Lagarde dismisses the idea that the IMF may find itself at cross-purposes with the new administration. "We are an agent of financial stability in any country where we operate," she said. "A leading power like the United States has a vested interest in economic prosperity, stability and peace."
Almost everyone likes those things; it's how to get them that provokes arguments. On that question, there are signs the U.S. and the IMF are diverging.
"We must protect our borders from the ravages of other countries making our products, stealing our companies, and destroying our jobs," Trump said in an inaugural address far removed from the IMF worldview. "Protection will lead to great prosperity and strength."
Then, consider where and why the IMF has made its biggest loans lately. To Greece, with the goal of holding the EU together; Trump says he'd welcome its breakup. To Ukraine, helping prop up a fledgling anti-Russian regime; Trump wants to get along with Russia.
More broadly, the Fund channels rich countries' cash to poorer ones, often requiring austerity and export-oriented policies in return. Trump says he'll stop using U.S. resources to make others rich, has no interest in imposing American templates, and wants to import less stuff anyway.
"The extreme manifestation of Trumpism is diametrically opposed to the founding principles of the IMF," said James Boughton, the IMF's official historian for two decades until 2012. The Fund is "going to have to play a very delicate game."
To be sure, it's not clear how much of Trump's campaign rhetoric will survive into government. And the dealmaker-president might discover that the Fund has its uses, said Benn Steil, the author of "The Battle of Bretton Woods," a history of the IMF's founding conference. "I could paint a scenario in which he effectively looks like a multilateralist, because he finds a way to do deals that are in America's interests," Steil said.
Still, some Trump aides have been critical. David Malpass, the former Bear Stearns chief economist, is said to be the top candidate to head international affairs at Trump's Treasury, where he'd be a key liaison with the IMF. During the Asian crisis of the 1990s, Malpass scolded the Fund for driving borrowers into recession by requiring them to devalue and raise taxes.
That concern with weakened currencies is likely to redouble in the Trump era as the U.S. seeks to move toward balanced trade. Treasury Secretary Steven Mnuchin told Lagarde in a phone conversation that he expected the IMF to "provide frank and candid analysis of the exchange rate policies of IMF member countries," the Treasury said.
Republican lawmakers have long had reservations. They balked when world leaders agreed to double the IMF's capital after the financial crisis. The measure only got through Congress when the Treasury agreed to oppose extra-large bailouts.
Like the one Greece got in 2012. "I could see this new administration being pretty heavy on the Fund on these issues," said Michael Bordo, director of the Center for Monetary and Financial History at Rutgers University in New Jersey.
Greek bond yields surged again this year on speculation the next loan installment will be withheld amid a clash over terms, with the IMF supporting further debt relief and the EU opposed. After talks with the German government, Lagarde said the question of debt restructuring will have to be addressed when the bailout program ends next year. Trump's position could be pivotal.
There's a case to be made that the U.S. gets good value out of the Fund. Each dollar it commits only adds 2 cents to America's budget, because defaults rarely happen, according to the Congressional Budget Office. In return for its contribution, which currently stands at approximately $164 billion, America has the biggest say on the Fund's board. It can't veto individual loans, but when U.S. interests are aligned with the EU's -- which they mostly were, before Trump -- they tend to prevail.
Bordo says he's not worried about the Fund becoming redundant. "They're always thinking of how they're going to fit in," he said.
The IMF has already survived one major mission-change. It's known today as the lender of last resort to countries facing balance-of-payments crises. But in its first three decades, the Fund managed the world's currency order.
That was the role assigned at Bretton Woods in 1944, when the IMF and World Bank were set up. Forty-five nations attended the summit, but two men dominated it: John Maynard Keynes and America's Harry Dexter White. From the back of her car in Uganda, Lagarde calls them the "founding fathers."
Their goal was to avoid a repeat of the 1930s, when competitive devaluations and tariff wars led to the collapse of world trade. Keynes wanted the IMF to act as a central bank of central banks, denominating their accounts in a new global currency. It would let members devalue or borrow with relative ease. Both creditors and debtors would pay interest on their holdings, discouraging large trade surpluses as well as deficits.
White's plan was more creditor-friendly, reflecting the U.S. position as world lender. There would be no new currency: IMF members would tie their money to the dollar. They couldn't devalue without consulting the Fund, and were only supposed to borrow short-term to close balance-of-payments gaps.
"The British wanted an automatic source of credit, the Americans a financial policeman," wrote Keynes's biographer Robert Skidelsky. The English economist was one of the 20th century's sharpest thinkers, but it was the U.S. Treasury official who got his way.
The system turned out to have a flaw: It depended on the supply of U.S. dollars backed by gold. That link came under pressure as America, financing social programs at home and war in Vietnam, slipped into persistent deficit. In 1971, President Richard Nixon took the dollar off the gold standard, ending phase one at the IMF.
Today there's a patchwork of floating rates, pegs and currency unions like the euro. It's not working to everyone's satisfaction -- notably Trump's. His team has called out several countries, from China to Germany, for gaming the system.
Money courses around that system on a scale that would have been unimaginable at Bretton Woods. Massive trade imbalances built up. The dollar remains central. The risks were laid bare in 2008, when a collapsed U.S. housing bubble led to world recession.
Since then, some financial leaders -- among them the governor of the People's Bank of China, Zhou Xiaochuan, and his U.K. counterpart Mark Carney -- have gently hinted that something more like Keynes's plan might be in order, to reduce the world's dollar dependency.
Lagarde doesn't see that happening on her watch. "It didn't happen in 1944, when the world had destroyed itself," she said. "I'm not a dreamer."
She argues instead that what the IMF is doing today will remain useful tomorrow. Countries will always be getting in a financial mess. Someone has to clean it up. Ukraine needed money in 2015: without the IMF, "where would the $17.5 billion come from? Whose pocket would it be?"
