A recent slump in oil prices may give consumers more income to play with, but it's not enough to generate a global recovery, according to Andrew Kenningham, senior global economist with Capital Economics said.

Oil prices have fallen $30 since May, putting the price below $90 per barrel and creating an oil price benchmark that is close to Capital Economic's year-end forecast of oil selling at $85 per barrel.

Oil plummeted again after the Fed decided not to introduce further economic stimulus, or quantitative easing, this week. Negative business surveys also contributed to the drop in demand, Kenningham said.  

Usually, for every $10 drop in oil prices there is a transfer of income equivalent to 0.5% of the world GDP from oil producers to consumers. In addition, lower oil prices means lower headline inflation, which makes it easier for central banks to keep interest rates hovering around the zero point, Kenningham said.

But he doesn't see that happening here.

"For a start, the actual boost to global demand from each $10 fall in the oil price will probably be less than 0.5% of GDP, and perhaps less than 0.25% depending on the propensities to spend and save among producers and consumers," Kenningham said. "Assuming oil settles around $85 per barrel, this would be some $20 below its average price during 2011, boosting global demand by around 0.5% of GDP over the coming twelve months or so."

He added that central banks lack room to loosen their monetary policies further, and its unlikely new easing would prove to be more effective than earlier QE initiatives.

"Finally, it makes little sense to expect a fall in the oil price to kick-start global growth if it is weak demand which pushed prices down in the first place," Kenningham said. "Cheaper oil may cushion the fall in demand, particularly in the U.S., where the pass-through from crude oil to gasoline prices is high. But it cannot reverse the slowdown. Nor will cheaper oil do anything to resolve the financial and economic imbalances which threaten to break up the euro-zone. So in short, cheaper oil may help, but not much."