What is the best way to ration a scarce good?

Government officials and hospitals are trying to devise the best way to decide who gets remdesivir, the first drug shown to help treat COVID-19 (WSJ, May 2020). The article mentions using 

1. first come, first served, 
2. a lottery with some people getting more "tickets" than others, 
3. anonymous applications, 
4. equal distribution across regions of a state, 
5. allocating to a region of a state based on the number of COVID-19 patients in hospitals, 
6. how long a patient has been sick or on a ventilator, and
7. the severity of illness or a patient's oxygen level.

The article does not mention selling the drug at its equilibrium price. 

Here are some questions.

1. Would people tend to purchase remdesivir if it sells at the equilibrium price and offers little promise for improvement in their outcome? What if it shows great promise, based on their conditions?
2. When would the quantity of remdesivir available to patients be greater, when it sells at the equilibrium price or when price is low and the drug is allocated by lottery?
3. Who should get the drug, someone who is sickest or someone whose life expectancy would increase the most, or someone with the biggest difference between probabilities of survival from COVID-19 with and without the treatment?
4. Should health care workers with COVID-19 get first priority for the drug?
5. Should people who get COVID-19 because they fail to keep distant from other people get low priority for the drug?
6. Is giving health care workers more tickets in a lottery fair? Low-income patients?

Supply and demand works even (or especially) during pandemics

The coronavirus pandemic is affecting equilibrium prices in many markets (WSJ, May 2020). Here are two questions raised by the article. 

1. Why might diners at a restaurant more readily accept a coronavirus surcharge or fee than a simple increase in price?
2. Why might some retailers keep prices low even when they recognize that their price is below the equilibrium price and a shortage exists?

Which is better, an expensive mask or no mask?

Price controls created a shortage of masks during the coronavirus pandemic (WSJ, May 2020).