Calculation of Real Exchange Rate

[jigglypuff]

Hi
I am confused about the calculation formula of the real exchange rate.
It is stated that the formula is
Real exchange rate (d/f) = nominal exchange rate (d/f) x (CPIforeign / CPIdomestic)
I learned that d/f means cost of a foreign currency unit in terms of domestic currency units.
Here is an example taken from SN Book2 pg231
[question removed by admin]
The answer given is $1.60/ x 112/110 = $1.629/
In this case U.K GBP is the base currency and USD is the price currency. So CPIdomestic will be UK’s CPI. My question is why not $1.60/ x 110/112 based on the formula?
Thanks for explaining in advance!

 

[S2000magician]

Recall that:
USDreal = USDnom / CPI-USD
and
GBPreal = GBPnom / CPI-GBP
Thus, the real exchange rate (USDreal / GBPreal) relates to the nominal exchange rate (USDnom / GBPnom) by:
USDreal / GBPreal = (USDnom / CPI-USD) / (GBPnom / CPI-GBP)
= (USDnom / CPI-USD) × (CPI-GBP / GBPnom)
= (USDnom / GBPnom) × (CPI-GBP / CPI-USD)

 

[jigglypuff]

Thanks! Much clearer now.
In that case, this formula stated in the notes does not hold?
Real exchange rate (d/f) = nominal exchange rate (d/f) x (CPIforeign / CPIdomestic)

 

[S2000magician]

jigglypuff wrote:Thanks! Much clearer now.
In that case, this formula stated in the notes does not hold?
Real exchange rate (d/f) = nominal exchange rate (d/f) x (CPIforeign / CPIdomestic)

This formula is correct.
Look at the last bit I posted:

S2000magician wrote:
USDreal / GBPreal = (USDnom / GBPnom) × (CPI-GBP / CPI-USD)

With USD the domestic currency and GBP the foreign currency, this is exactly your formula.