Question

Q5. 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 realise 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

Optimum number of weeks you stay back home ( as a selfish person)=6 weeks

It means ,we have to find out profit maximising quantity,which is determined at the point where Marginal cost equals to Marginal benefit.

MC=MB

# 10+5Q=40

Q=6 weeks

# Socially efficient number of werks to dtay back home = 12 weeks

where AC=AR(price or MB)

MC=10+5Q

TC=10Q+5/2Q²

AC=10+5/2Q

At Equilibrium---

10+5/2Q=40

Q=30×2/5=12

# Fine to be imposed by govt= $240

differenence in weeks between being selfish & socially efficient = 12--6=6 weeks

Cost to govt per day =$40

Fine to be imposed= 6×$40=$240