This article analyzes 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, when both strategic variables are strategic complements, 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. When both variables are strategic substitutes, protecting the intensive margin harms privacy at the extensive margin, but still increases consumer surplus.