What it means
The law of one price is a statement about market efficiency. If the same gold bar sells for $2,000 in New York and the equivalent of $1,900 in Toronto, a trader can buy in Toronto, sell in New York and pocket the difference.
That buying pushes the Toronto price up and the New York price down until the gap vanishes. This process is called arbitrage, which means profiting from a price difference without taking on market risk.
Because many traders watch for these gaps, they tend to close very quickly for financial assets and commodities that are easy to move and trade. The law therefore holds well for items such as currencies, shares listed in two countries and standard commodities.
For other goods the law often fails, and the reasons matter to a business. Shipping costs, import duties, local taxes, differing rules and the cost of distribution all create wedges between prices in different places.
Services and non-tradable items such as haircuts or rent cannot be moved at all, so their prices differ freely. Finance teams use the idea in several places.
It underpins purchasing power parity, which compares what a basket of goods costs in different countries to judge whether a currency looks cheap or expensive. It also guides how multinationals check whether their international transfer prices and list prices are consistent.
The nuance is that firms sometimes deliberately charge different prices in different markets, called price discrimination, because customers differ in how much they will pay. The law is best seen as a force pulling prices together rather than a guarantee that they are identical.
In practice
Real-world examples.
Example
An investment bank notices that a share listed on two exchanges trades at a slightly lower price, after currency conversion, on one of them. Its trading desk buys on the cheaper exchange and sells on the other within seconds. The price gap closes and the desk keeps a small profit on a large volume.
Example
A manufacturer exports identical machine parts to three countries and sets the list price in dollars. Differences in import duties mean the final shelf prices vary by up to 12% between markets. The finance team explains the variation by customs duty and freight, not by any breach of the law.
Example
A global coffee chain compares the price of its standard latte in different countries to judge local cost levels. Where the converted price is far below its home price, local rent and wages are probably lower. The group uses the gaps as a rough guide when setting local budgets.
Formula
Calculation
Price in home currency = price in foreign currency x exchange rate (home currency per unit of foreign currency)
A bar of gold sells in New York for $2,000. In Toronto the same bar sells for CAD 2,375, and one Canadian dollar buys $0.80, so the Toronto price in US dollars is 2,375 x 0.80 = $1,900. The law of one price predicts a gap of $2,000 - $1,900 = $100 cannot last. A trader who buys in Toronto and sells in New York earns $100 per bar, and if shipping and insurance cost $30 a bar, the profit is $100 - $30 = $70 per bar, which traders will chase until the gap shrinks towards the $30 cost.Case study
Seen in the real world.
Bluewater Metals Trading is an illustrative, fictional firm that buys and sells copper cathodes across two regional exchanges. Its analyst noticed that, after converting currencies, copper on the eastern exchange was consistently $60 a tonne cheaper than on the western one.
After allowing for $45 a tonne in shipping and insurance and $5 in handling fees, the firm saw a net gain of $10 a tonne. On a monthly volume of 2,000 tonnes that was worth $20,000, but within a few weeks other traders spotted the gap and it narrowed to $50, which just covered costs. The illustrative lesson is that arbitrage profits are small and temporary, because the very act of trading removes the gap.
Watch out
Common mistakes.
- Expecting prices of every product to be equal across countries, when the law applies only to identical, easily traded goods without frictions.
- Forgetting to convert currencies before comparing prices, which makes a cheap-looking price in another country meaningless.
- Treating a price gap as free money, without deducting transport, tax, financing and execution costs.
Questions
People also ask.
Is the law of one price the same as purchasing power parity?
They are closely related, but purchasing power parity applies the idea to whole baskets of goods and to exchange rates, while the law of one price applies to a single identical item.
Why does the law fail for services?
Services such as haircuts or legal advice cannot be shipped and resold, so traders cannot arbitrage differences away.
Does the law apply to financial markets?
Yes, it works best there because assets can be moved and traded quickly at low cost, which is why arbitrage gaps in shares and currencies are often tiny.
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