Knowledge, germs, and output

This paper studies the equilibrium and the social optimum in an economy where knowledge diffusion interacts with disease transmission. Knowledge increases productivity and is diffused through learning. A learner chooses the intensities in normal learning, isolated learning and production. Normal learning is more effective than isolated learning but requires a learner to contact a teacher. A higher intensity in normal learning increases a learner's contact rate with a teacher, thereby speeding up both knowledge diffusion and the transmission of an infectious pathogen. An infection reduces productivity and possibly results in death. Calibrating the pathogen to Covid-19, the model shows that the unexpected arrival of the pathogen induces a susceptible learner to adjust the normal learning intensity in a V-shaped pattern over time. Aggregate output also follows V-shaped adjustments. Switching from the equilibrium to the social optimum reduces infections and deaths substantially and increases social welfare. I also examine temporary lockdowns in the equilibrium.