When a positive externality exists, the socially optimal level of output will be than that resulting from a private market.

When a positive externality exists, the socially optimal level of output will be higher than that resulting from a private market.

Here's why:

1. A positive externality is a benefit that is enjoyed by a third-party as a result of an economic transaction. In other words, it's a benefit that's not directly involved in the transaction but still benefits from it.

2. In a private market, the level of output is determined by the supply and demand of the individuals or firms involved in the transaction. They will produce and consume goods and services until their private marginal benefit equals their private marginal cost.

3. However, when a positive externality exists, the social marginal benefit (the private marginal benefit plus the benefit to the third party) is greater than the private marginal benefit.

4. Therefore, in order to achieve social efficiency (where the social marginal benefit equals the social marginal cost), a higher level of output is needed compared to the level of output in a private market.

5. In other words, the socially optimal level of output is higher than the level of output resulting from a private market when a positive externality exists.