Intermediate Macroeconomics
Intermediate Macroeconomics 161B Amjad Toukan Spring 2024 PROBLEM SET 1 Due on April 19th, 2024 1. Suppose quotes for the dollar–euro exchange rate E$/ € are as follows: in New York $1.05 per euro, and in Tokyo $1.15 per euro. Describe how investors use arbitrage to take advantage of the difference in exchange rates. Explain how this process will affect the dollar price of the euro in New York and Tokyo. 2. Consider a Dutch investor with 1,000 euros to place in a bank deposit in either the Netherlands or Great Britain. The (one-year) interest rate on bank deposits is 1% in Britain and 5% in the Netherlands. The (one-year) forward euro–pound exchange rate is 1.65 euros per pound, and the spot rate is 1.5 euros per pound. Answer the following questions, using the exact equations for uncovered interest parity (UIP) and covered interest parity (CIP) as necessary. a. What is the euro-denominated return on Dutch deposits for this investor? b. What is the (riskless) euro-denominated return on British deposits for this investor using forward cover? c. Is there an arbitrage opportunity here? Explain why or why not. Is this an equilibrium in the forward exchange rate market? d. If the spot rate is 1.5 euros per pound, and interest rates are as stated previously, what is the equilibrium forward rate, according to CIP? e. Suppose the forward rate takes the value given by your answer to (d). Compute the forward premium on the British pound for the Dutch investor (where exchange rates are in euros per pound). Is it positive or negative? Why do investors require this premium/discount in equilibrium? f. If UIP holds, what is the expected depreciation of the euro (against the pound) over one year? g. Based on your answer to (f), what is the expected euro–pound exchange rate one year ahead? 3. You are a financial adviser to a U.S. corporation that expects to receive a payment of 60 million Japanese yen in 180 days for goods exported to Japan. The current spot rate is 100 yen per U.S. dollar ( E$/ ¥ = 0.01000 ). You are concerned that the U.S. dollar is going to appreciate against the yen over the next six months. a. Assuming the exchange rate remains unchanged, how much does your firm expect to receive in U.S. dollars? b. How much would your firm receive (in U.S. dollars) if the dollar appreciated to 110 yen per U.S. dollar ( E$/ ¥ = 0.00909 )? c. Describe how you could use a forward contract to hedge against the risk of losses associated with the potential appreciation in the U.S. dollar. 4. In recent years China has been routinely accused of currency manipulation. In this question you are asked to use the freely available finder.com Starbucks Index to investigate these claims. Go to http://www.finder.com/starbucks-index to access the most recent version of their data. a. What is the most recent price of a Starbucks tall latte in China? What is the implied yuan/dollar exchange rate based on these prices? b. Does this measure suggest that the Chinese yuan is overvalued or undervalued relative to the dollar? Why might this be beneficial to the Chinese economy? c. The fundamental assumption of this index is that the cost of producing a Starbucks tall latte is identical across countries. Why might this assumption be violated? How might this violation affect your answer in part (b)? d. Which three countries are most undervalued relative to the U.S. dollar in the most recent year? Which three are most overvalued? 5. Suppose that two countries, Vietnam and Côte d’Ivoire, produce coffee. The currency unit used in Vietnam is the dong (VND). Côte d’Ivoire is a member of Communauté Financière Africaine (CFA), a currency union of West African countries that use the CFA franc (XOF). In Vietnam, coffee sells for 4,500 dong (VND) per pound. The exchange rate is 30 VND per 1 CFA franc, EVND/XOF = 30 . a. If the law of one price holds, what is the price of coffee in Côte d’Ivoire, measured in CFA francs? b. Assume the price of coffee in Côte d’Ivoire is actually 160 CFA francs per pound of coffee. Compute the relative price of coffee in Côte d’Ivoire versus Vietnam. Where will coffee traders buy coffee? Where will they sell coffee in this case? How will these transactions affect the price of coffee in Vietnam? In Côte d’Ivoire? 6. Consider each of the following goods and services. For each, identify whether the law of one g price will hold, and state whether the relative price, q US / Foreign , is greater than, less than, or equal to 1. Explain your answer in terms of the assumptions we make when using the law of one price. a. Rice traded freely in the United States and Canada. b. Sugar traded in the United States and Mexico; the U.S. government imposes a quota on sugar imports into the United States c. The McDonald’s Big Mac sold in the United States and Japan. d. Haircuts in the United States and the United Kingdom 7. You are given the following information. The current dollar–pound exchange rate is $1.5 per pound. A U.S. basket that costs $100 would cost $120 in the United Kingdom. For the next year, the Federal Reserve is predicted to keep U.S. inflation at 2% and the Bank of England is predicted to keep U.K. inflation at 3%. The speed of convergence to absolute PPP is 15% per year. a. What is the expected U.S. minus U.K. inflation differential for the coming year? b. What is the current U.S. real exchange rate qUS /UK with the United Kingdom? c. How much is the dollar overvalued/undervalued? d. What do you predict the U.S. real exchange rate with the United Kingdom will be in one year’s time? e. What is the expected rate of real depreciation for the United States (versus the United Kingdom)? f. What is the expected rate of nominal depreciation for the United States (versus the United Kingdom)? g. What do you predict will be the dollar price of one pound a year from now? 8. Consider two countries: Japan and South Korea. In 1996 Japan experienced relatively slow output growth (1%), whereas South Korea had relatively robust output growth (6%). Suppose the Bank of Japan allowed the money supply to grow by 2% each year, while the Bank of Korea chose to maintain relatively high money growth of 15% per year. For the following questions, use the simple monetary model (where L is constant). You will find it easiest to treat South Korea as the home country and Japan as the foreign country. a. What is the inflation rate in South Korea? In Japan? b. What is the expected rate of depreciation in the Korean won relative to the Japanese yen (¥)? c. Suppose the Bank of Korea decreases the money growth rate from 15% to 12%. If nothing in Japan changes, what is the new inflation rate in South Korea? d. Using time series diagrams, illustrate how this increase in the money growth rate affects M P E the money supply K , South Korea’s interest rate, prices K , real money supply, and won / ¥ over time. (Plot each variable on the vertical axis and time on the horizontal axis.) e. Suppose the Bank of Korea wants to maintain an exchange rate peg with the Japanese yen. What money growth rate would the Bank of Korea have to choose to keep the value of the won fixed relative to the yen? f. Suppose the Bank of Korea sought to implement policy that would cause the Korean won to appreciate relative to the Japanese yen. What ranges of the money growth rate (assuming positive values) would allow the Bank of Korea to achieve this objective?
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