Public and private incentives for self-protection

Governments sometimes encourage or impose individual self-protection measures, such as wearing a protective mask in public during an epidemic. However, by reducing the risk of being infected by others, more self-protection may lead each individual to go outside the house more often. In the absence of lockdown, this creates a "collective offsetting effect", since more people outside means that the risk of infection is increased for all. However, wearing masks also creates a positive externality on others, by reducing the risk of infecting them. We show how to integrate these different effects in a simple model, and we discuss when self-protection efforts should be encouraged (or deterred) by a social planner.