Product Positioning in a Two-Dimensional Vertical Differentiation Model: The Role of Quality Costs

We study a duopoly model where consumers are heterogeneous with respect to their willingness to pay for two product characteristics and marginal costs are increasing with the quality level chosen on each attribute. We show that although firms seek to manage competition through product positioning, their differentiation strategies critically depend on how costly it is to provide higher quality. When the cost of providing quality is not too high, firms use only one attribute to differentiate their products: they maximally differentiate on one dimension and minimally differentiate on the other (a Max-Min equilibrium). Furthermore, they always differentiate along the dimension with the greater attribute range. As for the dimension with the smaller range and along which they agglomerate, firms either choose the highest quality level or the lowest quality level possible, depending on whether the marginal costs of quality provision are low or intermediate, respectively. However, for larger quality provision costs, firms exploit both dimensions to differentiate their products. In particular, we characterize a maximal differentiation equilibrium in which one firm chooses the highest quality level on both attributes while its rival offers the lowest quality level on both attributes (a Max-Max equilibrium). We discuss the managerial implications of our findings and explain how they enrich and qualify previous results reported in the literature on two-dimensional differentiation models.