Toward a Formal Model of Steiner’s Dual Stage Theory of Manufacturing and Retailing

This paper provides the formal mathematical model of Robert Steiner's Dual Stage Theory described and simulated in my paper “Why economists are wrong to neglect retailing and how Steiner's theory provides an explanation of important regularities” published in The Antitrust Bulletin, Vol. XLIX, No. 4, Winter, 2004 now available on SSRN at http://ssrn.com/abstract=1972383, with the permission of Bill Curran, editor of the Antitrust Bulletin. Even in this simple case we need to consider at least two manufacturers, many retailers and many consumers. Manufacturers and retailers choose prices to maximize profits. Both have fixed costs and both manufacturers and retailers take rivals prices as given, i.e., they behave as Cournot-Nash oligopolists using Bertrand pricing. Each retailer is assumed to carry two products, a leading national brand [LB] and a competing store brand [SB]. Free entry into retailing is assumed to eliminate any excess profits and determines the number of retail outlets. So retailing is assumed to be monopolistically competitive. Consumers are assumed to know LB prices across stores, but not SB prices. An important, and somewhat unusual, assumption is that a consumer's choice between any two stores to shop at is based only the ratio of the LB prices at those stores. This assumption produces a particularly simple market share equation, wherein an individual retailer's share of consumers is proportional to the ratio of its LB price raised to a power µ divided by the sum of all such terms for all the retailers in the market. The assumption implies that the exponent µ is the same for all retailers. This exponent can be interpreted as a measure of “visibility” of an LB and the higher it is the more elastic the demand curve facing an individual retailer. Consumers buy either one unit of the LB or the SB, but not both. Through brand advertising, manufacturers can increase the visibility of their brand, and so increase the elasticity of demand as seen by individual retailers. The model produces both “inverse associations” described by Steiner, and thus demonstrates that his Dual Stage theory is consistent with profit-maximizing behavior by retailers and manufacturers