- 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.
- 1. Consider that the Reserve Bank of Australia (RBA) uses a floating exchange rate system.
- (a) Calculate the U.S. price level in 1 year (the new long-run price level in the U.S.), PeUS. [3 marks]
- (b) Calculate the expected exchange rate in 1 year (the new long-run exchange rate), EeAU/US.
- [3 marks]
- (c) Calculate the exchange rate today, EAU/US. [3 marks]
- (d) According to the purchasing power parity, the real exchange rate, qAU/US, will be 1 in 1 year. However, the real exchange rate is different from 1 today since the prices in two countries do not change at all today. Calculate the real exchange rate, qAU/US, today. [2 marks]
- (e) Based on your answers to (b), (c), and (d), using time series diagrams below, illustrate how (i) the exchange rate, EAU/US; and (ii) the real exchange rate, qAU/US, change over time in response to the permanent decrease in the U.S. money supply. Be sure to label all axis, and draw vertical dashed lines for time T and T+1 year, and horizontal dashed lines for the initial long-run equilibrium as
shown in the diagrams below to get full marks.EAU/US qAU/US
T T+1 year Time
2. Now assume that Australian dollar is pegged to the U.S dollars with the exchange rate of EAU/US = 2.
T T+1 year TimeThe RBA maintains this exchange rate all the time.
- (A) Should the RBA raise or reduce the money supply in Australia today to maintain the par value of the exchange rate at AU$2 per US$1? Briefly explain the reason. [3 marks]
- (B) What should be the interest rate in Australia today, iAU, to maintain the par value of the exchange rate at AU$2 per US$1? [hint: Use UIP and consider the expected exchange rate and the spot rate if the exchange rate is pegged]. [4 marks]
- (C) What should be the Australian money supply in the long-run to maintain the par value of the exchange rate at AU$2 per US$1?