The “Law of One Price” in 1901

I. INTRODUCTION The "Law of One Price" states that absent search (information) costs, a particular good is sold at the same price by all sellers in the same market. As first pointed out by Stigler (1961), however, search costs can cause an equilibrium characterized by price dispersion. It is no longer optimum for consumers to search until the lowest price is found. As Stigler observes, "Price dispersion is a manifestation--and, indeed, it is the measure--of ignorance in the market" (p. 214). Various studies over the past four decades report evidence that price dispersion is ubiquitous and that its magnitude is affected by the costs and benefits of search. For example, relative dispersion (the coefficient of variation) is less for more expensive and frequently purchased goods where the benefits of search are greater. Some recent works have examined the issue in the context of Internet markets (e.g., automobiles, books, and CDs), testing the presumption that lower online search costs lead to lower price dispersion (and also price levels). Perhaps surprisingly, these studies find that dispersion in Internet markets differs little from their conventional counterparts. (1) The present study extends the record on price dispersion in local markets back more than a half-century before the earliest "modern" studies, circa 1960. (2) This is possible because of a unique U.S. government survey conducted and published in 1901. The survey yields retail prices of four products at more than 1500 stores nationwide. Three of these are still sold today, allowing comparisons based on modern survey data. The intervening century saw the introduction of search cost-reducing technology at least as dramatic as the Internet in both transportation (e.g., the automobile) and communication (e.g., telephone, radio, and television). (3) Also, the general migration of people from the farm to cities during the early twentieth century produced a broadening of markets, although not as dramatic as that created by the Internet. Was price dispersion in 1901 more than that observed today? The answer is that, if anything, dispersion was less in 1901. The article is organized as follows. Section I describes the data used in the present study. Section II reports price dispersion for the four 1901 products. Section III presents the modern data and makes comparisons. Section IV provides a summary and conclusions. II. THE 1901 SURVEY In 1901 the U.S. Industrial Commission (USIC) conducted an investigation of "the local differences in prices of articles produced by certain industrial combinations" (USIC [1901], 773). The motivating concern was what is today called predatory pricing, which was alleged to occur in local or regional geographic markets. (4) The investigation consisted of a national survey to gather information on the prices of certain products. The USIC sent questionnaires "to 5,000 retail dealers ... [from whom] 1,578 replies were received, representing every state in the Union [at that time]" (773-74). Six products were included: illuminating oil (kerosene), granulated sugar, three grades of salt, and Royal Baking Powder, a specific brand. The USIC stated that "these were chosen primarily because of the fairly uniform quality of the product, which, it was believed, would make it possible to compare accurately the prices in different localities" (773). Individual dealer responses (anonymous) for four of these products (excluding two salt grades) were published in tabular form by state and city, and constitute the data source for the present study. (5) The issue at hand is price dispersion in a given local market. The USIC identifies dealers by their city of residence (only), and so that is the basis for market definition. (6) To measure dispersion (deviations from the mean) there must be at least two dealers per city. The first column of Table 1 summarizes the number of cities (markets) with multiple dealers by product. …