Question

In the coming year, prices in Peru are expected to increase by 75%. Today the spot dollar-new sol exchange rate is $0.3063. What is the forecast of the spot exchange rate one year from now according to relative purchasing power parity if the forecast of inflation for the next year in the United States is:

a. 2%?

b. 4%?

Answer 1

Relative purchase power parity theorem states that,

The currency rates should reflect, approximately, the same purchasing power.

For instance, if you can buy a brick of gold in USA, for $100 and you can buy a brick of gold in australia with 200 Australian $, then the price of US$ should be 2 Australian$.

So that when an australian converts his currency to USD, for 200 AUD, he should get 100 USD so he can buy the same brick of gold ideally.

So, we can use the same to estimate the future prices between two currencies based on the inflation of their domestic countries.

Several common items used for Relative Purchase power parity include, I-Pad, Big Mac etc

So, the theory states

===> S_T = (1+d)S

S_T = Future Spot price after time T

S = Spot price

d = inflation differential

d = inflation in domestic country - inflation in foreign country

or [ inflation in currency - inflation in commodity, (here commodity is new-sol)]

i)  d = 2% - 75% = -73%

===>

S₁ = (1 - 0.73) * $0.3063 = $0.08270 / New Sol

ii) d = 4% - 75% = -71%

===>

S₁ = (1 - 0.71) * $0.3063 = $0.08883 / New Sol