Using a simple model of two-sided markets, we show that, in the social optimum, platform pricing leads to an inherent cost recovery problem. This result is driven by the positive externality of participation that users on either side of the market exert on the opposite side. The contribution of this positive externality to social welfare leads the social planner to increase users' participation by setting prices at both sides of the market such that the total price is below marginal cost. This causes operational losses for the platform. Our result holds for both interior pricing and skewed pricing in two-sided markets.