This study introduces a subsidy policy on product quality in a quality-then-price game to remedy the quality distortion under a mixed oligopoly (one public firm and one private firm) framework. We show that the multi-stage setting for firms is crucial for the validity of privatization neutrality. Since firms have different objectives, their asymmetric strategic consideration on price will spill over to the quality competition if there exists price differentiation in equilibrium under partial privatization. This spillover effect results in lower social welfare levels than the first-best outcome, and the neutrality of privatization in White (Economics Letters 53:189–195) no longer holds in our multi-stage model. Specifically, the optimal privatization policy is either fully public or completely private, where the social welfare attains the first-best outcome.