Product Positioning in a Two-Dimensional Market Space

We examine the optimal composition of the firm product portfolio in multi-attribute markets, where customer preferences are defined by multiple (two) dimensions. Every product offers utility to consumers through its quality level and through its conformance to the customer's ideal feature. The feature choice has no impact on cost, while product quality has. The end-products are development intensive, i.e. extremely small production costs compared to design and development ones. Such cost structures are often encountered in the software industry. Customers are heterogeneous in their quality valuation and their ideal feature preference, and they suffer a quadratic loss from feature deviations. A monopolist positions an arbitrary number of products in the market and optimizes the number of products, and their features, prices, and qualities. If customers are uniformly distributed in this market and if the deviation losses are the same for all products, it is not optimal to vertically differentiate. Instead the only differentiating factor in the product portfolio is the product features. When the market is either asymmetric or the deviation costs differ, we show numerically that the positioning changes such that products differ in price and quality.