We provide, calibrate and test a realistic model of the spread of SARS-Cov-2 in an economy with di_erent risks related to age and sectors. The model considers hospital congestion and response of individuals adjusting their behavior to the virus' spread. We measure precisely the size of these e_ects using real data for Italy on intensive care capacity and mobility decisions; thus our claim is that the tradeo_s we estimate are quantitatively, rather than qualitatively, approximately correct.

We characterize the policies of containment of the epidemic that are e_cient with respect to number of fatalities and GDP loss. Prudent policies of gradual return to work may save many lives with limited economic costs, as long as they di_erentiate by age group and risk sector. More careful behavior of individuals induced by the perceived cost of infection may contribute to further reduce fatalities.

JEL-Code: I12, I18, D6, H84

Keywords: Covid-19,SARS-Cov-2 SEIR model, post lockdown policies.

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