We analyze the relationship between privacy protection and market competition. We consider a model where firms collect data to price discriminate consumers in a competitive product market, and we distinguish two margins of privacy. Firms strategically choose the number of consumers on whom they collect data-the extensive margin of privacy-as well as the precision of information-the intensive margin of privacy. We show that policymakers can efficiently protect both margins of privacy and consumer surplus by safeguarding the intensive margin. Indeed, restricting the amount of information that firms have on each consumer (the intensive margin) also induces firms to collect data on fewer consumers, thereby protecting the extensive margin of privacy. This softens the intensity of competition, but also reduces rent extraction by firms, and total consumer surplus increases. * We thank for useful remarks and comments members of the French Data Protection Agency (CNIL), and participants to the EARIE conference. Patrick Waelbroeck thanks for insightful discussions members of the Chair Values and Policies of Personal Information of Institut Mines Télécom, Paris. This research has also been conducted within the Chair "Digital Finance" under the aegis of the Risk Foundation, a joint initiative by Groupement des Cartes Bancaires CB,