Law of one price explained

The law of one price (LOOP) states that in the absence of trade frictions (such as transport costs and tariffs), and under conditions of free competition and price flexibility (where no individual sellers or buyers have power to manipulate prices and prices can freely adjust), identical goods sold at different locations should be sold for the same price when prices are expressed in a common currency.^{[1] [2] [3] [4] [5] [6]} This law is derived from the assumption of the inevitable elimination of all arbitrage.

Overview

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.^[7]

Example in regular trade

Assume different prices for a single identical good in two locations, no transport costs, and no economic barriers between the two locations. Arbitrage by both buyers and sellers can then operate: buyers from the expensive area can buy in the cheap area, and sellers in the cheap area can sell in the expensive area.

Both scenarios result in a single, equal price per homogeneous good in all locations.

For further discussion, see Rational pricing.

Example in formal 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. 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:^[8]

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 Debreu (1944).

Non-application

• 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 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).^[9]
• 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.

Prerequisite

• absence of trade frictions
• free competition
• price flexibility^[10]

The law of one price has been applied towards the analysis of many public events, such as:

• In 2015, An International Monetary Fund working paper found that the law of one price holds for most tradeable products in Brazil but does not apply in the same way to its non-tradeable goods.^[11]
• A director of the Council on Foreign Relations held in 2013 that the then-current Apple iPad mini followed the law of one price, as far as its price nearly reached the same US dollar exchange rate in each applicable country.^[12]
• Indonesian governmental oil subsidies against oil smugglers; The smugglers selling stolen government-discounted oil back to its market rate.^[13]
• An apparent violation of the law involving international Royal Dutch/Shell stocks. 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%.^[14] This discrepancy disappeared with their final merger in 2005. In recent years the company has had two different shares, "A" and "B" shares. Although each carries the same rights to dividends etc, they usually trade at different prices. This can be explained by different tax treatments.

See also

• Big Mac index
• Christmas Price Index
• Equal pay for equal work
• KFC Index
• Hemline index
• Men's underwear index
• Price
• Price discrimination
• Price dispersion
• Rational pricing
• Recession index
• Search theory
• Supply and demand

References

• Fan. C. Simon. Wei. Xiangdong. The Law of One Price: Evidence from the Transitional Economy of China. Review of Economics and Statistics. November 2006. 88. 4. 682–697. 10.1162/rest.88.4.682. 16524994.

Further reading

• Benn Steil & Dinah Walker, Move Over Big Mac: The Law of One Price Is Lovin' Our Little Mac Index, Geo-Graphics, Council on Foreign Relations (February 25, 2015)
• Kenneth Rogoff, Kenneth Froot & Michael Kim, The Law of One Price Over 700 Years, International Monetary Fund Working Paper (WP/01/174) (November 2011)

Notes and References

1. Book: Feenstra. Robert. International .There is a basic principle in economics called "the law of one price". This states that identical goods should have identical prices. For example, an ounce of silver should cost the same in the New York and Paris, otherwise silver would flow from one city to the other. Of course, this law does not always hold in practice, unless there are competitive markets, no transaction costs and no trade barriers....
2. Web site: Law of one price Definition. NASDAQ. 3 December 2015. An economic rule stating that a given security must have the same price no matter how the security is created. If the payoff of a security can be synthetically created by a package of other securities, the implication is that the price of the package and the price of the security whose payoff it replicates must be equal. If it is unequal, an arbitrage opportunity would present itself..
3. Web site: law of one price. Cambridge University Press 2015. 3 December 2015. ECONOMICS[:] [T]he principle that in a perfect financial market goods would have the same price everywhere[.].
4. Web site: Law of One Price Definition. Investopedia. 3 December 2015. The theory that the price of a given security, commodity or asset will have the same price when exchange rates are taken into consideration. The law of one price is another way of stating the concept of purchasing power parity[...]The law of one price exists due to arbitrage opportunities. If the price of a security, commodity or asset is different in two different markets, then an arbitrageur will purchase the asset in the cheaper market and sell it where prices are higher[...]When the purchasing power parity doesn't hold, arbitrage profits will persist until the price converges across markets..
5. Rashid. Salim. The "Law" of One Price: Implausible, Yet Consequential. Quarterly Journal of Austrian Economics. Spring 2007. 10. 1. 79. 10.1007/s12113-007-9001-7. 17745635. The law of one price (hereafter LoP) is one of the most basic laws of economics and yet it is a law observed in the breach. That a given commodity can have only one price, except for the briefest of [disequilibrium] transitions, seems to be almost an axiom....
6. Mankiw, N. G. (2011). Principles of Economics (6th ed.). Mason, OH: South-Western Cengage Learning. Page 686.
7. Web site: Karl Gunnar Persson. Definitions and Explanation of the Law of One Price. eh.net. Economic History Services. 28 September 2014. 10 February 2008.
8. Web site: What is Law of One Price?. WebFinance, Inc.. 3 December 2015. An economic rule which states that in an efficient market, 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..
9. Burdett, Kenneth, and Kenneth Judd (1983), 'Equilibrium price dispersion'. Econometrica 51 (4), pp. 955-69.
10. Book: Taylor. Alan. Feenstra. Robert. International Macroeconomics. 65. 2012.
11. Carlos Góes. Troy Matheson. 2015. Domestic Market Integration and the Law of One Price in Brazil. IMF Working Paper, Western Hemisphere Department. International Monetary Fund. Working Paper No. 15/213. 3 December 2015. This paper presents the first assessment domestic market integration in Brazil using the law of one price. The law of one price is tested using two panel unit root methodologies and a unique data set comprising price indices for 51 products across 11 metro-areas. We find that the law of one price holds for most tradable products and, not surprisingly, non-tradable products are found to be less likely to satisfy the law of one price. While these findings are consistent with evidence found for other countries, price convergence occurs very slowly in Brazil, suggesting relatively limited domestic market integration..
12. Web site: The New Geo-Graphics iPad Mini Index Should Calm Talk of Currency Wars. Steil. Benn. Dinah Walker. Council on Foreign Relations. 3 December 2015. ...We’ve created our own index which better meets the condition that the product can flow quickly and cheaply across borders: meet the new Geo-Graphics iPad mini Index[...]The iPad mini is a global product that travels by plane in a coat pocket, unlike a burger, and its manufacturer, Apple, is highly attuned to shifting currency values[...]“We made some pricing adjustments due to changes in foreign exchange rates,” Apple spokesman Takashi Tabayashi told Bloomberg News after Apple raised Japanese iPad prices 15% in May, offsetting the early effect of Abenomics on the yen[...]As this week’s Geo-Graphic shows, there are no major violations of the law of one price in the global market for iPad minis – unlike the market for Big Macs.[...]This is particularly the case after stripping out Value-Added Tax distortions.[...](Sales tax in many countries, like the United States, is not included in the sales price Apple advertises, but VAT is included in such prices for VAT-levying countries. VAT is also at least partly refundable for foreigners exporting the product.)....
13. Web site: Law of One Price defeats oil subsidy. Prasodjo. Darmawan. The Jakarta Post. 3 December 2015. ...These fuel subsidies place a serious burden on the government budget and it is sad to see its good intentions thwarted to such an extent. Although the fight against fuel smuggling may be noble, an economics theory makes it look like a losing battle: the Law of One Price says you can’t stop it[...]The Law of One Price says the same gasoline should have the same price anywhere (with transportation costs factored in) and that particular price is set by sellers flocking to the highest price. In an efficient market, this activity leads to equilibrium as supply and demand constantly respond to ongoing conditions.[...]But smugglers hijack these market principles while stealing the fuel. They steal subsidized oil and flock to a full-price market as the price differential and market boundaries create an opportunity....
14. Lamont . Owen A . Thaler . Richard H . Anomalies: The Law of One Price in Financial Markets . Journal of Economic Perspectives . November 2003 . 17 . 4 . 191–202 . 10.1257/089533003772034952. free .