I knew I had read this story before, and after poking through Asimov's stories (the plot point in the end is that household robots are used to meet the required consumption levels), it turns out dmckee was right about the story being by Frederik Pohl. It's titled "The Midas Plague", and is included in the Midas World anthology, as well as being adapted into an episode of "Out of the Unknown"
In a world of cheap energy, robots are overproducing the commodities
enjoyed by mankind. The lower-class "poor" must spend their lives in
frantic consumption, trying to keep up with the robots' extravagant
production, while the upper-class "rich" can live lives of simplicity.
Property crime is nonexistent, and the government Ration Board
enforces the use of ration stamps to ensure that everyone consumes
their quotas. The story deals with Morey Fry, who marries a woman from
a higher-class family. Raised in a home with only five rooms she is
unused to a life of forced consumption in their mansion of 26 rooms,
nine automobiles, and five robots, causing arguments. Trained as an
engineer, Morey modifies his robots to enjoy helping to consume his
family's quota. He fears punishment when his idea is discovered, but
the Ration Board—which has been looking for a way to abolish
itself—quickly implements Morey's idea across the world.
You can read the full story online here