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.Find the marginal social benefit function.

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.Find the marginal social benefit function.

Quizplus · Accepted Answer

The marginal social benefit function takes into account the benefit to all parties involved, not just the individual stores. Since security is a public good, the marginal social benefit is equal to the sum of the marginal benefit to each store. Therefore, the marginal social benefit function is:
MSB = 4 x MB = 44 - 2S
To find the optimal level of security patrols, we need to equate the marginal social benefit to the cost of patrols:
44 - 2S = 25
Solving for S, we get:
S = 9.5
Therefore, the optimal level of security patrols is 9.5 person-hours per week. Note that this represents a compromise between the individual stores' desire for more patrols and the overall societal benefit of the patrols.

Four Stores Have a Problem with Theft and Security Is