Two-sided platform firms serve distinct customer groups that are connected through interdependent demand, and include major businesses such as the media industry, banking, and the software industry. A well known textbook result in one-sided markets is that a government may increase a monopolist's output and reduce the deadweight loss by subsidizing output. The present paper shows that this result need not hold in a two-sided market. On the contrary, a higher ad-valorem tax rate - rather than a subsidy - could increase output and enhance welfare.