A key inflation measure released on Thursday showed that prices are climbing at the fastest pace in 40 years and broadening to touch nearly every corner of the American economy, heightening the risk that they will stay elevated for longer and that policymakers may have to react more aggressively.

Markets tumbled after the government released Consumer Price Index data for January, which showed prices jumping 7.5 percent over the year and 0.6 percent over the past month, exceeding forecasts. More worrying were the report’s details, which showed inflation moving beyond pandemic-affected goods and services, a sign that rapid gains could prove longer lasting and harder to shake off.