Positioning and Pricing of Horizontally Differentiated Products

We provide structural results and a solution method for designing horizontally differentiated product lines – optimizing product positions and prices – under fairly general consumer choice behavior. Our choice model is a generalization of the basic Hotelling-Lancaster locational choice model: Consumer tastes (ideal products) follow a general distribution; substitution disutility (transportation cost) can be an asymmetric convex function of product-spatial distance; and the market may not be fully covered. We formalize the notion that a shift of consumer tastes toward one end of the product space cannot result in a shift of the optimal product line in the opposite direction. For a unimodal taste distribution, we show that with respect to the product that covers the mode (or one of two products adjacent to it) prices and market shares drop toward the tails. Hence, higher popularity is always associated with higher price – although pricing, positioning, relative market share and popularity of products are all endogenous in our model. Our solution method is exact for discrete consumer taste distributions. Whereas, for continuous distributions, it requires lower and upper bounds, which can be computed efficiently using shortest path formulations and they asymptotically converge to the optimal profit.