What is the correlation between the socially optimal quantity and the free-rider problem?

The free-rider problem is a market failure that occurs when the beneficiaries of resources and public goods do not pay for them, which might cause the goods to be underused, overused, or degraded. Due to fewer contributions, the producers might produce fewer goods than is socially optimal. The relationship between these two variables can be said to be direct. In that, as the problem becomes wider, reduction in the number of people who contribute to the provision of the good, production also decreases to lower optimal levels. On the other hand, if more people were to contribute then, production would be socially optimal.