The goal of this paper is to show that the market structure for an industry which features cost efficiencies differences may be determined by either lump-sum tax or excise tax. We found that competition between firms may not be able to lead to production efficiency for the industry. When an excise tax is imposed and the increased cost may lead a pre-tax duopoly market into a monopoly market that is operated by the efficient firm. However, instead of excise tax, when a lump-sum tax is considered, for some particular amount of tax, the less efficient one may monopolize the market. It is possible that a distortional tax (excise tax) generate higher social surplus than that under lump-sum tax, a non-distortional tax.