Purchasing power parity theory in a model without international trade of goods

In recent discussions it frequently occurs that the Purchasing Power Parity Theory is identified with Jevons law of one price. By pointing to real world obstacles working against perfect goods arbitrage it is then erroneously concluded that the Purchasing Power Parity Theory cannot be valid while a dinstiction between an absolute version and a relative version of the Purchasing Power Parity Theory is neglected. In the present paper it is shown that the Purchasing Power Parity Theory in the relative sense holds even in a world without international trade in goods and that the propositions of that version of the Purchasing Power Parity Theory are not related to international trade in goods but are implications of the quantity theory of money. Although on occasion oral references to this result are made, formal and rigorous demonstrations of its validity seem not to be available. The validity of the Purchasing Power Parity Theory in a world without international trade of goods is symmetric to the finding that interest rate parity to hold does not presuppose international capital movements.