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 (£) 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 2.00 trill., the money supply (M£) is £1.00 trill., the price level (P£) is £1.00, and the nominal interest rate (i£) is 4.00% per annum. In Australia, the real income (Y$) is 1.00 trill., the money supply (M$) is AU$0.75 trill., the price level (P$) is AU$1.50, and the nominal interest rate (i$) is 4.00% per annum. These two countries have maintained these long-run levels. 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.
1. Now, consider time T when the U.K. real income falls permanently by 10% unexpectedly so that the new real income in the U.K. becomes Y£ = 1.8 trill. With the new real income, the interest rate in the U.K. falls to 2% per annum today. Assume that Australia and the U.K. use the floating exchange rate system.
(a) Calculate the U.K. price level in 1 year (the new long-run price level in the U.K. at T+1), Pe£ (round to 3 decimal places).
(b) Calculate the expected exchange rate in 1 year (the new long-run exchange rate at T+1), Ee$/£ (round to three decimal places).
(c) Calculate the exchange rate today, E$/£ (round to three decimal places).