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Economists teach us that resources don't just run out. As something becomes scarcer, its price rises, triggering a search for new supplies or the discovery of substitutes.

We've seen it happen over the past two decades in the oil market, as dwindling reserves triggered the U.S. boom in oil derived from shale. Unexpectedly, the U.S. has surpassed even Russia and Saudi Arabia as the world leader in crude oil production.

Even so, the shale boom is already petering out, as we've nearly tapped most of the easily extracted oil, a comprehensive new study suggests. Huge investments and the drilling of nearly 10,000 new wells every year are now required to keep production at current levels. We're putting in ever more energy for every barrel we get out.

That trend highlights a looming problem for our economy. It takes energy to find or produce energy, and, year by year, it requires ever more, as we turn to lower-quality energy sources, including oil from shale and tar sands. Things will get tighter still as we move into renewable sources, including solar and wind power. The weak economic growth of the past decade may be due, at least in part, to the changing nature of our energy sources. And in the future, as the world works to protect the climate by turning to low-carbon fuel sources, lower economic growth may be an unwanted consequence.

A half-century ago, a barrel of oil gave us around 100 times as much energy as we spent on finding the oil, drilling wells and pumping it out. This ratio - known as the energy return on investment, or EROI - has fallen below 10 for conventional oil produced in the U.S., and to around 20 to 30 for conventional oil produced elsewhere in the world. The EROI from shale or tar sands is much worse, perhaps as low as 2.

Of course, it takes energy to do anything - from transporting materials to building satellites or running computers. Energy is linked to economic activity. Three years ago, economists Florian Fizaine and Victor Court looked at the performance of world economies from 1960 to 2010 and found a correlation between periods of higher energy expenditures - the fraction of gross domestic product spent on obtaining energy - and lower economic growth. It makes sense: A society that devotes a larger fraction of its output to producing energy has less to spend on other useful outputs, such as research, education and manufacturing.

This link between energy and growth suggests that many of the advances that the global economy has experienced over the past two centuries have been due to the availability of cheap, high-quality fossil-fuel energy. Conventional oil and coal provided so much more energy than it took to produce that there was plenty of energy left for building cars, roads and airports, for manufacturing industrial goods, growing food, and investing in sophisticated science and medicine. But we're now about to enter a different era.

Some researchers argue there is a limit to how much energy a modern economy can devote solely to finding more of it. Beyond this limit, sustained economic growth becomes impossible. Empirically, Fizaine and Court estimate, the U.S.'s limit is around 11% of GDP, which also implies a minimum average EROI of 8 to 13 from all energy sources. The average EROI for most nations is currently higher, mainly because we still rely on oil, natural gas and coal for power. But the numbers are trending downward.

If we reduce CO2 emissions by turning from coal and oil to renewable energy sources such as solar and wind, we may have a chance to avoid the worst consequences of climate change. But we'll also be turning to sources with EROI values that are well below those for oil; estimates for nuclear energy give it an EROI of around 14, with lots of variation depending on a reactor's technology. Moreover, these numbers may be overly optimistic: Many estimates of EROI fail to include all the energy used start to finish, from finding the energy source to production to the final point of use. Current estimates for solar or geothermal energy see an EROI of roughly 10. Wind is somewhat higher, around 18, but only in some locations, and there are limits on how much wind energy we can expect to harvest.

We may find that a green-energy future is also one that lacks the vibrant economic growth to which we're accustomed. In that case, we'll have to divert more of our efforts to finding more energy, rather than to the activities that result in growth. That future is preferable to continuing to seek high-EROI fuels and magnifying the consequences of global warming, which will also spell the end of growth as we know it while bringing many other problems as well. Either way, enormous social transformation is probably on the horizon.

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Mark Buchanan, a physicist and science writer, is the author of the book "Forecast: What Physics, Meteorology and the Natural Sciences Can Teach Us About Economics." He wrote this for The Washington Post.

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