One kind of market failure arises because there are situations when it is impossible to charge the customer for the service, for example if someone arranges an air show or fireworks, this can be seen from a far place as well as seen by paying for the event making it impossible to limit this for only those who pay for that. This is one kind of failure which is non-excludable (You cannot exclude those watching from far) and non-rival (One person’s watching does not limit other one’s sight).
Second kind is the presence of externality. It arises when the cost or benefits accrue to someone other than the buyer and seller. For example cigarette is affecting the third party by making the environment pollute.
Both can happen simultaneously. For example a firework show keeps both attributes of first kind and the second kind as well.
