A small neighborhood comprised of 10 homes has a problem with break-ins and find the local police to be effective. They are considering hiring private security. Each household can calculate their marginal benefit of having a private security guard by the formula MB=100 / (1+S) where S is the number of hours of security patrol provided per week.

If private security is a public good and the cost is $20 per hour, what is the efficient level of security? Do you expect this to be the equilibrium outcome?

Question

Josue Morgan

Business

15 September, 16:16

A small neighborhood comprised of 10 homes has a problem with break-ins and find the local police to be effective. They are considering hiring private security. Each household can calculate their marginal benefit of having a private security guard by the formula MB=100 / (1+S) where S is the number of hours of security patrol provided per week.

If private security is a public good and the cost is $20 per hour, what is the efficient level of security? Do you expect this to be the equilibrium outcome?

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Answers (1)

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Lea Harrison · Answer 1

The efficient level of security is 4 hours of security.

The equilibrium may not be sustainable.

Explanation:

In order to calculate the efficient level of security we would Set MB=MC i. e. guard's wage for net benefit maximization.

Hence, 100 / (1+S) = 20

20 * (1+S) = 10

1+S=5

S=4

Therefore, 4 hours of security is needed. The efficient level of security is 4 hours of security.

In the followig case Security guards is public good in this case, Public good is non-excludable and non-rivalrous. People cannot be stopped from using it without paying for it. Payment for security guard is voluntary. So, equilibrium may not be sustainable.