# Law of one price

For the esoteric book series, see The Law of One (Ra material).

The law of one price (LOP) is an economic concept which posits that "a good must sell for the same price in all locations".[1] The law of one price constitutes the basis of the theory of purchasing power parity and is derived from the no arbitrage assumption (see Intuition).

## Intuition

The intuition behind the law of one price is based on the assumption that differences between prices are eliminated by market participants taking advantage of arbitrage opportunities.[2]

Assume different prices for a single identical good in two locations, no transport costs and no economic barriers between both locations. The arbitrage mechanism can now be performed by both the supply and/or the demand site: All sellers have an incentive to sell their goods in the higher-priced location, driving up supply in that location and reducing supply in the lower-priced location. If demand remains constant, the higher supply will force prices to decrease in the higher-priced location, while the lowered supply in the alternative location will drive up prices there. Conversely, if all consumers move to the lower-priced location in order to buy the good at the lower price, demand will increase in the lower-priced location, and - assuming constant supply in both locations - prices will increase, whereas the decreased demand in the higher-priced location leads the prices to decrease there. Both scenarios result in a single, equal price per homogeneous good in all locations.[2]

In efficient markets the convergence on one price is instant. For further discussion, please refer to Rational pricing.

### Example: financial markets

Commodities can be traded on financial markets, where there will be a single offer price (asking price), and bid price. Although there is a small spread between these two values the law of one price applies (to each). No trader will sell the commodity at a lower price than the market maker's bid-level or buy at a higher price than the market maker's offer-level.[2] In either case moving away from the prevailing price would either leave no takers, or be charity.

In the derivatives market the law applies to financial instruments which appear different, but which resolve to the same set of cash flows; see Rational pricing. Thus:

"A security must have a single price, no matter how that security is created. For example, if an option can be created using two different sets of underlying securities, then the total price for each would be the same or else an arbitrage opportunity would exist.[3]"

A similar argument can be used by considering arrow securities as alluded to by Arrow and Debreu (1944).

## Where the law does not apply

• The law does not apply intertemporally, so prices for the same item can be different at different times in one market. The application of the law to financial markets in the example above is obscured by the fact that the market maker's prices are continually moving in liquid markets. However, at the moment each trade is executed, the law is in force (it would normally be against exchange rules to break it).
• The law also need not apply if buyers have less than perfect information about where to find the lowest price. In this case, sellers face a tradeoff between the frequency and the profitability of their sales. That is, firms may be indifferent between posting a high price (thus selling infrequently, because most consumers will search for a lower one) and a low price (at which they will sell more often, but earn less profit per sale).[4]
• The Balassa-Samuelson effect argues that the law of one price is not applicable to all goods internationally, because some goods are not tradable. It argues that the consumption may be cheaper in some countries than others, because nontradables (especially land and labor) are cheaper in less developed countries. This can make a typical consumption basket cheaper in a less developed country, even if some goods in that basket have their prices equalized by international trade.

## Apparent violations

• A well-known example of an apparent violation of the law was Royal Dutch/Shell shares. After merging in 1907, holders of Royal Dutch Petroleum (traded in Amsterdam) and Shell Transport shares (traded in London) were entitled to 60% and 40% respectively of all future profits. Royal Dutch shares should therefore automatically have been priced at 50% more than Shell shares. However, they diverged from this by up to 15%.[5] This discrepancy disappeared with their final merger in 2005.