In order to reduce negative externalities in production, such as when the production of goods and services cause pollution (CO2 emissions), the government can begin by researching the size of the market failure, and understand how much over-production there is of that good or service.
The government will know that qs is the socially optimal quantity, and they will issue the according number of pollution permits to firms, so that pollution does not exceed the optimal quantity.
This shows the market for pollution permits. D1 represents the demand for pollution permits, and S1 represents the perfectly inelastic supply of pollution permits. It is perfectly inelastic because the quantity supplied does not vary at all with price, because the quantity of available permits is pre-determined by the government. In theory, no matter how much demand varies, the equilibrium quantity will never change. Another benefit of this market is that firms who want to pollute more will have to buy additional permits, so they get punished with higher costs of production, whilst firms who pollute less get rewarded as they can sell their permits for additional revenue, or profit. The price mechanism will incentivise firms to invest in renewable sources of energy over time, which reduces the need for government investment or enforcement.
However, tradeable pollution permits may not be ideal as they could lead to certain forms of government failure. For example, it is extremely difficult to accurately measure CO2 emissions, and it is also hard for the government to understand how much damage CO2 does to society. They may set the wrong quantity permits in the market. Furthermore, similar to how firms may avoid taxes, some firms may avoid reporting their CO2 emissions accurately to the government. It may be costly to the government to send out enforcement. If the costs are too high, it may not be worth setting pollution permits in the first place. Lastly, the local government have no control over pollution in neighbouring areas.