Question

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 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.

1.    Calculate the new long-run price level in Australia, P^*_$ (round to 4 decimal places).

2. Calculate the new long-run exchange rate, E^*_$/£ (round to 4 decimal places).   

3. Calculate the expected exchange rate 1 year from today (T+1), E^e_$/£ (round to 4 decimal places).     

4.    Calculate the real exchange rate today (T), q_$/£ (round to 4 decimal places).  

5.    Based on the half-life of the deviation from PPP, calculate the expected real exchange rate 4 years from today (T+4), q^e_$/£,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 (P^e_$,4 = 21.00). Calculate the expected exchange rate 4 years from today (T+4), E^e_$/£,4(round to 4 decimal places).     

Answer 1