Positive externalities occur when the actions of an individual or business engaging in a market exchange unintentionally benefit third parties who are not involved in the transaction. A common example is education. When people pursue higher education, they not only gain personal knowledge and skills that benefit their future earnings but also society as a whole, which benefits from an educated workforce that leads to increased productivity and innovation across the economy.

In economic terms, markets typically provide the quantity of goods and services at a level where the private marginal benefit equals the private marginal cost. This is the point where the supply curve, representing the cost to producers, intersects with the demand curve, representing the private marginal benefit to the individual consumer. However, this equilibrium doesn't account for the external benefits that comprise the positive externalities enjoyed by society.

For example:

1. Education boosts societal economic and civic productivity.
2. Public transportation reduces traffic congestion and pollution.
3. Vaccinations reduce the spread of disease, leading to healthier communities.

The socially optimal quantity of output occurs where the social demand curve, which includes both private and external benefits, intersects with the supply curve. However, the market equilibrium occurs at a lower quantity where the private demand curve, which only reflects the private benefits, intersects with the supply curve. This gap between the market equilibrium quantity and the socially optimal quantity creates a deadweight loss to society.

Key concepts to understand include:

1. Private marginal benefit: Benefit to the individual involved in the transaction.
2. External benefit: Unintended positive effects on others outside the market exchange.
3. Social demand curve: Includes both private and external benefits.
4. Deadweight loss: The loss in social welfare due to the under-provision of goods like education or vaccines.

When positive externalities are present, society benefits from increasing the production of goods or services beyond the market-provided level to achieve the socially optimal quantity.