Under the three-countries-two-firms duopolistic structure, Lai (2006) incorporates the rent-shifting effect in the typical tax competition model. He finds that when firms compete in terms of quantity, the rent-shifting effect aggravates the under-provision of public goods in a Cournot duopoly, i.e., the Oates hypothesis still holds. However, in this note we find that the number of firms plays an important role in the result which Lai (2006) has obtained. Moreover, if the number of home country manufacturers is larger than the foreign country's under the homogeneous cost structures of the home country manufacturers, the rent-shifting effect will increase (not reduce) the provision of public goods and mitigate (not aggravate) the inefficiency arising from tax competition. On the other hand, under the heterogeneous cost structures of the home country manufacturers, the effect of allocative production efficiency will enhance the above result.