# Introduction to Exchange Rates and the Foreign Exchange Market

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1 Introduction to Exchange Rates and the Foreign Exchange Market 2 1. Refer to the exchange rates given in the following table. Today One Year Ago June 25, 2010 June 25, 2009 Country Per \$ Per Per Per \$ Australia Canada Denmark Euro Hong Kong India Japan Mexico Sweden United Kingdom United States Source: U.S. Federal Reserve Board of Governors, H.10 release: Foreign Exchange Rates. a. Compute the U.S. dollar yen exchange rate, E \$/, and the U.S. dollar Canadian dollar exchange rate, E \$/C\$, on June 25, 2010, and June 25, 2009 Answer: June 25, 2009: E \$/ = 1 / (94.86) = \$0.0105/ June 25, 2010: E \$/ = 1 / (89.35) = \$0.0112/ June 25, 2009: E \$/C\$ = 1 / (1.084) = \$0.9225/C\$ June 25, 2010: E \$/C\$ = 1 / (1.037) = \$0.9643/C\$ b. What happened to the value of the U.S. dollar relative to the Japanese yen and Canadian dollar between June 25, 2009 and June 25, 2010? Compute the percentage change in the value of the U.S. dollar relative to each currency using the U.S. dollar foreign currency exchange rates you computed in (a). Answer: Between June 25, 2009 and 2010, both the Canadian dollar and the Japanese yen appreciated relative to the U.S. dollar. The percentage appreciation in the foreign currency relative to the U.S. dollar is: % E \$/ (\$ \$0.0105) / \$ = 6.17% % E \$/ (\$ \$0.9225) / \$ = 4.53% S-5

7 Solutions Chapter 3 Exchange Rates I: The Monetary Approach in the Long Run S-13 In the previous table: PPP holds only when the real exchange rate q US/F 1. This implies that the baskets in the home country and the United States have the same price in a common currency. If q US/F 1, then the basket in the United States is more expensive than the basket in the home country. This implies the U.S. dollar is overvalued and the Home currency is undervalued. According to PPP, the Home country will experience a real appreciation (Mexico, South Africa, and Zimbabwe). If q US/F 1, then the basket in the home country is more expensive than the basket in the United States. This implies the U.S. dollar is undervalued and the Home currency is overvalued. According to PPP, the Home country will experience a real depreciation (Brazil and India). 4. Table 3-1 in the text shows the percentage undervaluation or overvaluation in the Big Mac, based on exchange rates in July Suppose purchasing power parity holds in the long run, so that these deviations would be expected to disappear. Suppose the local currency prices of the Big Mac remained unchanged. Exchange rates in January 4, 2010, were as follows (source: IMF): Country Per U.S. \$ Australia (A\$) 0.90 Brazil (real) 1.74 Canada (C\$) 1.04 Denmark (krone) 5.17 Eurozone (euro) 0.69 India (rupee) Japan (yen) Mexico (peso) Sweden (krona) 7.14 Based on these data and Table 3-1, calculate the change in the exchange rate from July to January, and state whether the direction of change was consistent with the PPP-implied exchange rate using the Big Mac Index. How might you explain the failure of the Big Mac Index to correctly predict the change in the nominal exchange rate between July 2009 and January 2010?

8 S-14 Solutions Chapter 3 Exchange Rates I: The Monetary Approach in the Long Run Answer: (The complete table is included in the Excel workbook for this chapter in the solutions manual.) Exchange rate Big Mac prices (local currency per U.S. dollar) Exchange Percent Over (+) / rate actual change under ( ) Jan. 4, July 13, Actual, valuation 2010 (local 2009 In local In U.S. Implied July against currency Jan. 4, PPP correct currency dollars by PPP 13th dollar, % per U.S. \$) 2010 or not? (1) (2) (3) (4) (5) United States \$ Australia A\$ % % Correct direction, but depreciation was way more than predicted. Brazil R\$ % % PPP predicted depreciation, but currency actually appreciated. Canada C\$ % % Correct direction, but appreciation was way more than PPP predicted. Denmark Kr % % PPP predicted [ic] depreciation, but currency actually appreciated. Euro area % % PPP predicted depreciation, but currency actually appreciated. Japan % % PPP predicted appreciation, but currency actually depreciated. Mexico Peso % % Correct direction, but appreciation was way less than PPP predicted. Sweden Kr % % PPP predicted [ic] depreciation, but currency actually appreciated.

11 Solutions Chapter 3 Exchange Rates I: The Monetary Approach in the Long Run S-17 d. Using time series diagrams, illustrate how this increase in the money growth rate affects the money supply, M K ; Korea s interest rate; prices, P K ; real money supply; and E won/ over time. (Plot each variable on the vertical axis and time on the horizontal axis.) Answer: See the following diagrams. Bank of Korea increases money growth rate Bank of Korea reduces the money growth rate to less than 7% M K M K % P K P K M K / P K M K / P K g g E won/y E won/y K2 J Note that E actually falls here because the won appreciates K1 J K1 J K2 J 0 T T

12 S-18 Solutions Chapter 3 Exchange Rates I: The Monetary Approach in the Long Run 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? Answer: To keep the exchange rate constant, the Bank of Korea must lower its money growth rate. We can figure out exactly which money growth rate will keep the exchange rate fixed by using the fundamental equation for the simple monetary model (used above in [b]): % E e won/ ( K g K ) ( J g J ) The objective is to set % E e won/ 0: ( * K g K ) ( J g J ) Plug in the values given in the question and solve for * K : ( * K 6%) (2%. 1%) * K 7% Therefore, if the Bank of Korea sets its money growth rate to 7%, its exchange rate with Japan will remain unchanged. 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? Answer: Using the same reasoning as previously, the objective is for the won to appreciate: % E e won/ 0 This can be achieved if the Bank of Korea allows the money supply to grow by less than 7% each year. The diagrams on the following page show how this would affect the variables in the model over time. 8. This question uses the general monetary model, in which L is no longer assumed constant and money demand is inversely related to the nominal interest rate. Consider the same scenario described in the beginning of the previous question. In addition, the bank deposits in Japan pay 3% interest; i 3%. a. Compute the interest rate paid on Korean deposits. Answer: Fisher effect: (i won i ) ( K J ) Solve for i won (6% 1%) 3% 8% b. Using the definition of the real interest rate (nominal interest rate adjusted for inflation), show that the real interest rate in Korea is equal to the real interest rate in Japan. (Note that the inflation rates you calculated in the previous question will apply here.) Answer: r i J 2% 1% 1% r won i won K 8% 6% 2% c. Suppose the Bank of Korea increases the money growth rate from 12% to 15% and the inflation rate rises proportionately (one for one) with this increase. If the nominal interest rate in Japan remains unchanged, what happens to the interest rate paid on Korean deposits? Answer: We know that the inflation rate in Korea will increase to 9%. We also know that the real interest rate will remain unchanged. Therefore: i won r won K 1% 9% 10%.

13 Solutions Chapter 3 Exchange Rates I: The Monetary Approach in the Long Run S-19 d. Using time series diagrams, illustrate how this increase in the money growth rate affects the money supply, M K ; Korea s interest rate; prices, P K ; real money supply; and E won/ over time. (Plot each variable on the vertical axis and time on the horizontal axis.) Answer: See the following diagrams. Bank of Korea increases money growth rate M K 2 1 P K i won M K / P K E won/y T T 9. Both advanced economies and developing countries have experienced a decrease in inflation since the 1980s (see Table 3-2 in the text). This question considers how the choice of policy regime has influenced this global disinflation. Use the monetary model to answer this question. a. The Swiss Central Bank currently targets its money growth rate to achieve policy objectives. Suppose Switzerland has output growth of 3% and money growth of 8% each year. What is Switzerland s inflation rate in this case? Describe how the Swiss Central Bank could achieve an inflation rate of 2% in the long run through the use of a nominal anchor. Answer: From the monetary approach: S S g S 8% 3% 5%. If the Swiss Central Bank wants to achieve an inflation target of 2%, it would need to reduce its money growth rate to 5%: * S S g S 2% 3% 5%.

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