Use the money market with the general monetary model and foreign exchange (FX) market to answer the following questions. The questions consider the relationship between the U.S. dollars (US$) and the Australian dollar (AU$). Let the exchange rate be defined as Australian dollars per 1 U.S. dollar, EAU/US. In the U.S., the real income (YUS) is 1,000, the money supply (MUS) is US$5,000, the price level (PUS) is US$10, and the nominal interest rate (iUS) is 3% per annum. In Australia, the real income (YAU) is 100, the money supply (MAU) is AU$1,000, the price level (PAU) is AU$20, and the nominal interest rate (iAU) is 3% per annum. These two countries have maintained these long-run levels. Thus, the nominal exchange rate (EAU/US) has been 2. Note that the uncovered interest parity holds all the time and the purchasing power parity holds only in the long-run. Assume that the new long-run levels are achieved within 1 year from any permanent changes in the economies.
Now, today at time T, the Federal Reserve Bank of the U.S. (FRB) permanently reduces the money supply (MUS) by 2% so that the new money supply in the U.S. (MUS) becomes US$4,900. With the new money supply, the interest rate in the U.S. rises to 5% per annum today.