How efficient are the lockdown measures taken for mitigating the Covid-19 epidemic?

Various lockdown measures have been taken in different countries to mitigate the Covid-19 pandemic. But, for citizens, it is not always simple to understand how these measures have been taken. Should they have been more (or less) restrictive? Should the lockdown period have been longer (or shorter)? What would have been the benefits of starting to confine the population earlier? To provide some elements of response to these questions, we propose a simple behavior model for the government decision-making operation. Although simple and obviously improvable, the proposed model has the merit to implement in a pragmatic and insightful way the tradeoff between health and macroeconomic aspects. For a given tradeoff between the assumed cost functions for the economic and health impacts, it is then possible to determine the best lockdown starting date, the best lockdown duration, and the optimal severity levels during and after lockdown. The numerical analysis is based on a standard SEIR model and performed for the case of France but the adopted approach can be applied to any country. Our analysis, based on the proposed model, shows that for France it would have been possible to have just a quarter of the actual number of people infected (over [March 1, August 31]), while simultaneously having a Gross Domestic Product loss about 30% smaller than the one expected with the current policy