Study summary from NLIHC story:
.."They split the population into 10 income deciles and find that carbon emissions per capita in the highest income decile are more than 6 times greater than in the lowest decile; however, as a share of their income, carbon per dollar of expenditure is more than twice as high in the poorest decile as in the richest. This means that while lower income households have a much smaller carbon footprint than higher-income households, they would be paying a larger share of their income on increased energy costs
The next step in finding the net impact on households is to observe how the revenues from the permit auctions are redistributed. The authors analyze how households would be affected if 80% of the revenue were returned to the households as dividends (the other 20% could be spent on transitional assistance to communities, workers, or firms that would be adversely affected by decreasing reliance on fossil fuels). They find that the average annual cost of carbon to consumers for higher fossil fuel prices ranges from $135 per person in the lowest income decile to $618 per person in the highest-income decile.
If each household were to receive an equal dividend of $386, then the bottom seven deciles would all receive more in dividends than they pay in higher prices, the eight decile breaks even, and the top two deciles experience a net cost. As a percentage of income, this is a 6.5% gain for people in the lowest decile and a 0.3% loss for people in the highest decile, turning this into a progressive climate change policy."
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