Effects of an ad valorem Web Tax in a Cournot-Nash market for digital advertising

I extend the theory of tax incidence under Cournot-Nash oligopolistic competition to study the effects of an ad valorem sales tax on Web services that are provided free of charge to users, and produce advertising space sold to businesses. Ads are more valuable to advertisers the more users are served by a Web service. Users have ads-neutral preferences and Web companies compete in a Cournot-Nash fashion on the advertising market but enjoy monopolistic power in the service market they serve. I demonstrate that the equilibrium market price may be reduced by such tax, while ads sold increase. The conditions for such a tax-induced change depend upon the functional form and the elasticity assumed for ads demand.