As a result of such arbitraging, the price would be bid up at the market where the price was previously lower due to a rise in demand while at the same time due to a rise in supply, the price would come down in the market with the higher price and finally as a result of this process the arbitraging would result in equalized prices in all markets. However, it is pertinent to note that there are three conditions required for the law of one price to hold – a) transport costs, transaction costs and other trade barriers should be insignificant. b) All associated markets should be competitive in nature and c) The goods concerned must be tradable. The law of one price does not hold for non-traded goods.
Suppose that the price of good X per unit is $20 in the US market while it is sold at P (Peso) 150 per unit in Mexico. Suppose the spot exchange rate (Ep/$) is given to be 10 Pesos per Dollar. The dollar price of good X in Mexico can be derived as [P 150 / (Ep/$)] = $15 per unit of X. So in this case, the prices are not yet equalized thereby under insignificant transport costs offering a profitable opportunity of arbitrage in purchasing from Mexico and selling in the US market for a per-unit gain of $5. However once such activity burgeons, through the interaction of demand-supply forces in the markets, the prices will start moving towards one another so that finally they are equalized provided that the transport and transaction cost barriers do not change due to the increased international arbitraging activity.
The law of one price, therefore, requires the foreign currency-denominated price to be equivalent to the home currency price of any domestic good and vice –versa. Thus the law of one price, in essence, can be translated into the following equation:
The law of one price is applicable to the market for foreign exchange as well. Since the exchange rate itself serves as the price in the market for foreign exchange, the law of one price intimates that in the presence of discrepancies in the different domestic prices of .particular currencies, the exchange rate itself will adjust to re-establish equilibrium. Otherwise, profitable arbitraging opportunities will remain open.