The Obama administration proposed far-reaching limits Monday on power-plant emissions that contribute to global warming, but tailored the rule in ways that would give mean far fewer costs to states such as California that have already taken steps to cap carbon pollution.

The proposed rule represents the heart of what has become President Obama’s signature issue of his second term, tackling climate change. It would cut carbon emissions from power plants by 30 percent by 2030, compared with 2005 levels, which would amount to one of the most significant actions any nation has taken on global warming.

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