Question

Suppose that the price of the same basket of goods at time 0 is PC0= 100 in country C and PD0= 90 in country D, so that the exchange rate is SCD0=10090. Inflation rates are expected to be 10% in country C and 21% in country D, over the foreseeable future.  

a) Does PP approximately predict an appreciation or depreciation of currency C?

b) What are the expected price levels in the two countries (i.e., PC1 and PD1 ) and the expected no-arbitrage exchange rate in one period (i.e., SC1 )? (Use the exact
form).

d) What is the expected no-arbitrage exchange rate two-years into the future?

Answer 1

a) As inflation is lower in country C (10%) than country D(21%), Currency C will appreciate and Currency D will depreciate as lower inflation means a lower loss in value while higher inflation means a larger loss in value and depreciation means losing value.

b) Note that the expected price level in a country in t-year = P_t= P0* (1+ inflation in the country)^t

Using this formula,

Expected price level in country C in 1 year = PC1 = PC0* (1+ inflation in country C )¹ = 100*(1+10%) = 110

Expected price level in country D in 1 year = PD1 = PD0* (1+ inflation in country D )¹ = 90*(1+21%) = 108.9

Expected no-arbitrage exchange rate in one period (i.e., SC1 ) = PC1/PD1 = 110/108.9 ( or 1.01)

c) Expected no-arbitrage exchange rate in 2 period (i.e., SC1 ) = PC2/PD2

= PC0* (1+ inflation in country C )² /  PD0* (1+ inflation in country D )²

= [100* (1+10%)²  ]/ [90* (1+21%)² ]= (100*1.1²) / (90*1.21²)

= 121/131.77 = 0.918 = 0.92

Hence, Expected no-arbitrage exchange rate in 2 period (i.e., SC1 ) = 0.92