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 MB = 200 - 2S.Patrols cost $20 per hour.What is the socially efficient level of security?
A) 90 person-hours of patrols per week
B) 100 person-hours of patrols per week
C) 92.5 person-hours of patrols per week
D) 97.5 person-hours of patrols per week

Question

Quizplus · Accepted Answer

The socially efficient level of security is determined where the marginal benefit (MB) equals the marginal cost (MC). Given MB = 200 - 2S and the cost of patrols is $20 per hour, set MC = $20. Therefore, 200 - 2S = 20. Solving for S gives S = 90, but since the question involves four stores and the formula given is for each store, the total is 90 * 4 = 360 person-hours for all stores combined. However, to find the per store figure, we divide by 4, which was mistakenly not considered in the calculation. The correct approach is to equate the marginal cost directly without multiplying by the number of stores, as the formula already represents the combined marginal benefit for security patrols, not per store. Thus, solving 200 - 2S = 20 correctly gives S = 90, but this error in explanation led to a confusion in the final answer. The correct process is to solve 200 - 2S = 20 directly for S, which actually leads to the conclusion that the initial calculation step was correct but misinterpreted in the explanation regarding the multiplication by the number of stores. The correct answer should be found by directly equating MB = MC without additional adjustments for the number of stores, as the question implicitly asks for the total optimal level of security, not the per store level.

Four Stores Have a Problem with Theft and Security Is