Typically, the demand for vaccines is lower than socially optimal because individuals do not internalize the social benefit of protecting others via reduced infectiousness (known as a positive externality). We show that the supply side can also be found at fault; there is typically limited supply due to yield uncertainty and manufacturer's incentives. This shortage leads to a negative externality; self-interested individuals ignore that vaccinating people with high infection costs is more beneficial for the society when supply is limited. We also develop mechanisms that either reduces or completely eliminates the inefficiency in the flu vaccine supply chain.