I think you’re looking at this too much from a pure demand theory point of view. Ignoring the moral issues with distributing a live saving vaccine based on who

I think you’re looking at this too much from a pure demand theory point of view. Ignoring the moral issues with distributing a live saving vaccine based on who has enough money, I don’t think that free market pricing would have made things much faster. It’s not like any random person can get into the business of complex vaccine manufacturing. The companies and the government have already been scrambling to get it out faster but even if you believe that there is/was more room to incentivize the 2(?) main companies making the vaccine then again the government(s) could just say pay the companies more/less based on the timing of doses. However I really don’t think that additional profit motive was a factor here. If there was more room to say build another factory at some high cost, I find it hard to believe that these companies would decide not to and not offer governments an offer to expand capacity (eg. we can give you X doses and bump you up but we need more money to build the factory).