Why would we want to do that?
If the production and/or consumption of a good results in uncompensated costs on others who are not producers or consumers of the good, it is is termed an "external cost". It is a not absorbed into the price consumers pay for the good or that producers incur by producing the good.
Goods consumed and produced with heavy doses of fossil fuels as an input are nice examples goods that impose significant external costs on society and are not reflected in the market price.
A "Carbon Tax" is one way to "internalize" the external, uncompensated costs that arise out of the use of fossil fuels in the production and/or consumption of goods.
Below I excerpted key paragraphs on a discussion of a carbon tax that puts in simple language the goal of the tax.
The beauty of a carbon tax is its market-based simplicity. Economists since Adam Smith have insisted that prices are by far the most efficient way to guide the decisions of producers and consumers. Carbon emissions have an “unpriced” societal cost in terms of their deleterious effects on the earth’s climate. A tax on carbon would reflect these costs and send a powerful price signal that would discourage carbon emissions.
Producers and consumers would adjust their behavior in response to this signal in ways that are most efficient for them. And these efficient micro decisions would support efficient societal outcomes.
There’s much debate about what the proper “social cost of carbon” might be, but there is no debate that carbon emissions are seriously underpriced. Any tax on carbon would be an important step in the right direction, and it could be gradually increased to give consumers and producers time to modify their decisions.
Here is my abbreviated PPT presentation I use for my AP Microeconomics class to illustrate graphically how the presence of a negative externality in the market place affects social welfare when the full costs of consuming and producing a good are not factored into the market price. I hope it is helpful in understanding the issue.
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