We study a firm which serves two unequally-sized markets and must choose where to locate its first production plant, and whether to open a second plant to serve the other market through local sales rather than exports. An exporter pays taxes only to the country where it locates its single production plant. A double- plant multinational pays taxes in both countries, but may shift taxable profits across countries, at a cost. We show that the usual proximity-concentration trade- off between fixed and trade costs is modified, depending on both the average tax of, and the tax difference between, the two countries. Moreover, in contrast to a standard result of the FDI literature, we find that increased market size asymmetry may make it more likely that the firm engages in horizontal FDI. From a global welfare viewpoint, it is always desirable to control the firm's profit shifting when the multinational structure is taken as given. However, the fact that the firm may react by changing its production structure may be a reason not to control profit shifting activities.