Eek. You have two very poor assumptions (sorry).
1) "Especially given our objective is probably not maximising profit (ethnical consideration)". You are wrong here.
All companies have the objective of maximizing profits. All companies have the incentive to PRETEND that they don't.
If you do some reading, you'll see that a lot of these promises by vaccine companies to keep prices low only go until July, 2021...when less than 10-20% of the developed world population will likely have been vaccinated. These companies still want to make money
2) "The government has a budget constraint". Not at all! The government has tons of $ to throw at this problem! Operation Warp Speed threw billions at this. Heard of Kodak? Heard of their $765 Million Dollar Moment? So, the US government does not have a budget constraint in anything that involes 1) Public image (i.e. pandemic) and 2) Military
Sorry to burst the bubble there!
Now, given this news, you now know the objective is to maximize profits without appearing to in the context of a government willing to pay a lot. How does this change your framework :)
Clarifying questions are key here!