What is then the explanation of this discrepancy between the _à priori_ assumption and the facts of the case. The explanation is that the actual exchange rates correspond to the purchasing power parities of two currencies not with regard to _all_ commodities but with regard to _some_ only. In this connection it is better to re-state the doctrine of the relation of the purchasing power parities to exchange rates with the necessary qualification. A rigorously strict formulation of the doctrine should require us to state that Englishmen and others value Indian rupees inasmuch as and in so far as those rupees will buy _such Indian goods as Englishmen want_; while Indians value English pounds inasmuch as and in so far as those pounds will buy _such English goods as the Indians want_. So stated it follows that the actual exchange rates are related to purchasing power parities of the two currencies with regard to such commodities only as are internationally traded. To assume that the actual exchange rate is an exact index of the purchasing power parity of the two currencies with regard to _all_ the commodities is to suppose that the variations in [pg 253] the purchasing power of a currency over commodities which are traded and which are not traded are the same.³⁸⁶ There is certainly a tendency for movements in the prices of these two classes of goods to influence one another _in the long run_; so that it becomes possible to say that the exchange value of a currency will be determined by its internal purchasing power. The doctrine of purchasing power parity as an explanation of exchange rates is valuable as an instrument of practical utility for controlling the foreign exchanges _and_ it is as such that the doctrine was employed in an earlier portion of this study to account for the fall in the gold value of the rupee. But to proceed, on the basis of this relationship between the purchasing power of a currency and its exchange value, to argue that at any given time the exchange is more or less an exact measure of general purchasing power of the two currencies, is to assume what cannot always be true, namely, that the prices of traded and non-traded goods move in sympathy. This assumption is too large and can only be said to be more or less true according to circumstances. Now as Prof. Kemmerer³⁸⁷ points out: ³⁸⁶ Prof. Cassel, the modern exponent of this old doctrine of the relation of exchange rates to purchasing power parities, admits that the correspondence between the two depends upon the fulfilment of this assumption, for he says: