We study optimal lockdown decisions taken by a policymaker facing a pan-
demic modelled according to the standard SIRD deterministic model. The poli-
cymaker trades off the economic costs and the mortality record of the pandemic
which depend on the severity and duration of the lockdown. We contrast the
shortsightedness versus the farsightedness of the policymaker. Policy-related
peaks and rebounds are characterized and explain why a no-accommodating pol-
icy is self-defeating. A farsighted policy should not be too severe so as to avoid a
rebound. The shortest duration consistent with a given health goal is not the less
costly. There exists an optimal pair of duration and lockdown severity resulting
in herd immunity.

Keywords: Pandemic; lockdown policy; Covid-19.

JEL classification: D61; H51; I18.

Highlights:

• We analytically characterize the impact of lockdown policy on the dynamics

of a pandemic.

• We show the importance of foreseeing the post-lockdown evolution of the

pandemic.

• We explain how rebounds are linked to lockdown policy.

• There exists an optimal policy combining duration and lockdown severity,

consistent with herd immunity.