Assignment Questions

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_$) is 1.00trill., the money supply (M_$) 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), P^e_£ (round to 3 decimal places).               

(b) Calculate the expected exchange rate in 1 year (the new long-run exchange rate at T+1), E^e_$/£ (round to three decimal places).

(c) Calculate the exchange rate today, E_$/£ (round to three decimal places).

(d) Based on your answers to (b) and (c), using time series diagrams below, illustrate how the exchange rate, E_$/£ changes over time in response to the permanent decrease in the U.K. real income. Be sure to (i) label all axis, (ii) draw vertical dashed lines for time T and T+1 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.

2. The Brexit referendum result was announced on the morning of 24 June 2016. Go to the Federal Reserve Economic Data (FRED) at the U.S. Federal Reserve Bank - St. Louis and get the daily exchange rates for the U.S. dollar against the Australian dollar, and against the U.K. British pound. Note that the exchange rates are quoted based on American terms for the U.S.

N.B.: In the following questions, the U.K. pound is considered to be the home currency.

(a) Find the exchange rates of the U.K. pound against the US$ and the AU$, E_£/US$ and E_£/AU$, on 23 June 2016 and 24 June 2016. (Round to 3 decimal places).

(b) Find the depreciation rate of the U.K. pound against the US$ and the AU$, %?E_£/US$ and %?E_£/AU$, over one day, from 23 June 2016 to 24 June 2016. (Round to 3 decimal places)

3. Bonus Question: Now, consider that today is time T-1. Today, all real incomes, money supplies, and the interest rates in two countries do not change at all. Explain what will happen to the exchange rate today, E_$/£, (rise/fall) if everyone realizes that the U.K. real income will fall permanently by 10% one year later, at time T. The answer should have the reasons for the change of the exchange rate.