Question

If the daily marginal cost of security guards is $500, what is the socially optimal number of security guards for the community?

Answer 1

More information is needed but i will still try to explain the concept to you.

The socially optimum outcome will come at the quantity where the externality is take into account.

If there is no externality the quantity where marginal cost equals price level ( basically where marginal cost equals the demand curve ).will be the point of social optimum

If there is a positive externality then the externality has to be taken into account in the demand curve ( also knwon as marginal benefit curve). The amount of externality is to be added to Marginal benefit curve so that it becomes marginal social benefit curve. Marginal social benefit = Marginal benefit + positive externality value.  The quantity where marginal cost equals MSB curve will be the socially optimum point.

If there is a negative externality then the externality has to be taken into account in the dmarginal cost curve. The amount of externality is to be added to Marginal cost curve so that it becomes marginal social cost curve. Marginal social cost = Marginal cost + negative externality value.  The quantity where marginal cost equals Marginal Benefit curve will be the socially optimum point.