Citation needed for the idea that zero is the optimal price for public benefit. Among other issues, I expect medication compliance would be higher when the patient has to pay for the medication.
I think we probably have data on that (at least in general). That is assuming people react to out-of-pocket payments, and not to how much their insurance or the NHS etc is paying.
That is exactly what I have in mind. "Eminent domain" doesn't mean just taking things with no recompense, but I don't think the company should be entitled to profit maximization at the expense of literally billions of people worldwide.
Eminent domain would be on a jurisdiction by jurisdiction basis. No country has 'billions of people'.
It adds up to the same thing in aggregate.
But also, if you change it to "millions of people", the point is no less valid.
India and China each have billions of people.
The drug companies are presumably pricing optimally for profit (but not for maximum public benefit, for which the optimum price is ~0). You could calculate the net present value of the drug companies' total profits attributable to the patent, add on 10% as a bonus, and pay them off. If the welfare gains of having cheap drugs are genuinely greater than the value of the patent to the holder, this would be win/win.