In a recent paper in this journal, Arevalo-Tome and Chamorro-Rivas claim. to have shown that, in a two-stage game where Cournot duopoly firms discriminate over two marketplaces on a line, a social planner can, use the firm's location variable as an instrument for reallocating production from the equilibrim spatial pattern to the optimal outcome. This note points out that with linear demand there is no nee(l to use such an instrument for social welfare improvement, because the equilibrium locations are indeed socially optimal. The note also discusses the possibility of using such an instrument for general demand.