2. Two countries, Britain and the U.S. produce just one good, beef. Suppose that
ID: 2620516 • Letter: 2
Question
2. Two countries, Britain and the U.S. produce just one good, beef. Suppose that the price of beef in U.K. is £2.80 per pound, and in US, it is $3.70 per pound. (6 points) (a) What should the S/E spot exchange rate be, according to PPP theory? b) Suppose that the price of beefis expected to rise to £3.10 in the U.K. and to $4.65 in the US by the same time next year. What should the one year forward S/£ exchange rate? (c) Given your answers to parts (a) and (b), and given that current interest rate in UK. is 10%, what would you expect current U.S. interest rates to be? pound. and iExplanation / Answer
Solution :
(a) According to PPP Theory exchange rate between two currencies is given by the following formula
Exchange rate = Cost of goods or services in currency x / cost of goods or services in currency y
Here currency x = US Dollars and Currency y = Pound
Thus the $ / £ exchange rate = 3.70/ 2.80 = $ 1.3214
(b) If the price of beef increases to £ 3.10 in UK and to $ 4.65 in the US by the same time in the next year, the one year forward $ / £ exchange rate =
= 4.65/3.10 = $ 1.5
(c ) As per the purchasing power parity theory
(Forward rate /spot rate) = {( 1 + Interest rate in Currency ‘x’ )/ 1 + Interest rate in Currency ‘y’}
Here Curreny X = US Dollars ; Currency Y = British Pound
Spot exchange rate $ / £ = $ 1.3214 ; One year $ / £ forward rate = $ 1.5 ; Interest rate in the UK = 10 % = 0.1
Substituting the above values in the formula we have
( 1.5 / 1.3214) = {( 1+ x) / ( 1 + 0.1) }
1.1352 = { (1+x) / 1.1}
1.1352 / 1.1 = 1+ x
1+x = 1.1352/ 1.1
1+x = 1.0320
X = 1.0320-1 = 0.320 = 3.2 %
Thus the current interest rates in US would be equal to 3.2 % .
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