A Note on Quality Competition and Social Welfare in Markets with Partial Coverage

We study the social welfare optimum for a vertically differentiated duopoly under partial market coverage and variable costs. Costs are specified as linear in quantity and quadratic in quality. We demonstrate that the spread of product quality observed under a profit maximizing duopoly is too high, relative to the social welfare optimum. We also find that high quality firms in a duopoly will have higher profits but lower market shares than low quality firms, after quality and price competition is resolved. Finally, we demonstrate that the social welfare optimum results in greater total output than the duopoly and has both firms producing equal amounts.