Oil prices appear to have stabilized — and may even be on their way back down. At least, so says the International Energy Agency’s monthly oil report for April, which notes that Saudi Arabia and other OPEC countries seem to be pumping out enough crude to offset the oil lost by sanctions on Iran.

(David Goldman/AP)

It should, though the boost is likely to prove fairly modest. Last year, Steve Goldstein of Marketwatch came up with a rough estimate of the stimulus effect from lower oil prices. A 5 percent reduction in the price of crude, sustained for a year, would save the average American about $250 from lower gasoline prices, smaller utility bills, and lower inflation. That’s not bad, though it’s only about one-fourth the size of the payroll tax cut passed this year.

Instead, the real impact of oil prices stabilizing would likely be that they can’t wreak further havoc on the economy. This was a real worry. Many car industry analysts, for example, have been encouraged by the strong auto sales figures in the past few months. But, they warn, if gasoline prices keep bouncing around, consumers might put off buying a car yet again. A March survey by research firm TechnoMetrica found that the number of Americans hoping to buy or lease a car in the next six months had halved of late, thanks to higher fuel prices.

Of course, even if the oil prices stabilize or dip slightly, they’re still high by historical levels. As Stuart Saniford demonstrates with charts, current oil prices are well above the levels during the 1970s oil shocks, even after adjusting for inflation.

But there are some signs that the U.S. economy is adapting to those high prices. James Hamilton, an oil expert at UC San Diego, has long argued that oil prices mainly only cause serious economic harm when they reach new peaks. When that happens, consumers tend to get nervous and put off buying cars and other durable goods. But if oil prices simply return to previous highs — as is the case right now — then the impact is blunted. Psychology plays a big role here.

On the flip side, Hamilton notes, that also means that falling oil prices usually don’t provide much of a kick. People don’t necessarily rush out to buy new cars when gasoline prices fall, for instance. “One very well-established observation,” he writes, “is that although oil price increases were often associated with economic recessions, oil price decreases did not bring about corresponding economic booms.”

So that’s the bottom line: Falling oil prices won’t necessarily juice the economy very much, but we’ll at least avoid further shocks and serious damage.

Related: How will the world replace Iran’s lost oil?