The Mechanics of Individually- and Socially-Optimal Decisions during an Epidemic

Vandenbroucke, Guillaume

doi:10.20955/wp.2020.013

Working Paper Revision

The Mechanics of Individually- and Socially-Optimal Decisions during an Epidemic

Abstract: I present a model where work implies social interactions and the spread of a disease is described by an SIR-type framework. Upon the outbreak of a disease reduced social contacts are decided at the cost of lower consumption. Private individuals do not internalize the effects of their decisions on the evolution of the epidemic while the planner does. Specifically, the planner internalizes that an early reduction in contacts implies fewer infectious in the future and, therefore, a lower risk of infection. This additional (relative to private individuals) benefit of reduced contacts implies that the planner’s solution feature more social distancing early in the epidemics. The planner also internalizes that some infectious eventually recover and contribute further to a lower risk of infection. These mechanisms imply that the planner obtains a flatter infection curve than that generated by private individuals’ responses.

Keywords: SIR model; epidemic; social optimum; social distance; contact rate;

JEL Classification: E1; H1; I1;

https://doi.org/10.20955/wp.2020.013