Supposed that:

the demand function for alcohol-based hand sanitizer last week was P=100- 0.08Q and

the supply function was P=0.02Q, where P is measured in dollar ($) and Q is measured as number of bottles of alcohol-based hand sanitizer sold per week.

(i) Calculate the price and quantity in equilibrium for the alcohol-based hand sanitizer market.

Further supposed that government decided to regulate the market by setting a price ceiling at $10 per bottle.

(ii) Evaluate the potential outcomes of such a price regulation in terms of market efficiency while assuming that there are no black markets for alcohol-based hand sanitizer. Be specific about the well-being of consumers, producers and the society by using proper diagrams.

In addition, soon after the price regulation, a vaccine for the virus was invented which can reduce the risk of infection to a large extent.

(iii) Discuss with diagrams potential changes in the market equilibrium after the invention of vaccine by assuming that the price ceiling at $10 and the supply of hand sanitizer remains the same.