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. 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

i).

Consider the given problem here “Australia” is the home country and “UK” is the foreign country. Now, in the LR price become flexible, => adjust equilibrate the “demand” and “supply” of money.

=> At the equilibrium “Md=Ms”, => P*Y/i = Ms, => P = 10*1/0.9 = 11.11, => P=$11.11. So, the new LR price is “$11.11”.

ii).

So, here the new price in home is “Ph=$11.11” and in foreign is “Pf=10”. In the LR the “PPP” hold, => E = Ph/Pf.

=> the LR exchange rate is given by “E(H/F) = Ph/Pf = 11.11/10 = 1.11, => E() = 1.11.

iii).

Now, under the given the new SR exchange rate is given by “E=2.2848”, => under the UIP the following condition holds.

=> ih = if + (Ee-E)/E, => 1 = 2 + (Ee-2.2848)/2.2848, => (-1)*2.2848 = (Ee-2.2848).

=> (-1)*2.2848 + 2.2848= Ee, => Ee = 0. So, the expected exchange rate is “0”.

iv).

The real exchange rate is given by.

=> q = E*Pf/Ph = 2.2848*10/11.11 = 2.0565, => q = 2.0565, be the real exchange rate.