In this paper we investigate tax/subsidy competition for FDI between countries of different size when a welfare-maximizing and relatively inefficient public firm is the incumbent in the largest market. First, we analyze how the presence of a public firm affects the investment decision of a multinational operating in the same sector as the former and willing to serve both markets. When the public firm stops exporting to the small country due to the investment of the multinational in the region (or does not export altogether), policy competition between the two countries is irrelevant to the foreign firm's choice. But if the country receiving FDI has to pay a subsidy, only the multinational will be better off provided that it would have invested there anyway absent policy competition. By contrast, when the public firm exports to the small country, policy competition increases the attractiveness of the big country. Second, we show that privatizing the public firm makes the big country a relatively more attractive location for the investment. However, when the privatized firm stays in the market, welfare always decreases. After privatization, policy competition decreases the attractiveness of the big country, which may be willing to tax the multinational in order to discourage FDI from taking place there, and gives the small country the opportunity of benefiting from the investment.