Endogenous Product Design: A Linear Demand Approach
Afonso Rodrigues
TL;DR
This paper develops a linear-demand, quasi-linear quadratic utility framework in which product attributes drive both utility and competitive interactions, enabling endogenous product design across any finite number of goods, firms, and attributes. It derives a general attribute-based measure of competition and shows that under Bertrand competition, monopolists tend to implement vertically differentiated, aligned attribute vectors, while horizontal differentiation emerges mainly in latent attributes; with endogeneity, monopoly can yield higher consumer surplus than competition due to greater effective quality. The analysis covers one- and multi-attribute monopolies, two equilibria for single-product firms (exclusive vs non-exclusive attributes), and extensions to latent utility estimation and multiple consumer types, with numerical simulations illustrating the robustness of the orientation result and welfare implications. The framework yields testable predictions about the structure of product differentiation and the welfare effects of endogenous design, offering a flexible tool for empirically studying how firms choose product characteristics in differentiated markets.
Abstract
This paper develops a linear-demand framework to investigate endogenous product design. The key assumption is that the same product characteristics which drive goods utility also (at least partially) shape competitive interactions across products. I model this relationship allowing for differences in each characteristic's relevance to competition, their absolute intensity per good, and correlations to other characteristics. The framework is novel in its broad applicability to settings with any finite number of goods, firms, and attributes, allowing for both vertical and horizontal differentiation, all in an empirically testable model. Under Bertrand price competition I show that across different market structures, a pattern emerges: product differentiation along product attributes that firms control is primarily vertical, with horizontal differentiation only in latent attributes. Counter to standard intuition, simulations show that allowing for endogenous design can imply higher consumer surplus under monopoly than under competition, as monopoly's stronger incentives for attribute investment translate into higher effective quality.