We investigate the optimal duration of the COVID-19 suppression policy. We ？nd that absent extensive suppression measures, the economic cost of the virus will total over $9 trillion, which represents 43% of annual GDP. The optimal duration of the suppression policy crucially depends on the policy’s effectiveness in reducing the rate of the virus transmission. We use three different assumptions for the suppression policy effectiveness, measured by the R0 that it can achieve (R0 indicates the number of people an infected person infects on average at the start of the outbreak). Using the assumption that the suppression policy can achieve R0 = 1, we assess that it should be kept in place between 29 and 34 weeks. If suppression can achieve a lower R0 = 0.7, the policy should be in place between 11 and 12 weeks. Finally, for the most optimistic assumption that the suppression policy can achieve an even lower R0 of 0.5, we estimate that it should last between seven and eight weeks. We further show that stopping the suppression policy before six weeks does not produce any meaningful improvements in the pandemic outcome.