How does the existence of positive externalities cause free markets to misallocate resources?

If a person gets benefitted from the activity of other persons, without paying for the benefit it is known as positive externality. For example, if a person opens a garden then the neighborhood will also benefitted as they can enjoy fresh air without paying for it.

A good is priced at a point where private marginal cost equals to the private marginal benefit. But in case of positive externality causes free market to misallocate due to following reasons:

• If there is positive externality of consumption then social benefit exceeds the private marginal cost and causes over consumption of goods without charging the prices from the consumers consuming the goods without being paid.
• If there is a positive externality of production then social marginal cost falls short of the private marginal benefit and causes under utilization of resources.