Law of one price

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][2][3][4][5][6][7]} This law is derived from the assumption of the inevitable elimination of all arbitrage.

The law of one price constitutes the basis of the theory of purchasing power parity, an assumption that in some circumstances (for example, as a long-run tendency) it would cost exactly the same number of, for example, US dollars to buy euros and then to use the proceeds to buy a market basket of goods as it would cost to use those dollars directly in purchasing the market basket of goods.

History

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

• In 2015, The International Monetary Fund holds 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.^[8]
• 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.^[9]
• Indonesian governmental oil subsidies against oil smugglers; The smugglers selling stolen government-discounted oil back to its market rate.^[10]
• 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%.^[11] This discrepancy disappeared with their final merger in 2005.

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.^[12]

Example in regular trade

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.^[13]

Both scenarios result in a single, equal price per homogeneous good in all locations.^[12]

In efficient markets the convergence on one price is instant. For further discussion, please refer to 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.^[12] 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.^[5]"

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).^[14]
• 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.

See also

• Oneness (disambiguation)
• Price
• Gresham's law is an economic principle that states: "When a government overvalues one type of money and undervalues another, the undervalued money will leave the country or disappear from circulation into hoards, while the overvalued money will flood into circulation."
• Engel's law is an observation in economics stating that as income rises, the proportion of income spent on food falls, even if actual expenditure on food rises.
• Hotelling's law is an observation in economics that in many markets it is rational for producers to make their products as similar as possible.
• Pizza Principle is the claim that "the price of a slice of pizza has matched, with uncanny precision, the cost of a New York subway ride."
• Iron law of wages is a proposed law of economics that asserts that real wages always tend, in the long run, toward the minimum wage necessary to sustain the life of the worker.
• Diminishing returns is the decrease in the marginal (incremental) output of a production process as the amount of a single factor of production is incrementally increased, while the amounts of all other factors of production stay constant.
• Iron law of prohibition posits that as law enforcement becomes more intense, the potency of prohibited substances increases.
• Okun's law can state that for every 1% increase in the unemployment rate, a country's GDP will be roughly an additional 2% lower than its potential GDP.
• Verdoorn's law states that in the long run productivity generally grows proportionally to the square root of output.
• Supply and demand
• Men's underwear index
• Hemline index
• Big Mac index
• Recession index
• Christmas Price Index
• Rational pricing
• Price dispersion
• Search theory

References

1. Spritzer, George. "Performance Law of One Price: Works for Berkshire, But Not Chipotle Mexican Grill". Seeking Alpha. Retrieved 3 December 2015. ...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. "Law of one price Definition". NASDAQ. Retrieved 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. "law of one price". Cambridge University Press 2015. Retrieved 3 December 2015. ECONOMICS[:] [T]he principle that in a perfect financial market goods would have the same price everywhere[.]
4. "Law of One Price Definition". Investopedia. Retrieved 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. "What is Law of One Price?". WebFinance, Inc. Retrieved 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.
6. Rashid, Salim (Spring 2007). "The "Law" of One Price: Implausible, Yet Consequential". Quarterly Journal of Austrian Economics 10 (1): 79. 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...
7. Mankiw, N. G. (2011). Principles of Economics (6th ed.). Mason, OH: South-Western Cengage Learning. Page 686.
8. 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). Retrieved 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.
9. Steil, Benn; Dinah Walker. "The New Geo-Graphics iPad Mini Index Should Calm Talk of Currency Wars". Council on Foreign Relations. Retrieved 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.)...
10. Prasodjo, Darmawan. "Law of One Price defeats oil subsidy". The Jakarta Post. Retrieved 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...
11. Lamont, O.A. and Thaler, R.H. (2003), "Anomalies: The Law of One Price in Financial Markets". Journal of Economic Perspectives 17 (Fall 2003), pp. 191–202.
12. Karl Gunnar Persson (10 February 2008). "Definitions and Explanation of the Law of One Price". eh.net. Economic History Services. Retrieved 28 September 2014.
13. Worstall, Tim. "The Great Norwegian Diaper Shortage Of 2013: Ricardo's Iron Law Of One Price". Forbes. Retrieved 3 December 2015. This is rather fun: an explanation for the Great Norwegian Diaper Shortage of 2013. It would appear that the stores in the south of that great country have got themselves locked into a price war on a loss leader. The result of which is just yet another proof of Ricardo’s iron law of one price. Or, if you prefer, the futility of trying to fix prices at any point other than their market clearing price. Or if you want to go a bit further, why and how there is arbitrage and speculation in financial markets[...]The basic story is here: 'Supermarkets in the south however trying to lure local customers by undercutting rivals on the price of nappies inadvertently made it profitable enough for residents of nearby countries to start trading in them. “They buy every last diaper, I mean everything we have on the shelves, throw it in the back of their car and take them home, where they sell it for a nice profit,” says Terje Ragnar Hansen, a regional director for retail chain Rema 1000.'
14. Burdett, Kenneth, and Kenneth Judd (1983), 'Equilibrium price dispersion'. Econometrica 51 (4), pp. 955-69.

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

Further reading

• ConocoPhillips Will Ship First US Crude After End Of Export Ban: "...US oil products have remained over those 40 years at the world prices plus or minus transport costs, as the law of one price would predict. The cost of crude oil within the US has fallen below the global price more recently: but that’s because the export ban only applied to crude, not refined products. Thus there was a transfer of rents from drillers to refiners: something that actually reduced the amount of US crude produced, not the point and intention at all." -Tim Worstall
• The law of one price has been violated, Michael A. Gayed
• Move Over Big Mac: The Law of One Price Is Lovin’ Our Little Mac Index, Benn Steil and Dinah Walker
• Definitions of The Law of One
• The Law of One Price Over 700 Years, Issues 2001-2174; Kenneth Rogoff, Kenneth Froot, Michael Kim
• Saturday Morning Breakfast Cereal, June 10, 2015; Zach Weinersmith