Voluntary vaccinations and vaccine shortages: A theoretical analysis

Abstract

A simple dynamic model of vaccination is presented and analyzed to study how the amount of vaccines available affects people’s vaccination decisions. In addition, the model is used to examine how the level of vaccination in equilibrium compares to the efficient or socially optimal level. It is shown that, when the stock of vaccines is large so that a shortage could never arise, an equilibrium is generically unique, and there is too little vaccination compared to the social optimum. When the stock of vaccines is small so that not everyone in a population could get vaccinated, a shortage could occur in equilibrium. Moreover, the occurrence of a shortage could be self-fulfilling: when agents expect a shortage to develop, they have a greater incentive to demand the vaccine right away, which increases the likelihood that a shortage will result; and when agents do not expect a shortage to arise, they are more willing to delay their vaccination decision, which reduces the likelihood of a shortage developing. This leads to the possible co-existence of multiple equilibria that differ in the level of vaccination. Multiple equilibria can arise, however, only if agents are uncertain about the cost of being infected – if agents are sufficiently certain about the cost of infection, then an equilibrium is unique. Furthermore, when the stock of vaccines is small, an equilibrium level of vaccination may be too high relative to the socially optimal level. Increasing the vaccine stock could have ambiguous effects on the level of vaccination in equilibrium but unambiguously increases social welfare.