover?

(c) Is there an arbitrage opportunity here? Explain why or why not.

(d) If the spot rate is 1.5 euros per pound, and interest rates are as stated previously, what is the equilibrium forward rate, according to the covered interest rate parity (CIP)?

(e) Suppose the forward rate takes the value given by your answer to (d). Compute the forward premium on the British pound for the Dutch investor (where exchange rates are in euros per pound).  Is it positive or negative?  Why do investors require this premium/discount in equilibrium?

(f) If uncovered interest rate parity (UIP) holds, what is the expected depreciation of the euro (against the pound) over one year? What is the expected euro-pound exchange rate one year ahead?



2023-03-23