The euro zone is mired in a seemingly endless recession, and the European Central Bank is meeting on May 2nd to decide whether to cut interest rates and provide a little stimulus.

Trouble is, that's not an easy decision, as this interesting chart by Benn Steil and Dinah Walker of the Council on Foreign Relations suggests. Different countries within the euro zone are in vastly different economic situations, and ECB head Mario Draghi will have a hard time satisfying everyone:

As the chart shows, ECB interest-rate cuts have had little effect over the past five years on two of the countries that really need economic stimulus — Greece and Portugal — in part because their banking systems are in tatters. (This "transmission mechanism" isn't quite as broken for Spain and Italy, but even those two struggling countries get less of an economic boost from rate cuts than their neighbors up north.)

For the rest of the euro zone, meanwhile, it's hard to find a central-bank policy that will satisfy everyone. France would certainly welcome an interest-rate cut, as it has low inflation (around 1.1 percent) and high unemployment (10.8 percent). By contrast, a country like Austria has inflation that's above the ECB's 2 percent target (namely, 2.4 percent) and low unemployment (4.8 percent) — so Austrians wouldn't be thrilled with an extra bit of stimulus. Neither would Germany.

Here's the caption from Steil and Walker:

The ECB’s official inflation-rate target is “below, but close to, 2%.” Both Portugal and Greece have inflation under 1% , but the transmission mechanism from ECB rates to business borrowing rates in those two countries has been virtually severed by the crisis. In short, they need a rate cut, but the ECB can’t deliver them one.

In those Eurozone countries where the monetary transmission mechanism is still working normally—Austria, Finland, France, Germany, and the Netherlands—the GDP-weighted-average inflation rate is 1.8%, right near the ECB’s target. ... Some will argue that a bout of robust inflation in the north is just what is needed to restore competitiveness in the south. But the ECB will have to willfully ignore its price-stability mandate if it is to justify a rate cut right now, and it will almost certainly need to apply more radical tools if it is to aid the south quickly.