There are many ideas concerning the purpose of the state: why it appears, what its functions are and so on. The economical science has a simple answer to this question that is limited to one phrase: the free-rider problem.
The free-rider problem is an economical problem that is based on the fact that certain members of the society consume the resources they haven’t paid for. For example we can use the law enforcement and road maintenance. It is next to impossible to determine to what extent every particular person uses them. The idea of private law enforcement and private roads is almost absurd. If I need a road, I can pay for it to be constructed; but I won’t be the only one to use it, there will be a lot of other people who didn’t pay for it, but will use it anyway. It is impossible to collect money from them in advance; and nobody will pay anything if one doesn’t have to and may simply wait for someone else to lay the road. The same goes for law enforcement. If I hire a private policeman to guard my house, won’t he guard the adjacent houses just by his presence?
This is the sole reason for the existence of state. It is too difficult to collect money for something of this kind according to the degree every person used them. There should be some organization that deals with these problems, collecting a set amount of money from everyone. All the rest functions the state assumes are not what it is supposed to be doing.