FormalPara Definition

The law of one price states that, in a nearly perfect market, two identical goods must have nearly identical prices.

Introduction and History

The term ‘law of one price’ refers to the notion that, in a perfect market, two identical goods must have equal prices. Although this idea preceded the nineteenth-century formalization of economic theories, the name can largely be attributed to Alfred Marshall, who defined it in his Principles of Economics (1890) as

the more nearly perfect a market is, the stronger is the tendency for the same price to be paid for the same thing at the same time in all parts of the market: but of course if the market is large, allowance must be made for the expense of delivering the goods to different purchasers.

(Although Marshall probably borrowed this notion from William Jevons’ Theory of Political Economy (1871), which states ‘In the same open market, at any one moment, there cannot be two prices for the same kind of article’, the very fact that Jevons referred to it as the ‘law of indifference’ rather than the ‘law of one price’ suggests that the latter term does indeed belong to Marshall.)

Initially, the economic theory was most commonly used to explain the prices of commodities. Thus, the law of one price has been widely used in international trade theories as stating that, without regulatory constraints, the prices of a commodity in different countries at any given time should be the same after properly accounting for taxes, transport costs, currency exchange rates and other similar monetary factors. As applied to currency exchange rates, the law is sometimes interpreted as implying that, in the absence of government intervention, purchasing power parity exchange rates should equal open market exchange rates (see, e.g., Isard 1977). The theoretical appeal of this interpretation diminished after it has been noted that, in the deregulated and increasingly open economies of the post-Second World War era, purchasing power parity often diverges greatly from the official open-market exchange rate. Whether this is due to a failure of theory or a measurement error is not necessarily clear: since different countries have different economic structures and degrees of economic monetization, purchasing power parity is not easy to ascertain for sure.

As applied to financial markets, the law of one price is often restated as the law whereby securities with identical state-specific payoffs will have identical prices. In other words, two different goods valued for the stream of payoffs they provide will have equal prices regardless of their composition provided that the streams of payoffs are the same. Again, some deviations have been noted (see, e.g., Lamont and Thaler 2003); but, of course, whenever there is a discrepancy one can question whether there are states of nature not usually considered in which payoffs are different (such as, for example, a nationalization of a market economy or the bankruptcy of a company in which the beneficiaries are not clear and are decided by a court).

A third and more direct application of the law of one price is that, at any one time in a ‘nearly perfect’ market, prices of a homogenous good (such as a particular edition of a certain book) must be nearly the same. The remainder of this article will consider the appropriate interpretations of and qualifications for this statement.

Information Asymmetry and the Law of One Price

There are two caveats to confirming (testing) whether the law of one price holds in practice. The first one is that it is supposed to hold only in equilibrium. For example, according to Jevons, a market in which this law does not apply is ‘clearly’ (i.e., by definition) not in equilibrium. The second one is the definition of what it means for a market to be perfect. In the simplest interpretation, this means that the market is free from regulation and is driven by economic incentives. Clearly, this is not enough. Although the early economists were not concentrating on the role of incomplete information, they generally stipulated that a perfect market should also allow all economic agents easy and free access to information. In practice, information is never completely free since it has at least a time or a mental cost.

It seems intuitive that the outcome of such a ‘nearly perfect’ market should be the same as the outcome of a perfect market, that is, with prices equal and defined by the intersection of supply and demand curves. Although intuitive, the above argument is actually circular: it assumes that market agents obtain the information, even though there is nothing to gain by obtaining more information if the law of one price already applies. Careful theoretical consideration suggests that any, even infinitesimally small, costs of price information in equilibrium result in monopolistic market competition unless market participants face incomplete information (Diamond 1971).

To appreciate the philosophical issue in relation to the applicability of the law of one price to realistic markets, let us consider the following argument, reprinted here with minor changes from Butters (1977) (although the argument itself belongs to Diamond 1971). Assume a particular equilibrium with a price distribution known to all agents and consider buyers all having a cost of search greater than some positive lower bound c. Suppose the lowest price in the price distribution is below the monopoly price. Then the seller charging this lowest price could increase it by a small amount (lower than c) without provoking further search and thus without losing any demand to competitors. Therefore in the vicinity of the lowest price, the incentives of the seller are the same as those of a monopolist, and thus the lowest price is equal to the monopoly price. It is equally easy to argue that the highest price is at most the monopoly price, and thus all prices are the same and equal to the monopoly price.

Subsequently, a number of theoretical models were developed to address the problem of monopolistic price. These normally assume a large degree of uncertainty (e.g., Reinganum 1979; Stiglitz 1979) or a strictly positive fraction of consumers with perfect information (e.g., Varian 1980; Stahl 1989); another interpretation of the differences in consumer behaviour is that some consumers are loyal rather than uninformed: see Narasimhan (1988); see also Villas-Boas (1995), for some empirical support of such mixed-strategy equilibrium in a CPG market and Lal and Villas-Boas (1998), for a characterization of the equilibrium price dispersion in a channel with multiproduct retailers) to obtain price reduction considerably below the monopoly price, although Kuksov (2006) shows that (small) uncertainty about market fundamentals in the amount proportional to the (small) consumer search costs is enough to counteract the anti-competitive effect of buyer search costs. An alternative possibility is to change the notion of equilibrium (e.g., Baye and Morgan 2004).

Distinguishing incomplete information, which implies unobservable exogenous variation of market fundamentals driving variability in unobservable actions, from imperfect information, which is due only to actions not being observable, one can then formulate the above discussion as stating that, in the absence of perfect information, incomplete information is essential for market outcomes to be nearly perfect. Note that uncertainty (in the sense of incomplete information) about product features could also resolve the above paradox of monopoly price in a ‘nearly perfectly competitive’ market (e.g., Anderson and Renault 1999), but such uncertainty is contrary to the identical-product assumption of the law of one price.

The Internet provided an attractive empirical setting to test whether the arguably much lower search costs for price result in a strong tendency for the same price to be paid for the same thing at the same time in all parts of the market. Several empirical studies (e.g., Brynjolfsson and Smith 2000; Clay et al. 2002; Clemons et al. 2002; Baye and Morgan 2004) found that the price dispersion online is significant and, depending on the measure used, may be higher than offline (Brynjolfsson and Smith 2000). Kuksov (2004) argues that one possible explanation is endogenously increased seller differentiation. Baye and Morgan (2005) and Iyer and Pazgal (2003) also consider the effect of endogenous market structure on price dispersion.

An additional complication with comparing the internet marketplace to the offline market is that the Internet has many more sellers. Some theoretical research suggests that uncertainty about prices may lead to the possibility of higher prices and price dispersion when the number of firms is higher (Stiglitz 1987; Kuksov 2006).

See Also