The Social Cost of Contacts: Theory and Evidence for the Covid-19 Pandemic in Germany

Building on the epidemiological SIR model we present an economic model with heterogeneous individuals deriving utility from social contacts creating infection risks. Focusing on social distancing of individuals susceptible to an infection we theoretically analyze the gap between private and social cost of contacts. To quantify this gap, we calibrate the model using German survey data on social distancing and impure altruism from the beginning of the Covid-19 pandemic. The optimal policy reduces contacts drastically in the beginning, to almost eradicate the epidemic, and keeps them at around a third of pre-pandemic levels with minor group-specific differences until a vaccine becomes tangible. Private protection efforts stabilize the epidemic in the laissez faire, though at a prevalence of infections much higher than optimal. Impure altruistic behaviour closes more than a quarter of the initial gap towards the social optimum. Our results suggests that private actions for self-protection and for the protection of others contribute substantially toward alleviating the problem of social cost.