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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.K. pound (Ã‚Â£) and the Australian dollar ($). Let the exchange rate be defined as Australian dollars per pound,
$/Ã‚Â£. In the U.K., the real income (
Ã‚Â£) is 10.00 trill., the money supply (
Ã‚Â£) is Ã‚Â£50.00 trill., the price level (
Ã‚Â£) is Ã‚Â£10.00, and the nominal interest rate (
Ã‚Â£) is 2.00% per annum. In Australia, the real income (
$) is 1.00 trill., the money supply (
$) is AU$10.00 trill., the price level (
$) is AU$20.00, and the nominal interest rate (
$) is 2.00% per annum. These two countries have maintained these long-run levels. Note that the uncovered interest parity (UIP) holds all the time, and the purchasing power parity (PPP) holds only in the long-run. The half-life of the deviation from the PPP is 4 years, that is, the deviation from PPP shrinks by 50% in 4 years.
Now, consider time
(today) when the Australian real income falls
by 10% unexpectedly so that the new real income in Australia becomes Y$ = 0.90 trill. With the new real income, the interest rate in Australia falls to 1% per annum today. With these changes, the exchange rate today becomes 2.2848, (
$/Ã‚Â£ = 2.2848). Assume that Australia and the U.K. use the floating exchange rate system.
1. Calculate the new long-run price level in Australia,
*$ (round to 4 decimal places).
2. Calculate the new long-run exchange rate,
$/Ã‚Â£ (round to 4 decimal places).
3. Calculate the expected exchange rate 1 year from today (
$/Ã‚Â£ (round to 4 decimal places).
4. Calculate the real exchange rate today (
5. Based on the half-life of the deviation from PPP, calculate the expected real exchange rate 4 years from today (
$/Ã‚Â£,4 (round to 4 decimal places).
6. Following the permanent fall of Australian income by 10%, the price level in Australia is expected to go up by 5% in 4 years (
$,4 = 21.00). Calculate the expected exchange rate 4 years from today (
7. Based on your answers to Q2 Ã¢â‚¬â€œ Q6, using time series diagrams below, illustrate how the nominal and real exchange rates,
$/Ã‚Â£, change over time in response to the permanent decrease in the Australian real income.
Be sure to
(i) label all axis, (ii) draw vertical dashed lines for time
+4 year, (iii) draw horizontal dashed lines for the initial long-run equilibrium as shown in the diagrams below, and (iv) draw the horizontal dashed lines for the new long-run equilibrium
to get full marks
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