This is The Other End of Time by Frederik Pohl. It is book one in the Eschaton series.
As you say, it is set in the near future where inflation is very high and rents are paid daily. For example in chapter four we find:
... the rents Rita collected were barely enough to keep her ahead of the taxes and the maintenance charges, and so he made a point of cooking enough for both of them. He knew that the other thing she wanted from him was his day's rent, so they settled that before they began to eat. "The good news," she said, ringing up her deposit, "is today's inflation adjustment was only two per cent."
A group of people are kidnapped by the aliens by a form of teleportation and they arrive naked in a mirrored room like the one you describe:
She (Pat Adcock) didn't like the six-sided chamber that was their prison, like a scaled-up honeycomb cell the size of a backyard swimming pool, or the bright mirrored surfaces that reflected their own naked bodies whichever way they looked.
And Pat is the person who is duplicated twice:
She forgot to swallow when she saw what was happening. Dopey was indeed entering through the wall, but he wasn't alone. He was leading two other human beings through the wall.
"Hey!" Jimmy Lin shouted in delight. "Naked women!"
So they were, being shepherded into the cell by a pair of Docs, looking terrified and angry at the same time. Each of them was rubbing the back of her neck with one hand as she clutched her bundle of clothing with the other. "You said," Dopey explained, "that you required additional breeding stock."
They looked very familiar to Pat Adcock. She swallowed the lump of paper as she stared at them, clutching Dannerman's arm. "Sweet Jesus," she gasped. "They're both me!