* ECB's Draghi confronts spectre of deflation on visit to Greece
* Low prices across euro zone dampen confidence
* Falling prices can compound problem of heavy debts
ATHENS, April 2 (Reuters) - The falling price of living in Athens presented the unmistakable spectre of deflation to European Central Bank President Mario Draghi during his visit to the Greek capital this week yet there is little he will do to heal this pain.
Whatever course of action the ECB opts for to bolster the euro zone's economy, it will take a long time before it trickles down in to Greece, where the prices of everyday purchases from traditional souvlaki meals to frappé coffees have dived.
The long lines of empty yellow cabs scouting the dusty streets of Athens for custom, offering fares at a fraction of peers in Frankfurt or Brussels, bear testament to the country's sudden adjustment.
All this set the backdrop this week for a meeting of European finance ministers and central bankers including Draghi. They gathered a short distance from Syntagma Square, the scene of earlier violent clashes over austerity imposed under the country's bailout.
But despite its desire to buoy prices across the 18 countries using the euro, the ECB will do little to halt Athens' tumbling prices.
Policymakers in Frankfurt draw a distinction between 'bad' deflation - spurred by a general downward economic spiral - and 'good' deflation, as in the case of Athens, where falling prices are part of a painful course of medicine to reform the economy.
"The deflation that we see in Greece is, in the eyes of the ECB, the price it has to pay for adjustment," said Carsten Brzeski, an economist with ING. "It's part of the formula - a necessary evil to get the peripheral countries back to growth."
During Greece's debt-fuelled economic boom after adoption of the euro, prices were rising faster than in the euro area. In 2001-2011, they rose by a cumulative 46 percent, compared with 29 percent in the euro area.
But the average annual inflation rate in Greece hit -0.9 percent in 2013, negative for the first time since 1962, and the fall in prices in Greece reached a new depth last November, when they were almost -3.0 percent from a year earlier.
While the International Monetary Fund predicts slower deflation of -0.4 percent in 2014, the OECD, a think tank, is forecasting a decline roughly four times as steep this year and next.
Low prices are not unique to Athens. Euro zone inflation slowed to 0.5 percent in March, its lowest since the economy was deep in recession in 2009, and its sixth month in what Draghi has called "the danger zone" below 1 percent.
Although the ECB is not expected to announce any new steps to bolster the economy when policymakers meet on Thursday, the sharper-than-expected fall in prices will fire up the debate as to whether Frankfurt should be doing more.
RISK OF FALLING PRICES
Falling prices, however popular they are with Greeks struggling to make ends meet, pose a threat.
Olli Rehn, the European Union's top economic official, pointed to one of the risks, warning that a long period of low inflation could hinder the 'rebalancing' of the economy, echoing similar concerns at the Bank of Greece.
In other words, shrinking prices make it more difficult for a country to shrug off heavy debts.
And debts in Greece, as in many other countries in Europe, are rising. Having drawn down almost 220 billion euros of emergency loans from its euro zone neighbours and the IMF, the country may now be forced to ask for more such aid.
Germany's finance minister, Wolfgang Schaeuble, said on Wednesday that Germany would be willing to help.
Taking on further debts as Greece grapples with the first price fall in some 45 years could squeeze the country.
"Greece, Italy, Spain and Ireland lost competitiveness in the boom years and need to restore it," said Alan Ahearne, an economist who advised the Irish government when it was sunk by its banking collapse.
"The problem is that ... you are forced to have deflation. For heavily indebted businesses and households, that is increasing the burden of debt. And if the burden is getting bigger, you will see more rhetoric on default." (Additional reporting by Harry Papachristou Editing by Jeremy Gaunt)