Yanis Varoufakis is telling me about the birth of his daughter, Xenia. “What I felt was an immense weight of responsibility,” he says. “Absolutely blind love and the sense of focusing on one individual.” But the experience didn’t make him feel like a different person. “It didn’t change my internal constitution or the way I looked at the world.”

He was in an odd situation. Xenia was born in Australia. But Varoufakis himself was “not exactly” living in Australia. “My daughter came to life as the result of a broken-down marriage. “My former wife and I managed to do that which I always loathed when people did it. We managed to have a child when we were breaking up. Not a good idea … but it turned out brilliantly.”

It was 2004. “Thirteen years later, everything is absolutely fantastic.” But at the time, it didn’t feel fantastic. He was torn. Bonding with Xenia, having split up with her mother. His heart in Australia, his head in Greece. Emotionally, he was being ripped apart. He tries to describe it. “A major tragedy,” he says.

He had met Margarite, Xenia’s mother, in Australia; he was working in the economics faculty at the University of Sydney. Margarite, who is Greek-Australian, is an academic, too – a historian. They fell in love, got married and moved to Athens. “We broke up in Greece, we tried to patch things up, we broke up again, we tried to patch things up. In the end, when we decided we were going to part … conception happened.”

Margarite moved back to Australia, not knowing she was pregnant. Then she found out. They talked on the phone. About “arrangements”, how they would do this. Varoufakis “rushed back” for the birth. After Xenia was born, he persuaded Margarite to come back to Greece “to see if we could make things work”.

It lasted a year. “Which was fantastic; I changed nappies for a year … incessantly and exclusively, fearing that every day would be the last day of me having the child.” Margarite was “always meaning” to go back to Australia, he says. “The relationship was not working. It was not patched up. And then she went back. That was a nightmare. Because I was missing my daughter so badly.”

He wondered what on earth he was going to do. But at least there was Skype. “I had a Skype screen installed next to her bed, and I would read to her, every night, a bedtime story. And she would fall asleep with Skype.” Xenia would close her eyes in Sydney at the end of the day. Varoufakis, watching in Athens, would look up, and his day would be just beginning.

I am with Varoufakis at his publisher’s office in London. A lot has happened since Xenia’s birth. He has remarried, worked in the economics faculty at the university of Athens, tried, and failed, to persuade the German government to stop squeezing Greece for every last euro; and written several books. The most recent of his books is aimed at Xenia. It’s called Talking to my Daughter About the Economy.

“In a sense,” he says, “one of the reasons why I wrote the book was because it allowed me, during the hours when I was imagining I was talking to her about the economy, [to feel] that I was close to her.”

In the book, he explains the history of capitalism. It is very clear and easy to understand. At first, we were apes. Then we came down from the trees, learned to speak, and over-hunted our prey. So we were forced to invent farming. Suddenly, we had a surplus of goods, namely grain, which we kept in communal silos. Hence the need for writing, to keep track of who owed what to whom. We wrote on shells, which became money. Next, we minted coins. Markets developed. The few who were literate invented religion to justify their power.

For Varoufakis, the world changed massively in the 17th century. Global trade had made merchants rich. Feudal lords were being left behind. So they kicked the serfs off their land, and re-hired them as debtors. In other words, serfs became entrepreneurs; in practice, these new entrepreneurs were never out of debt.

“It’s the Great Reversal, as I call it,” says Varoufakis. Originally, the economy had been driven by what people produced. Now, it was driven by debt. “The Great Reversal makes debt the economic turbocharger.”

What then followed was the modern world – the Industrial Revolution, factories, empires, great inequality – and, eventually, the huge backlash of communism.

Varoufakis’s father, Giorgios, was a communist. Born in the 1920s, Giorgios, whose parents were Greek, grew up in Cairo before going to the University of Athens to study chemistry. But he was caught up in the civil war. Asked by the police to denounce communism, he refused. He was imprisoned in a jail for communists for four years – which turned him into a communist. Afterwards, when Giorgios resumed his degree, a woman from a rightwing group was told to keep an eye on him. This was the woman who became Varoufakis’s mother, Eleni.

Giorgios’ left-wing ideas prevailed over Eleni’s conservative ones, and they both ended up towards the left of centre. Varoufakis tells me his family home was “modest”. Giorgios, a steel engineer, had trouble getting or keeping work during the far-right regime in the 50s. As a communist, he kept getting fired. “The secret police would come and ask the employer to fire him.” Eventually, one company, Halyvourgiki, hired him as personal assistant to the boss, at a massively reduced rate. “He was exploited,” says Varoufakis. “The nice ironic twist,” he says, “is that my father is the chairman of the board of that company. And he occupies the office of that man. To this day. As we speak.”

We talk about Varoufakis’s up-and-down life. He fizzes with energy. He tells me how his mother’s brother was arrested and jailed; the young Varoufakis visited him in his cell. It seemed liked a big adventure, he says. After the rightwing regime collapsed, the family’s fortunes took a positive turn. Yanis was sent to the private Moraitis School in Athens, and later studied maths and economics at Essex and Birmingham universities. After that, he became an academic. He got a job at the University of Sydney, met Margarite, and after a crazy few years, found himself back in Athens, looking at a baby on a Skype screen.

One day, during this period, he went to an art gallery in Athens, and something strange happened. In his heightened emotional state, he walked into a dark room in which there was an installation. “It’s dark. The floor is covered in red soil – thick red soil. There is a spotlight in the middle of the room creating a red circle on the floor. There was a very powerful soundscape. Deep breathing, like –”

Varoufakis breathes deeply. “And the whole of the floor in the middle was moving up and down. The whole room, the soil, the earth, was breathing … and I thought, Wow.” This was Breathe, a work by Danae Stratou – who is, incidentally, the person Jarvis Cocker wrote about in his song Common People. (Varoufakis won’t confirm this officially.) Shortly afterwards, Yanis met Stratou, who is from a very wealthy background, at a dinner party. They fell in love. Now he lives in Athens with Stratou and her two children.

Meanwhile, capitalism looks unhealthy, to say the least, and he has been trying to explain this to Xenia. “I try not to be negative in the book,” he says. “I try to tell her what is fascinating and what is wrong. All in one. Because you really don’t want to dump on a child with gloom and doom. Do you think my book is gloomy? If it is, I’ve failed.”

Well, I say, it has to be gloomy in some ways.

“In some ways, yes.”

Life, he says, is “fantastic”. It is certainly better than it was. He has just spent a month on the island of Aegina, with Danae, her two children, as well as Xenia, and Georgios, who is now 93. He has started the Democracy in Europe movement, an attempt to reform the EU. He will go to Sydney at Christmas to see Xenia. “She’s an Aussie kid,” he says. “But she’s also Greek. She’s very down to earth. She’s very bookish. She reads a lot … she’s a happy kid, I think.”

• Talking to My Daughter About the Economy by Yanis Varoufakis (Bodley Head Adults, £14.99). To order a copy for £10.49, go to guardianbookshop.com or call 0330 333 6846. Free UK p&p of more than £10, online only. Phone orders min p&p of £1.99