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MARKETING SCIENCE Vol. 7, No. 1, Winter 1988
irands on the perceptual dimensions of 'Ease of Use' and 'Power.' These subjective evaluations are in turn based on physical product characteristics such as servo motors, computer chips and the like and on psycho-social cues such as advertising and salesforce messages. The firm decides on a perceptual position ('ease of use' and 'power') and chooses the optimal characteristics and advertising (salesforce) to achieve that position. See Hauser (1986b), Hauser and Simmie (1980), or Schmalensee and Thisse (1985) for details and examples. Thus, from the firm's perspective, there is a resulting cost associated with each perceptual position. Figure 1 shows two dimensions and three products. The model has been applied to more dimensions (e.g. Hauser and Gaskin 1984), but analytical results have been limited by tractability considerations to two dimensions. There is no theoretical limitation on the number of products. The model assumes consumers choose the brand that maximizes value where value2 is a linear combination of"per dollar" dimensions, e.g., w, * ('power' per dollar) + xt efficient brand (e.g., I.ROBOT) below brand j. See examples in Figure 1. This is the basic analytical model. Note that it does not make any assumptions about symmetry or returns to scale. However, in their analysis Hauser and Shugan (1983) assumed constant returns to scale, no fixed costs, and modeled, in addition, awareness and availability as functions of advertising and distribution spending. This paper continues to assume constant returns to scale and leaves to future elaboration the impacts of nonconstant returns, of fixed costs, and of awareness and availability. Further assumptions for this paper. Intuitively, positioning decisions depend on the cost structure, the preference structure, and competition. For example, if 'power' were most costly than 'ease of use' we would expect firms to seek positioning nearer 'ease of use'. Similarly if consumer tastes, f(a), favor 'ease of use' we would expect firms to position toward 'ease of use'. See Hauser (1986b) for examples of these effects. However, if all competitors have freedom of movement, the tendency may not be so obvious. For example, with the Hotelling model and with a reasonable cost structure, Neven (1986) shows that firms avoid the center of the market even if the taste distribution peaks there. DePalma et al. (1985), citing marketing positioning models as motivation, show that consumer heterogeneity also can drive firms from the center of the market. In this paper I temporarily suppress the effects of nonuniform cost and tastes to isolate the effect of competition. In particular, I assume that all firms face the same marginal costs and that for these marginal costs firms can position on a quarter circle. That is, isocost curves are given by ('ease of use')2 + ('power')2 = k2. Thus, unlike the general Defender model, positioning decisions in this paper are reduced to a single numeraire, the ratio of the two dimensions. This ratio corresponds to tan O1in Figure 1. However, when