Hi, how do I calculate the long-run price level in Australia in this question?
Use the money market with the general monetary model and foreign exchange (FX) market to answer the following question. The question considers 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.
Any help would be greatly appreciated!