“Economist” and “celebrity” are not words usually spoken together, but both of these authors have been called rock stars. Thomas Piketty is famous for his surprise bestseller about inequality, Capital in the 21st Century, and Yanis Varoufakis is the academic who, for a short while, became the outspoken finance minister of Greece and challenged the austerity mindset of his eurozone counterparts. Although both are well-known economists, their scholarly backgrounds are rather different. Piketty – who became the founding director of the Paris School of Economics in 2006 – is very much part of the academic mainstream, whereas Varoufakis – who taught at Essex, Cambridge and Sydney before returning to Greece in 2000 – brings a more Marxian perspective to his analysis.

These are also very different kinds of book. Chronicles is a translation of Piketty’s French newspaper columns from 2008 to November 2015, showing how one economist tried to make sense of a rapidly changing world. In And the Weak Suffer What They Must? – its title taken from the Athenian historian Thucydides – Varoufakis attempts to tell a story about how the euro was created in the context of global macroeconomic history since the 1930s, and why a subsequent crisis was inevitable.

The subject matter of Piketty’s columns ranges widely, from the financial crash to French attitudes towards religion. Naturally, the theme of inequality occurs often. These columns are informed by Piketty’s academic work, but the language he uses is both more accessible and more direct. For instance, in two of the essays he argues that cutting the top rates of tax in the US and UK in fact encouraged the rapidly rising pre-tax incomes of the 1 Per Cent, because it gave the recipients the incentive to get the most they could out of their firms. He describes these compensation packages as “obscene” – certainly not the vocabulary of academia. Some of the discussion is geared towards his original French audience, but there are helpful introductions that explain, say, what the Bettencourt affair was all about. The subsequent reflection on the role of inherited wealth is universally applicable.

Piketty’s professional interest in inequality also informs discussions of apparently unrelated matters. The low level of corporation tax in Ireland crops up a few times, as does his disdainful view of it. He sees it as encouraging a race to the bottom between countries trying to attract international finance, which is bad because it is vital to tax the returns to capital. No doubt he would regard George Osborne’s cuts to the same tax as proof that the concern is warranted. His verdict on the International Monetary Fund is delicious: “For decades, the IMF has done everything possible to undermine the very principle of progressive taxation.”

The dominant subject of these pieces is not inequality, but the eurozone crisis. Although neither author mentions the other, their paths cross, in a way, in Piketty’s column written following the election of Syriza in Greece in January 2015. Its title, “Spreading the democratic revolution to the rest of Europe”, tells you how he saw that election. However, he also writes: “In order for this democratic revolution from the south to really change the course of things, the centre-left parties now in power in France and Italy need to take a constructive attitude, recognising their share of responsibility for the current situation.” In another essay, Piketty describes the absurdity of Germany and France denying debt relief, given their own history. He does not tackle what happened next, but I know from the July 2015 open letter to Angela Merkel that he and I signed (with Heiner Flassbeck, Dani Rodrik and Jeffrey Sachs) that he would be appalled at his government’s passive role in the face of German intransigence.

In many ways, it is France rather than Germany that is the enigma of the eurozone, and Varoufakis discusses this at length. The puzzle is that France has always placed a close relationship with Germany above its frequent suffering from that relationship. Why was France so keen on the euro, when its industry appears to lose out from Germany’s ability to keep wage costs down and thereby gain a competitive advantage?

To answer this and other questions about how the euro was formed, Varoufakis takes us back to the creation of the Bretton Woods system of fixed exchange rates after the Second World War, and to its architects Harry Dexter White and John Maynard Keynes. After Bretton Woods failed at the beginning of the 1970s, Europe repeatedly tried to fashion its own version of a fixed exchange rate system. But Varoufakis comments that the architects of these attempts were macroeconomic innocents in comparison to White and Keynes. Rather than make a new Bretton Woods for Europe, they created something more akin to the gold standard that gave us the Great Depression.

Varoufakis’s organising idea is the mechanism that “recycles” national current account surpluses: investing these surpluses wisely in countries that are in deficit. Bretton Woods managed this – albeit imperfectly – because the risk of devaluation kept investors cautious and because the US was generous with its postwar loans. By contrast, the eurozone had no robust mechanism for recycling German and other surpluses to the periphery. Instead it relied on its financial sector, and when that failed by lending far too much, the response was the disastrous policy of austerity.

The first part of the book, about the precursors to the eurozone, uses the device of discussing critical moments in history involving national leaders. This can lead to a disjointed narrative, particularly when we move back and forth in time. I also felt that the central idea of surplus recycling seemed too weak to do all the heavy lifting required of it. Issues you might have thought were crucial, such as battles with inflation, play a secondary role in Varoufakis’s version. The period of low inflation and stability before the global financial crisis of 2008 (the Great Moderation) is dismissed as depending “on the thin walls of an expanding bubble”, reflecting a view that the crisis was an inevitable result of US current account deficits rather than financial deregulation.

The book comes alive when the author talks about his own experiences rather than the deeds of past politicians. Varoufakis tells a story told by Franz, a German banker whom he met on a transatlantic flight. Once Franz used to be wined and dined by potential borrowers wanting to convince him of their creditworthiness, but in 1998 his job changed to trying to sell ever greater numbers of loans. Individual project risk was no longer important because his bank had learned from its US competitors how to slice and dice, and national risk had apparently disappeared, because everyone had the same currency.

In the US and the UK, when that system came crashing down, bad debts had to be written off and banks bailed out. In France and Germany some of that happened, but there was also the option of bailing out banks by the back door: giving loans to the governments of Greece and Ireland so they could repay these banks. It was an option that politicians found too attractive to ignore, but the loans brought ruinous aus­terity to Greece.

The book does not contain a blow-by-blow account of Varoufakis’s short time as finance minister, when he attempted to challenge that austerity and reduce the burden of Greece’s loans. He says that will have to wait “to be told, as it deserves to be, from a greater distance”. However, in the preface to his book he juxtaposes two stories that hint at the essence of what happened. He describes how his parents surreptitiously listened to Deutsche Welle radio as a beacon of hope during the Greek military dictatorship, and follows this with an account of the time he first met the German finance minister, Wolfgang Schäuble: the handshake that Varoufakis offered was shunned.

Piketty’s analysis of the eurozone ­crisis can be summed up in a statement that occurs, with variations, several times: a single currency with 19 public debts is fundamentally unstable. In other words, a monetary union without some sort of fiscal (and therefore political) union is bound to fail – though in an enhanced union Piketty would want as much devolution as possible. This vision is very different from the fiscal union proposed by Schäuble, which Varoufakis suggests would intensify already strong anti-democratic characteristics. And he argues further that the “changes necessary to create a proper European treasury . . . cannot, and must not, be held to precede resolution of this crisis”.

These two economists diverge in their ­vision of the best way forward. Piketty sees some form of fiscal and political union as inevitable, while Varoufakis is suspicious of what that may involve in practice, and believes the existing monetary union must be reformed first. However, they are united in their view that the eurozone must become more democratic to survive. Piketty writes that what is immobilising Europe is not lack of structural reform, but the EU’s “anti-democratic straitjacket”, and Varoufakis says the Union needs a “democratic stimulus”. On that, our two rock-star economists are playing the same tune.

Chronicles: On Our Troubled Times by Thomas Piketty is published by Viking (192pp, £16.99)