Sheila Dikshit, chief minister of the Indian capital territory of Delhi, looks neither fat nor nervous, but she was disarmingly frank this week about the difficulties of coping with an annual influx of half a million migrants into her metropolis of 16m.

“I’ve put on some weight merely because I want to drown my anxiety by eating,” she told a conference of the World Economic Forum and the Confederation of Indian Industry. If her administration did not meet the needs of Delhi’s inhabitants, she warned, one of the world’s largest cities would slide downhill. “Each one of them when they live in Delhi, they want more water, more power, they want more wages, more oil.”