For Theresa Clarke, a retiree in New Canaan, Conn., the rising cost of living means not buying Goldfish crackers for her disabled daughter because a carton costs $11.99 at her local Stop & Shop. It means showering at the YMCA to save on her hot water bill. And it means watching her bank account dwindle to $50 because, as someone on a fixed income who never made much money to start with, there aren’t many other places she can trim her spending as prices rise.

“There is nothing to cut back on,” she said.

Jordan Trevino, 28, who recently took a better paying job in advertising in Los Angeles with a $100,000 salary, is economizing in little ways — ordering a cheaper entree when out to dinner, for example. But he is still planning a wedding next year and a honeymoon in Italy.

And David Schoenfeld, who made about $250,000 in retirement income and consulting fees last year and has about $5 million in savings, hasn’t pared back his spending. He has just returned from a vacation in Greece, with his daughter and two of his grandchildren.

“People in our group are not seeing this as a period of sacrifice,” said Mr. Schoenfeld, who lives in Sharon, Mass., and is a member of a group called Responsible Wealth, a network of rich people focused on inequality that pushes for higher taxes, among other stances. “We notice it’s expensive, but it’s kind of like: I don’t really care.”

Higher-income households built up savings and wealth during the early stages of the pandemic as they stayed at home and their stocks, houses and other assets rose in value. Between those stockpiles and solid wage growth, many have been able to keep spending even as costs climb. But data and anecdotes suggest that lower-income households, despite the resilient job market, are struggling more profoundly with inflation.

That divergence poses a challenge for the Federal Reserve, which is hoping that higher interest rates will slow consumer spending and ease pressure on prices across the economy. Already, there are signs that poorer families are cutting back. If richer families don’t pull back as much — if they keep going on vacations, dining out and buying new cars and second homes — many prices could keep rising. The Fed might need to raise interest rates even more to bring inflation under control, and that could cause a sharper slowdown.