There is an economist named Anna Scherbina who has looked at the cost-benefit of all this.
https://www.nytimes.com/2020/03/31/business/coronavirus-economy-trump.html
Outside economists have been pumping out analyses on the optimal length of a shutdown almost daily. One that has been shared with officials inside the White House comes from Anna Scherbina, an author of the 2019 study who is now an economist at Brandeis University and the American Enterprise Institute.
It seeks to determine the optimal length of a national suppression of economic activity, which Ms. Scherbina does not define precisely in the paper. In an interview, she said it would encompass school closures, shutting down many businesses and the sort of stay-at-home orders that many, but not all, states have imposed.
“What it entails is something as drastic as you can get,” Ms. Scherbina said. In the United States right now, she added, “we don’t have it everywhere.”
Ms. Scherbina’s paper evaluates the trade-offs involved in slowing the economy to fight the spread of the virus by, as the paper puts it, “balancing its incremental benefits against the enormous costs the suppression policy imposes on the U.S. economy.”
In a best-case scenario, Ms. Scherbina concludes, a national suppression of economic activity to flatten the infection curve must last at least seven weeks. In a worst case, where the shutdown proves less effective at slowing the rate of new infections, it would be economically optimal to keep the economy shuttered for nearly eight months.
Suppression efforts inflict considerable damage on the economy, reducing activity by about $36 billion per week, the study estimates. Ms. Scherbina said the optimal durations would remain largely unchanged even if the weekly damage was twice that high.
But the efforts would save nearly two million lives when compared with a scenario in which the government did nothing to suppress the economy and the spread of the virus, Ms. Scherbina estimates, because doing nothing would impose a $13 trillion cost to the economy — equal to about two-thirds of the amount of economic activity that the United States was projected to generate this year before the virus struck.
Ms. Scherbina based her estimates on the models she built when she was a senior economist at the Council of Economic Advisers and an author of the September paper, “Mitigating the Impact of Pandemic Influenza Through Vaccine Innovation,” which warned of potentially catastrophic death tolls and economic damage from a pandemic flu in the United States.
“I accumulated all this knowledge, and then coronavirus came up,” Ms. Scherbina said in a telephone interview. “So I thought, I should put it to use.”
unfortunately there is a crucial paragraph in this article that is poorly edited and makes no sense...shame on the NY Times
I've tried to find links to Scherbina's work on this but nothing. She should put it up somewhere.