Question

Due to the sudden outbreak of the pandemic, you were asked to stay back in your home to maintain social distancing. If you do not follow the restriction, there is a possibility that you infect another 2.5 people, and on average, the government must incur $40 each person on their medical expenses. You realize that your marginal cost of staying back home is MC= 10 + 5 Q, where Q is the number of weeks you confine yourself in your home. Moreover, you enjoy a benefit of $40 each week for not traveling to your work. How many days will you stay back home at optimum (consider yourself a selfish person)? What is the socially efficient number of weeks you should stay back home? What fine should the government impose if you do not follow the rule?

Answer 1

The government pays $40 for not going out, meaning that we have P=$40/week. The marginal revenue would be as or or or . The optimim number of days would be where MC=MR or or or weeks or 42 days.

The socially efficient number of weeks would be where MC=P or or or weeks. Since the price doesn't change with Q, the MR=P and the optimal amount of Q and socially efficient Q would be the same.

The government should fine the cost of infected people incurred, ie per day. Each day, if 2.5 people are infected, the government would have to spend $40 per person and $100 per 2.5 person if one don't follows the rule, which should be imposed as fine by the government.

The price of P=$40 is taken as demand price, concerning that government pays this amount for the product, which is staying at home for 1 week. Here, the product is staying home for 1 week, and the price for the product given by government is $40 per output (1 output = 1 week).