Chapter 68: HL extension exchange rate calculations (3.2) HL extensions Exchange rate calculation Supply and demand linear functions Price of goods in another currency Using currency data Calculate the value of one currency in terms of another currency Plot demand and supply curves for a currency from linear functions and identify the equilibrium exchange rate Calculate the price of a good in different currencies using exchange rates Outline the changes in the value of a currency from a set of data HL will be required to do some simple computations on exchange rates. A few minutes revision of the HL sections in Chapters 4 to 6 is time well spent. Calculations and answers in the end of chapter summary. Exchange rate calculation The matrix below gives three different currencies and the US dollar s value against them. Currency April 2012 Japanese Yen (JPY) to the dollar Thai Baht (THB) to the dollar Norwegian Krone (NOK) to the dollar U.S. Dollar (USD) 80 30 6 1. What is the exchange rate for the NOK in terms of the THB? 2. What is the exchange rate for the THB in terms of the JPY?
Supply and demand linear functions Assuming a freely floating exchange rate regime and 100% convertibility between the USD and the Japanese Yen, the demand and supply functions for the USD are given as: QD (USD) = 2,400-15P (ex) QS (USD) = -800 + 25P (ex) 3. Calculate equilibrium exchange rate. 4. Draw a supply and demand diagram illustrating market equilibrium for the USD. 5. American speculators feel that the JPY is undervalued and there is speculative buying of the JPY via American dollars. The relevant curve shifts 20% at all price levels. Calculate the new equilibrium exchange rate for the USD (expressed in JPY). 6. After a few weeks at the new equilibrium, the US central bank (Fed) raises interest rates. This causes a shift in the relevant curve by 10% at all price levels. Calculate the new equilibrium exchange rate for the USD. Price of goods in another currency My lady Bell finally gets hold of the Seiko Orange Monster automatic divers watch for me! It costs JPY18,500 in Kyoto, NOK2,400 in Oslo and THB7,200 in Bangkok. 7. Where should she buy my new watch? Oh, yes, she gets paid in USD. 8. Should she order the watch and have it sent to our home address in Indonesia? Using currency data Figure 68.1 shows how the Swiss Franc (CHF) compared to the EURO ( ) has developed over a five year period. Figure 68.2 shows the Australian dollar (AUD) vs the EURO during the same period.
Figure 68.1 Price of the CHF in Figure 68.1 Price of the in AUD 9. How has the EURO done during this period of time has it become stronger or weaker? 10. How has the exchange rate for the AUD evolved in terms of the EURO? 11. What say you about the exchange rate for the CHF in terms of the AUD? 12. If you had a time machine and could go back to January 2008, would you have put your savings into Francs or Australian dollars? This is question eleven. Q12
Summary and revision 1. The NOK is trading at THB5 to the NOK. (THB30/NOK6) 2. The THB is trading at JPY2.667 to the NOK. (JPY80/THB30) 3. Equilibrium (solving for price); 2,400 15P (ex) = -800 + 25P (ex) 3,200 15P (ex) = 25P (ex) 3,200 = 40P (ex) P USD = JPY80 Solving for quantity; 2,400 15x80 or -800 + 25 x 80 2,400 15 x 80 = 1,200 4. (Rory, you d best check my math-speak! Also, could you stick the diagram here please?) 5. Speculative buying by US speculators means an increase in the supply of the USD. The new supply function is -640 + 25P (ex) (i.e. the Q-axis intercept for the S-curve has increased by 20%). New equilibrium means solving P (ex) in 2,400 15P (ex) = -640 + 25P (ex) 3,040-15P (ex) = 25P (ex) 3,040 = 40P (ex) P USD = JPY76 6. When the Fed raises the rate of interest there will be speculative inflows to the US. This increases the demand for the USD. The new demand function is QD (USD) = 2,640-15P (ex) (an increase in the Q-axis intercept by 10%). New equilibrium price is 2,640 15P (ex) = -640 + 25P (ex). 3,280-15P (ex) = 25P (ex) 3,280 = 40P (ex) P USD = JPY82 7. In the US quite frankly since it is a most competitive market and far cheaper than the three options given. However, the USD price is USD231.25 in Japan; USD400 in Norway; and USD240 in Bangkok. 8. You kidding?! Revise Chapter 65. 9. The EURO has depreciated against both the AUD and the CHF. 10. The AUD has of course appreciated against the EURO.
11. The exchange rate for the CHF in EUROS went from CHF1 = 0.6 in January 2008 and CHF1 = 0.85 for the SFR in Jan 12. That means that the CHF has appreciated against the EURO by 14%. 12. In January 2008 the values were: 0.6 = CHF1 so 1 = CHF1.667. The Australian dollar was at AUD1.6 = 1. Thus AUD1.6 = CHF1.667. The exchange rate for the Swiss Franc was CHF1 = AUD0.96 (AUD1.6/CHF1.667) In January 2012 the situation was: 0.85 = CHF1 so 1 = CHF1.17. AUD1.25 = 1. Thus AUD1.25 = CHF1.17. The exchange rate for the Swiss Franc was CHF1 = AUD1.068 (AUD1.25/CHF1.17). In summa; one should have put one s savings in the Swiss Franc. Oh yes, I just remembered; I did! Nothing like a global economic crises to raise the value of safe-haven currencies. Let me stick my neck out a bit further while I m at it. If you are reading this during 2012 I strongly recommend you buy the Yuan. (Rory, I can t get this goddam diag into the Summary and revision box. Should be between question answers 3 and 4.) P USD in JPY 160 Qs = -800 + 25P (ex) S USD 80 Qd = 2,400-15P (ex) D USD -1.0-0.8-0.5 0 0.5 1.0 1.2 1.5 2.0 2.4 2.5 Q/t (billions USD/day)