Can you please give me an advice for the following essay question? I'm confused about which one should I pick between monopoly or perfect competition for the following situation.

"The government is able to get the country out of lockdown if the adult population can be vaccinated.

The government has the blueprints to an effective vaccine and is deciding between giving the rights to the blueprints to one company or to many companies.

Explain, using appropriate economic concepts and diagrams, what the welfare effects would be if the government gave the rights to produce and sell the vaccine to one company rather than many companies.

If you were advising the government, what one suggestion would you make to increase welfare in this situation with one company producing the vaccine."

I think perfect competition would make more sense as long as the government provide the company with R&D benefits. What do you think about this topic?