What is a negative externality and how can it be corrected?

A negative externality is a type of market failure that occurs when the consumption or production of a good has an external cost on a third party that is not involved in the transaction. This external cost is not taken into consideration when determining the price of this good in the free market, this results in the good being overproduced and overconsumed. This can be shown on a diagram (which of course, I would be happy to draw and go through). The free market allocates the good a price, P, lower than the socially optimal price, P* and this means the good is consumed at Q, a higher quantity that the socially optimal one Q*. Some real-world examples of negative externalities are second hand smoke inhaled by bystanders when someone smokes and goods that require a large amount of fossil fuels to consume (e.g. cars) or produce.The most common way of correcting the market failure caused by a negative externality is government intervention. An indirect tax levied on the good causing the externality leads to an increase in price, from P to P* and a fall in quantity consumed from Q to Q*, meaning that the good is no longer overconsumed and overproduced and the market failure is corrected.