absolute PPP=relative PPP

I have two questions: (1) law of one price means same good sell in USD, i.e. 2 USD should be sell at Japan 200 JPY, if USD:JPY=100, so does law of one price mean abosolute PPP? (2), abosolute PPP links expected exchange rate with price level, relative PPP links expected exchange rate with inflation rate, but I checked the TEXT, if price level in US and Japan is 1:100, inflation level will be 1:100 also, so under relative PPP and absolute PPP, we will get same expected exchange rate, right?

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Absolute PPP tries to predict exchange rates, so as to hold ‘law of one price’ between that pair of currencies. But since, each country has a different basket of consumables (in its contents and weightage), law of one price for 2 different baskets does not make good sense. Relative PPP is based on overall price levels in a country, reflected by its overall inflation level. So, Relative PPP is much more general than Absolute PPP. In your case, if the basket is exactly same in the 2 countries, yes, Absolute PPP and Relative PPP would predict same future exchange rate.

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