The law of one price states that any good must have a single price in all markets. If it does not, then there will be opportunities for arbitrage. However, arbitrage opportunities can only last a short time as markets will quickly work to cancel out the profit from arbitrage.
Example of law of one price in action
You have a diamond in Germany that you can sell for €10,000. The exact same diamond can sell in New York for $17,000. The exchange rate is $1.60/€1.00. If you take your diamond to New York and sell it you will want to change your dollars back into Euro to spend in Europe. At this exchange rate you will end up with €10,625: a nice profit for very little work!
As soon as other people notice this, more people will take their European diamonds and sell them in New York. Of course all these European sellers will also want to have Euros not dollars. So they go to the foreign exchange markets and sell their dollars for Euros. This means that there will be an increase in demand for Euros and a decrease in demand for dollars. What happens when there is a decrease in demand for something? The price does down. The situation might play out like this:
$1.60/€1.00 → $1.65/€1.00 → $1.70/€1.00
At a price of $1.70/€1.00 your Euro income from selling in New York will be $17,000/1.70= €10,000. There is now no advantage for you to go to New York to sell your diamond. In fact there is a slight disadvantage because you have transport and other costs.
The law of one price holds for most commodity goods. It does not hold for differentiated goods such as different types of car. Other factors can also stop the market from enacting the law. These could be:
Government interference, transportation costs, information costs, information asymmetry, perishability and difficulties in transportation.