The questions consider the relationship between the U.K. pound () and the Australian dollar ($). Let the exchange rate be defined as Australian dollars per pound, E$/. In the U.K., the real income (Y) is 10.00 trill., the money supply (M) is 50.00 trill., the price level (P) is 10.00, and the nominal interest rate (i) is 2.00% per annum. In Australia, the real income (Y$) is 1.00 trill., the money supply (M$) is AU$10.00 trill., the price level (P$) is AU$20.00, and the nominal interest rate (i$) 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 T (today) when the Australian real income falls permanently 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, (E$/= 2.2848). Assume that Australia and the U.K. use the floating exchange rate system.

a) Based on the half-life of the deviation from PPP, calculate the expected real exchange rate 4 years from today (T+4), qe$/,4 (round to 4 decimal places).

b) Following the permanent fall of Australian income by 10%, the price level in Australia is expected to go up by 5% in 4 years (Pe$,4 = 21.00). Calculate the expected exchange rate 4 years from today (T+4), Ee$/,4(round to 4 decimal places).