Can taxing foreign competition harm the domestic industry?

The answer to the question in the title is yes for the case of ad-valorem taxes, a foreign industry that produces a vertically differentiated good of higher quality, and costs that take the form of qualitydependent fixed costs for both the foreign and domestic firm. The domestic industry loses profits due to the foreign industry's lowering of product quality which intensifies price competition. This result carries through to the case of additional constant marginal costs, if this cost component does not increase too fast with increases in product quality produced. However, it does not hold with qualitydependent marginal costs. In this latter case, the foreign firm will reduce output rather than quality, which tends to reduce foreign competition.