Greek Finance Minister Yanis Varoufakis arrives at a news conference after an extraordinary Eurozone finance ministers meeting in Brussels.Eric Vidal/Reuters

Late Friday night, after the Eurozone's 19 finance ministers granted Greece a desperately needed economic lifeline, the country's finance minister Yanis Varoufakis announced that the deal provided a "way out" of Greece's problems. This is, in a narrow sense, true. Depositors have withdrawn €23 billion from Greece since December, including €1 billion on Friday alone, and a government source told Reuters that Greece faced bankruptcy as soon as next week. With an extension granted Friday, Greece is now in position to meet its obligations until the end of June.

But for a population that has endured years of hardship, Friday's deal provides no long-term relief. And by cooperating with the hated "troika" (a group that consists of the International Monetary Fund, the European Commission, and the European Central Bank), Greece's new, left-wing Syriza government must embrace the the very cost-cutting measures—known as austerity—voters elected it to avoid.

Since European governments bailed out Greece from its financial woes in 2010, the nation has struggled to overcome what economists call an "austerity trap." In order to meet the conditions of its European creditors, Greece must achieve a primary surplus (a budgetary surplus that doesn't include debt repayment) of 4.5 percent of GDP over 10 years. This is practically impossible: Only three countries between 1970 and 2000 accomplished this feat, and all three were in far better fiscal health than present-day Greece. In order to maintain a primary surplus, Greece must curtail government spending. This depresses the economy, and deprives the government of income. That, in turn, makes it hard to maintain a surplus without (you guessed it) cutting government spending even further. This extends even to the bailout: In order to receive the €270 billion it needs to keep the economy afloat through June, the Greek government must present an acceptable cost cutting plan to its European counterparts by Monday. And so the cycle continues.

One way for Greece to escape the austerity trap would be to exit the Eurozone. But European leaders are reluctant to do this for two main reasons. One, it would be very expensive. A Brussels think tank estimated that a "Grexit" would cost Europe €250 billion, further crippling the continent's sluggish economy. Secondly, Greece's departure would provide other struggling countries, like Portugal, an incentive to negotiate similar exits. Little wonder that on Friday, French President Francois Hollande expressed little ambiguity about the issue: "Greece must stay in the Eurozone," he said.

For Greece's beleaguered citizens, whose economy has contracted by a staggering 25 percent in the last five years, the bailout extension provides no long-term relief. Even Greece's newly elected prime minister, the youthful Alexis Tsipras, didn't deny that it is just a temporary solution: "The difficulties, the real difficulties ... are ahead of us."

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