Posted: January 23rd, 2023

Use the money market with the general monetary model

QUESTIONS:

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.

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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. [5
marks]

(b) Calculate the expected exchange rate in 1
year (the new long-run exchange rate), EeAU/US.
[5
marks]

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(c) Calculate the exchange rate today, EAU/US. [8
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. [5 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. [12 marks]

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2. Now assume
that Australian dollar is pegged to the U.S dollars with the exchange rate of EAU/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, iAU, to maintain
the par value of the exchange rate at AU$2 per US$1? [5 marks]

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(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? [5 marks]

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