The paper develops a two-stage capacity constrained duopoly model, in which the mode of competition is endogenous and the constraint is flexible, to investigate the impact of Tariff Rate Quotas (TRQs) and their liberalization. The model predicts that the greater the gap between the price of the licences plus the in-quota tariff and the out-of-quota tariff, the closer the outcome of the game to the pure Cournot outcome. The tariff equivalent changes according to the prevailing mode of competition under the TRQ. The model is used to address the issue of the tariffication of the non-ACP TRQ for EU banana imports. The results suggest that under the TRQ firms competed on quantity and that the tariff equivalent is higher than the tariff introduced by the EU in 2006.