In: Economics
The security guard can be considered a public because of two primary reasons-
Nonexcludable - Since there is one common parking lot, when the security guard is hired, he protects the parking lot. None of their shops can be excluded from the protection. One of the primary characteristics of any public good is that they are non excludable in nature, meaning it is not possible for one user to exclude the other user from using a public good. For e.g. if a street lamp is constructed and some people in the locality do not pay taxes, yet no tax payer can exclude anybody from benefitting from the street light.
Non rivalry - Well, when the security guard is patroling the parking lot, the protection of Diane's Depot does not rival (prevent) the protection of Sean's shop as they share the same parking lot. Non rivalry in consumption is a primary characteristic of a public good.
Also consider that a tax payer pays taxes for a public good depending on how much he values that good. A rich person in society would pay higher taxes for police service as he values a safe and crime free society more than a average person. Likewise here Diane values security more than Sean as she has more valuable inventory and hence is ready to pay lot more for the guard than Sean. This is the defining characteristic here that shows how the security guard is a public good in this economy.