This paper models a domestic oligopoly market in which domestic producers compete with importers, and both groups have market power. In the model, a tariff reduction results in the decrease in the marginal cost of importers. Simulation results show that tariff reductions in such a market have a far smaller effect on the equilibrium quantity and price than they would have in a competitive benchmark market, given the small share of imports within total consumption. Other simulation results demonstrate that a higher degree of market power results in smaller effect of tariff reduction on the equilibrium quantity and price. Notably, social welfare changes incurred by simulated tariff reductions are negative under inelastic demand when importer profits are excluded from the social welfare calculations. These results highlight that identification of market structure is very important in assessing the effects of tariff reduction.