Finocturne
Macroeconomics

Real Exchange Rate & PPP Calculator

Use matched baskets and an explicit quotation to calculate illustrative PPP, relative prices and deviation.

User inputs or hypothetical examples · Consistent units and periods · Local calculation

Inputs

Quote direction
Taiwan is the domestic economy. Changing direction takes the reciprocal of the entered quote.
More data settings

The two baskets should have comparable goods, quality and dates.

Use actual prices of a comparable basket, not arbitrary CPI levels with different bases. Taiwan prices use TWD and US prices USD. The quote direction changes the displayed exchange-rate value and formula; the real comparison remains the foreign basket relative to the domestic basket.

Results

Start with your numbers

Review or adjust your inputs, then calculate to see your results and interpretation.

Understand this calculation

A ratio above one means the US basket is more expensive after conversion to TWD; below one means cheaper. It is a defined basket comparison, not a forecast that market exchange rates must revert soon.

See calculation method and assumptions

Formula

Real Exchange Rate & PPP

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.

Variables, rates and periods

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.

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.

Use matched baskets and an explicit quotation to calculate illustrative PPP, relative prices and deviation.

Worked example

  1. Match baskets, quality and price bases, then choose quotation direction.
  2. Divide Taiwan's 3,000 by the US 100 for 30 TWD/USD.
  3. At 32 the US basket costs 3,200: divide by 3,000 for 1.0667. Quote inversion reciprocates both the market rate and PPP.

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.

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