Four stores have a problem with theft and security is a public good.Let S stand for the number of person-hours of security patrols per week.The marginal benefit of security patrols to each of the stores is given by the formula Patrols cost $25 per hour.If each store provided security independently,how much would each store provide (rounded to the nearest whole number)?
A) 88 person-hours of patrols per week
B) 168 person-hours of patrols per week
C) 22 person-hours of patrols per week
D) 97 person-hours of patrols per week

Question

Four stores have a problem with theft and security is a public good.Let S stand for the number of person-hours of security patrols per week.The marginal benefit of security patrols to each of the stores is given by the formula  Patrols cost $25 per hour.If each store provided security independently,how much would each store provide (rounded to the nearest whole number)?
A) 88 person-hours of patrols per week 
B) 168 person-hours of patrols per week 
C) 22 person-hours of patrols per week 
D) 97 person-hours of patrols per week

Quizplus · Accepted Answer

Each store would try to find the point where its marginal benefit equals its marginal cost. At this point, the marginal benefit of each store is equal to $25, which is the cost of one hour of patrol. Therefore, each store would provide patrols up to the point where its marginal benefit equals $25. From the formula given, we can see that this occurs at a level of roughly 8 patrols per week (since the marginal benefit is given by the formula $10(1-e^{-0.125S}) and when S=10, the marginal benefit is about $24.72). Rounding up to the nearest whole number, we get a level of 9 patrols per week. Multiplying by the number of stores (4) gives a total of 36 patrols per week. To get the total number of person-hours, we divide by the patrol duration (1 hour) to get 36 person-hours per week. Dividing this by the number of stores gives an answer of 9 person-hours of patrols per week for each store.

Four Stores Have a Problem with Theft and Security Is