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?

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.