This paper studies data collection by a monopolistic Internet platform. We show that the optimal strategy of the platform is either to cover the market or to choose the highest data exploitation level, excluding users with high privacy costs from the platform. For plausible parameter values, the platform chooses an excessive level of data exploitation from the point of view of users. We study how different tax instruments can be used to reduce the level of data collection and analyze the effect of an opting‐out option, letting users access the platform with no data collection. We show that a differentiated tax, taxing access revenues and data revenues at different rates, is the most effective instrument and that the introduction of an opting‐out option may harm users as it induces the platform to raise the level of data exploitation.