'He has a point': Christine Lagarde tackled Trump's trade war, climate change, and the gender pay gap on the Daily Show with Trevor Noah

After Lagarde identified climate change as a key global challenge, Noah asked her how she could begin to address it.

"Around the world you have roughly 5 trillion dollars that are being spent on subsidies to burn fossil fuel," Lagarde replied. "This is not a good use of public finance."

"Instead of that you should put that money in health, in education, in hospitals, in infrastructure," she said.

Noah asked Lagarde how investing in education, infrastructure, and health could boost economic growth.

"It helps by reducing the inequalities," Lagarde replied. "If young kids in all countries of the world, particularly the low income countries, can go to school, they will be better off."

"If women, instead of walking miles to get water as is the case in so many countries, can actually access a road, a highway, and go and fetch water without having to spend all those hours," she continued. "If kids are born in a hospital where there is appropriate care then clearly they're going to be better off for the rest of their life."

"So by doing that you improve the prosperity of people, not today, not tomorrow, but maybe in five, 10 years' time because that's critically important for the future," she concluded.

Trevor Noah and Christine Lagarde discussed her appointment to managing director of the International Monetary Fund in 2011, soon after the global financial crisis struck. Noah raised the idea of a "glass cliff," or putting a woman in charge during difficult times.

"Did it feel like you were stepping into a job where you were destined to fail?" Noah asked.

"It was intimidating, yes, but your point is so right," Lagarde replied. "Whenever the situation is really, really bad, you call in the woman."

"And the woman did a great job," Noah added.

Noah asked Lagarde about her longstanding push for gender equality.

The IMF chief highlighted the fact that investing in women's education and employment grows economies, raises income per capita, and boosts corporate profits. She also flagged the stubborn gaps in workforce participation and wages between men and women.

"This is a complete waste of time, and waste of energy, and waste of resources," she said. "Women have to be given the same opportunities, be given the same salary, and have the same exact rights as men."