Be careful not to confuse the first and second derivatives (I think that is the correct mathematical expression*):
Throughout the 20th century, the global economy was fueled by burning coal to run factories and power plants, and burning oil to move planes, trains and automobiles. The more coal and oil countries burned — and the more planet-warming carbon dioxide they emitted — the higher the economic growth.
And so it seemed logical that any policy to reduce emissions would also push countries into economic decline.
Now there are signs that G.D.P. growth and carbon emissions need not rise in tandem, and that the era of decoupling could be starting. Last year, for the first time in the 40 years since both metrics have been recorded, global G.D.P. grew but global carbon emissions leveled off. Economists got excited, but they also acknowledged that it could have been an anomalous blip.
But a study released by the International Energy Agency last month found that the trend continued in 2015. In another study published on Tuesday, Nathaniel Aden, a research fellow at the World Resources Institute, a Washington think tank, found that since the start of the 21st century, 21 countries, including the United States, have already fully decoupled their economic growth from carbon emissions. In those countries, while G.D.P. went up over the past 15 years, carbon pollution went down.
In any single time period, any constraint on economic activity will decrease the amount of economic activity. My guess is that GDP is these countries is increasing more slowly than if they could use as much of the dirty, cheap energy sources as they wanted. In other words, what may have been a 3% growth rate is now 2.5%.
That said, it is not unlikely that long term welfare (e.g., income, health, etc) is greater at 2.5% economic growth (and fewer emissions) than 3%.
*Math update (4/12/16):
Let's say Y is a function of X and Z where Y is production of goods and services, X is dirty energy (coal, oil with emissions positively correlated) and Z is clean (solar, wind). The first derivative (the slope of Y) is positive, dY/dX > 0, meaning that emissions and income are positively related. This relationship hasn't changed. The second derivative, the slope of dY/dX, may have changed from positive to negative. Instead of production increasing at an decreasing rate with emissions (meaning that more and more fuel is needed to production one more unit of output, i.e., diminishing returns), we may now be enjoying production increasing at an increasing rate with dirty energy. But that isn't what is really going on. With the substitutability of X and Z, we're using more Z and less X so it is the cross-partial derivative that is complicating things.
It is still true that a policy that constrains energy use will increase the costs of production in the short run (i.e., until new technology brings down the cost of solar and wind).
