Socially optimal lockdown and travel restrictions for fighting communicable virus including COVID-19

This paper examines the socially optimal lockdown and travel (social activity) restriction policies for communicable virus including COVID-19. In our simple model, we exploit the remarkable similarity in the structure of external costs causing market failure between the socially optimal choices of the COVID-19 pandemic case and the socially optimal urban traffic congestion level. By identifying this similarity, the results obtained from our simple model allow for future pandemic researchers to use the well-established research methodologies for designing socially optimal traffic levels and associated policy tools to find the socially optimal lockdown and travel restrictions. The key results obtained from our COVID-19 model are: (1) individuals do not internalize the external cost of infection risks they impose on others and health care system when making their own travel (social-activity) decisions; In order to induce individual travel decision makers to internalize this external cost, the government actions are necessary; The travel restrictions via lockdown or monetary penalty is one form of such actions; (2) the existence of external cost implies that the socially optimal length of lockdown is always longer than the privately optimal length of the lockdown period; (3) the strictness of the travel restriction and the amount of violation penalty should be higher in the areas with high population density and in larger cities because the external cost of spreading virus by a traveler would be higher. The monetary penalty in this model resembles the classical Pigouvian tax, which should increase with the city's population, people density, and economic prosperity; (4) when a government subsidizes or fully covers medical expenses of COVID-19 patients, stricter travel restrictions with heavier penalties are required. This is to avoid crowding out of the health care system.