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 Aus

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).           [1 marks]

2.    Calculate the new long-run exchange rate, E*$/£ (round to 4 decimal places).                       [1 marks]

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

                                                                                                                                             [2 marks]

4.    Calculate the real exchange rate today (T), q$/£ (round to 4 decimal places).                        [2 marks]

5.    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).                                                                                                                                         [2 marks]

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 (Pe$,4 = 21.00). Calculate the expected exchange rate 4 years from today (T+4), Ee$/£,4 (round to 4 decimal places).          [2 marks]

7.    Based on your answers to Q2 – Q6, using time series diagrams below, illustrate how the nominal and real exchange rates, E$/£ and q$/£, 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 T and T+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.                                                                                   [4 marks]