There've been many projections about how much American Clean Energy & Security Act could save (or cost) the US, but recent Energy Information Agency analysis is the first really quantifying the impact on imported oil. Climate Progress has a good breakdown of it:According to the EIA, oil imports would drop by 590,000 barrels per day by 2020 under ACES. Currently the US imports about 9.8 million barrels of crude oil per day.
So in terms of actually reducing US dependence on foreign oil that's not really that much, but it does add up in terms of money saved. Cumulatively though 2030 the US would save $658 billion -- or $5,600 per household. Or, using the same cumulative math, $466 per household per year through 2030 just from reduced oil imports. That's in constant 2007 dollars, by the way
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Joe Romm notes though that these savings really could be greater, as in his words the EIA "doesn't get peak oil" (unlike the IEA) and the effects it could have on oil prices -- Romm estimates that the savings could really be 50% greater than the EIA projections.
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