The optimal specific or ad valorem tax when the other tax is exogenously imposed in a free-entry Cournot oligopoly market

This study examines how optimal specific or ad valorem taxation in a free-entry Cournot oligopoly market is affected by a change in another exogenously given tax. We derive the sufficient conditions for the uniqueness of the optimal tax rate, which are related to the concavity of the marginal revenue and the log-concavity of the first derivative of the average cost function. By guaranteeing the uniqueness, we can conduct a comparative statics analysis on the optimal tax rate. We show that a marginal increase in another tax can paradoxically reduce prices and decrease the optimal tax rate.