An irrelevance result with differentiated goods

White (1996), Poyago-Theotoky (2001) and Myles (2002) prove that in the mixed oligopoly the optimal subsidy, equilibrium output level, all firms' profits and social welfare are identical irrespective of whether the public firm maximizes welfare or profit and moves simultaneously with private firms, or maximizes welfare and acts as a Stackelberg leader. They name this observation the `irrelevance result''. Previous results have assumed all firms produce a homogeneous product with quantity as the strategic variable. We show that the irrelevance result extends to product differentiation and to Bertrand competition with price as the strategic variable.