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, E_AU/US. In the U.S., the real income (Y_US) is 1,000, the money supply (M_US) is US$5,000, the price level (P_US) is US$10, and the nominal interest rate (i_US) is 3% per annum. In Australia, the real income (Y_AU) is 100, the money supply (M_AU) is AU$1,000, the price level (P_AU) is AU$20, and the nominal interest rate (i_AU) is 3% per annum. These two countries have maintained these long-run levels. Thus, the nominal exchange rate (E_AU/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 (M_US) by 2% so that the new money supply in the U.S. (M_US) 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.), P^e_US. [5 marks]

(b) Calculate the expected exchange rate in 1 year (the new long-run exchange rate), E^e_AU/US.

[5 marks]

(c) Calculate the exchange rate today, E_AU/US. [8 marks]

(d) According to the purchasing power parity, the real exchange rate, q_AU/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, q_AU/US, today. [5 marks]

(e) Based on your answers to (b), (c), and (d), using time series diagrams below, illustrate how (i) the exchange rate, E_AU/US; and (ii) the real exchange rate, q_AU/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. [12 marks]

2. Now assume that Australian dollar is pegged to the U.S dollars with the exchange rate of E_AU/US = 2. The 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. [5 marks]

(B) What should be the interest rate in Australia today, i_AU, to maintain the par value of the exchange rate at AU$2 per US$1? [5 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?