On the Internal Contradictions of the Law of One Price

As stated originally, the venerable law of one price succinctly describes long-run equilibrium in a perfectly competitive market. The law was later amended, defining a market as the geographic area within which the same thing sells for the same price at the same time, allowance being made for transportation costs. Modified in that way, the law has two plausible interpretations. By one interpretation, every production site is a market. By the other, prices in fact do not differ by transportation costs. The transportation-cost amendment thus introduces internal contradictions that render the revised law of one price either useless or wrong. (JEL D40, L10) A market, according to the masters, is the area within which the price of a commodity tends to uniformity, allowance being made for transportation costs. That is, two places are in the same market for a good if the prices at the two places differ by transportation costs. (Stigler, 1987, 77) Economic terms seem to pass in their historical development through a series of stages which, without pretension to rigidness, may be described as follows: first, no definition is given, but it is assumed that every one has a sufficiently clear idea of the subject to make a formal definition unnecessary; second, a definition is attempted and a number of exceptional forms are noted; third, with the further increase of data, the relative importance of the various forms changes, confusion in discussion is introduced, logomachy takes the place of constructive investigation; fourth, a complete classification of the forms embraced under the original term is made, and problems are investigated with reference to these classes. The bewildering vagueness of economic theory is largely due to the fact that the terms used are in all of these stages of development. (Moore 1906, 211) I. INTRODUCTION Delineating the boundaries of markets engaged economists' attention early on. Many product attributes are important to consumers, but price is an objectively measurable margin along which rivalry is sharply engaged. Market prices transmit information about changing demand and supply conditions to buyers and sellers, and widening price--cost margins signal profit opportunities to which alert entrepreneurs respond. Price consequently has held center stage in economists' attempts to define markets. Augustin Cournot (1927, 51), for instance, wrote that a market is "the entire territory of which the parts are so united by the relations of unrestricted commerce that prices take the same level throughout with ease and rapidity." Alfred Marshall (1930, 325) supplied a similar definition in his celebrated declaration that "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." More recently, Joseph Stiglitz (1993, 19) summarized what he called the law of the single price, stating that, "under this law, there is a uniform price in the market, and price differences are quickly eliminated by arbitrage." (1) Marshall (1930, 325) introduced an important qualification, however, when he observed that, "but of course, if the market is large, allowance must be made for the expense of delivering the goods to different purchasers; each of whom must be supposed to pay in addition to the market price a special charge on account of delivery." That qualification subsequently found its way into Stigler's price theory textbook, quoted in the epigraph. Intentionally or not, the law of one price was thereby converted into a law of different prices. Other economists subsequently added transaction costs and information costs to the list of caveats, culminating in a multiplicity of prices nevertheless claimed to be consistent with the law of one price. Economics has few laws. …