A serial killer is stalking the wealthy suburbs of Athens with an idiosyncratic choice of victims. They are all rich Greeks who have failed to pay their taxes, and their corpses have been left scattered among the ruins of the ancient city, dead of hemlock poisoning, the means of Socrates' execution.

Greece is going through a lot right now, including a significant surge in crime, but this particular horror is mostly fictional. It is the plot of the latest bestselling novel by Petros Markaris, who has combined the roles of thriller writer and social commentator in Greece to such an extent that he has become one of the most widely quoted voices in the crisis.

The murders at the heart of Markaris's new book, I Pairaiosi, or The Settlement, resonate strongly with a mass readership furious at the country's tax-dodging elite whose fecklessness has helped bring Greece to its knees. Many readers, like its hero-narrator, Inspector Costas Haritos, are torn between disgust and sneaking admiration for the murderer, who calls himself the National Tax Collector, and who is demanding money not for himself but for the national coffers. Such was the public sympathy for the killer that Markaris found it prudent to put a note on the book's back cover saying: "Warning: This novel is not to be imitated."

"I wanted to tell the real story of how this crisis has developed and how it affects ordinary people," Markaris said in an interview at his Athens flat. He said crime writing provided the best form of social and political commentary available, because so much of what was going on in Greece now was criminal.

"The title had a meaning in ancient Greek which meant the end of life, the settling of life's account," the 75-year-old author said. "But its modern meaning is a method of raising tax revenue. In return for a payment to the tax office – a settlement – the state gives amnesty to people who haven't paid their taxes."

Born in Istanbul to Greek and Armenian parents, Markaris settled in Athens in his 30s and still sees Greece's inherent problems with an outsider's eyes. "This is a system which has built up on a day-to-day basis, since the beginning of the century, and it has sped up in the past 30 years," he said.

The system in question is most commonly called clientelist. It involves the Greek elite – the shipowners, doctors, lawyers and top journalists – funding the two main parties and getting top civil service jobs for its sons and daughters in return for investment, as well as a lifelong tax holiday. It was an unsustainable bargain that was covered up in the national accounts, and that spectacularly unravelled when the country could no longer borrow on international markets to fund its habits.

When the outgoing government went after Athens doctors in a belated attempt to raise some revenue, it found that the majority paid nothing, having declared their income at just below the minimum tax threshold of €12,000 while driving cars worth many times that amount. In a battle of wills between reformists in government and the elite, the reformists lost. The government collapsed and elections last week brought only stalemate and the uncertain prospect of another vote.

Meanwhile the rich continue to fill the city's top-end bars and restaurants to bursting, while the working and much of the middle class face destitution. Markaris himself lives in a modest apartment in a central Athens block that clearly used to be far more agreeable. Now anger is splattered against the walls in the form of grafitti threatening immigrants with expulsion or worse. The streets crackle with the antipathy of local residents towards African street hawkers. When the writer looks out his window in the early hours, he sees proud middle-aged neighbours stealthily fishing for scraps in the dustbins.

His observations of the evolving crisis fill his books. The Settlement opens with a quote from a former president, Konstantinos Karamanlis, describing Greece as "an endless madhouse". In the first chapter, four old ladies kill themselves, leaving behind a note saying that with their pensions cut they could not afford their medicines or to see a doctor and so had chosen not to be a burden on society any longer. There have been similar documented cases in the past two years. Official statistics say the suicide rate has soared by 22% but that probably understates the problem. Pious Orthodox families will often cover up suicides out of shame.

Later in the book, when Inspector Haritos is called on to look into the murders of rich Athenians, his first instinct is concern that any investigation exposing the private affairs of the elite could endanger his expected promotion. He struggles to feel sympathy with the victims, observing of the first, a famous surgeon: "Before opening up his patients with a scalpel, he would open their wallet."

On discovering the self-proclaimed National Tax Collector's motives, Haritos notes drily that if all the country's tax cheats were murdered the population would be reduced to some "wage-earners, the unemployed and housewives".

Markaris and Haritos are channelling a dark undercurrent in Greek psyche that the economic crisis has brought to the surface, most palpably in the election to parliament of a neo-Nazi group, Golden Dawn. In a previous Markaris book, Expiring Loans, the victims are linked to banks, hedge funds and a ratings agency; they are all beheaded.

He is about to embark on the third novel in the trilogy but is waiting to see how which way Greece's real story goes. On the day of his interview, the president, Karolos Papoulias, was meeting party leaders trying to make them form a government of national unity, but Markaris did not rate his chances.

"The system which has run the country since the fall of the junta is dead," he said. "The austerity measures have destroyed the political landscape. The question is if Greece gets through the austerity measures and survives, and if Europe can survive a Greek collapse. I don't know what the answers are."