The law of one price is an economic law stated as: "In an efficient market all identical goods must have only one price."

The intuition for this law is that all sellers will flock to the highest prevailing price, and all buyers to the lowest current market price. In an efficient market the convergence on one price is instant.

Contents 1 An example: Financial markets 2 Where the law does not apply 3 Apparent violations 4 See also 5 References

[edit] An example: Financial markets

Commodities can be traded on financial markets, where there will be a single offer 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 offer-level or buy at a higher price than the market maker's bid-level. 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." A similar argument can be used by considering arrow securities as alluded to by Arrow and Debrue (1944).^[1]

[edit] 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).^[2]
• 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.

[edit] Apparent violations

• The best-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%.^[3] This discrepancy disappeared with their final merger in 2005.

[edit] See also

• Price dispersion
• Search theory

[edit] References

• Baye, Michael, John Morgan and Patrick Scholten, "Information, Search, and Price Dispersion," (in Handbook on Economics and Information Systems, T. Hendershott, Ed., Elsevier, forthcoming)
• Nash-Equilibrium.com