Privatization and government preference: Cournot vs Bertrand models

We will consider a mixed Bertrand duopoly model (that means, two firms decide simultaneously their prices for a substitutable good) to study the relationship between the privatization of a state-owned public firm and government preferences for tax revenue. In the model, we assume that the government imposes a specific tax rate on the quantity produced by each firm. The public firm aims to maximize social welfare, whereas the government’s objective function is a weighted sum between social welfare and tax revenue. Of course, the private firm aims to maximize its own profit. Furthermore, we also present the results for the Cournot duopoly model with differentiated goods, and we do a comparison between both models. We also present comparative static results.