This paper investigates the impact on fiscal revenues of taxing a two‐sided monopolistic platform offering personalized services to users and targeted advertising to sellers, based on the collection of users' personal data. We show that the introduction of a small tax on data collection, which has been proposed in the French context by Collin and Colin, fails to increase fiscal revenues if the value‐added tax (VAT) rate is high enough, due to a tax base interdependence effect between the two taxes. Under a supermodularity condition on the platform's profit function as a function of its prices, this result generalizes to any per‐unit tax. However, in some cases, an ad valorem tax on subscriptions or on advertising may raise fiscal revenues, irrespective of the VAT rate, as well as welfare.