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

PMC = 10 + 5Q

PMB = 40

Being a selfish person I will stay at home till PMB > PMC, and as PMB = PMC I will go out.

PMC = PMB

10 + 5Q = 40

Q = 6

Being a selfish person I will stay for 6 weeks at home.

But if I stay at home SMB = PMB + Benefit of 40$ which government don't have to spend on me as I am at home

SMB = 40 + 40 = 80

SMC = PMC at, if I am at home it's only costing me and no other entity.

Doing SMB = SMC

80 = 10 + 5Q

Q = 14

I should stay in for 14 weeks in home if I am not selfish.

If I come out government should fine me the amount which society suffers because of me coming out = 40$