Real Exchange Rates & PPP
Use matched baskets and an explicit quotation to calculate illustrative PPP, relative prices and deviation.
Question, try, then observe
What did you just see?
With a Taiwan basket at NT$3,000 and a US basket at US$100, PPP is 30 TWD/USD. At a hypothetical market quote of 32, the US basket costs NT$3,200, 6.67% more than the home basket. Invert the quote: 32 becomes 0.03125 USD/TWD and PPP 30 becomes 0.033333…, without changing the physical comparison.
The law of one price and absolute PPP
With identical tradable goods and no trading frictions, the same good should cost the same after currency conversion. Extending that intuition to matched baskets gives absolute PPP. Nontradable services such as rent and haircuts, transport, taxes, brand and quality differences, and segmented markets can sustain deviations. One product cannot represent a whole country's PPP.
Relative PPP concerns changes
Absolute PPP compares levels; relative PPP compares same-period inflation and nominal-rate changes. With q in TWD/USD and this real ratio held constant, q's growth factor equals Taiwan's price growth factor divided by the US factor. This is a conditional relation, not a guaranteed market path. Two CPI series independently based at 100 are not automatically comparable TWD/USD basket price levels for absolute PPP.
Define direction before real appreciation
This tool fixes R as foreign basket divided by home basket. Across comparable dates, falling R is TWD real appreciation and rising R real depreciation; relative prices can change R even with a constant nominal rate. Inverting displayed quotes reciprocates q and PPP, not R. Deviation is always defined using direct TWD/USD q relative to PPP, avoiding contradictory currency interpretations. A one-date gap between R and one is not an observed appreciation/depreciation rate.
Another example
- Match baskets, quality and price bases, then choose quotation direction.
- Divide Taiwan's 3,000 by the US 100 for 30 TWD/USD.
- At 32 the US basket costs 3,200: divide by 3,000 for 1.0667. Quote inversion reciprocates both the market rate and PPP.
Show formal definition and formula
For q quoted as TWD per USD, illustrative PPP is the Taiwan basket price in TWD divided by the matched US basket price in USD. q times the US basket price divided by the Taiwan basket price gives the foreign basket's price relative to the home basket.
PPP in TWD per USD
Foreign/home basket price ratio
Inverse quotation and the same real ratio
Deviation with a fixed direct-quote definition
For q quoted as TWD per USD, illustrative PPP is the Taiwan basket price in TWD divided by the matched US basket price in USD. q times the US basket price divided by the Taiwan basket price gives the foreign basket's price relative to the home basket.
- q
- Direct quotation: TWD per USD
- qinv
- Inverse quotation: USD per TWD
- PTW
- Taiwan basket price (TWD)
- PUS
- Matched US basket price (USD)
- qPPP
- Basket PPP: TWD per USD
- R
- Foreign/home basket price ratio
- d
- Fixed direct-quote deviation, decimal
- Units
- Prices are matched basket amounts in TWD/USD, not independently based index levels. R is unitless; decimal d displays times 100. PPP also reciprocates on quote inversion; R's physical definition remains fixed.
Common mistakes
Quote inversion must change numbers, not labels alone. Unmatched baskets, quality or independently based indices are not comparable prices. PPP deviations are neither guaranteed short-term arbitrage nor exchange-rate forecasts.
Frequently asked questions
Why does deviation stay unchanged after inversion?
Deviation retains its TWD/USD-relative-to-PPP definition and the foreign/home basket ratio; inversion changes only the rate presentation.
You can now explore…
- Define quotes, comparable baskets and real exchange rates
- Understand PPP deviations and limits to short-term prediction
Term reference1 terms
Open a term when you need a reminder. Underlined words in the article work too.