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We examine the relationship between equilibrium and efficient levels of product differentiation in a mixed duopoly, where a welfare‐maximizing public enterprise competes with a profit‐maximizing private firm. We introduce shadow costs of public funding (i.e., the excess burden of taxation). The profits of public firms obtained by the government reduce these costs. We find that in a mixed duopoly, the level of product differentiation is too low for social welfare. This result is in sharp contrast to the private oligopoly, where the level of product differentiation is too high. Finally, we show that when the shadow cost is high, privatizing the public enterprise improves welfare.