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. We find that the optimal policy reduces contacts drastically in the beginning, to almost eradicate the epidemic, until a vaccine becomes tangible. All groups substantially reduce contacts, and differences between groups are only of secondary importance. Private protection efforts are sufficient to stabilize the epidemic in the laissez faire, though at a prevalence of infections much higher than optimal; impure altruistic behaviour closes around a third of the initial gap towards the social optimum. Overall, our analysis suggests that private actions for self-protection and for the protection of others contribute substantially towards alleviating the problem of social cost.