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If that’s that case, the economy will end 2010 on weaker footing than it started. In the January-March quarter, the economy expanded at a 3.7 percent pace.

Even if the Fed’s plan works, economists said it is likely to provide only a modest boost to economic growth, perhaps a couple tenths of a percentage point in the final quarter of this year. Still, the extra economic activity wouldn’t be sufficient to drive down unemployment, economists said. The rate is still expected to be above 9 percent by the end of this year, even with Fed aid.

Under one rule of thumb, the economy would need to expand by 5 percent for a full year to knock the jobless rate down by a full percentage point.

For all of this year, the economy is expected to grow 2.6 percent. That would mark an improvement from 2009. The gross domestic product shrank that year by an equal amount, the largest annual decline since 1946. GDP measures the values of all goods and services — from machinery to manicures — produced in the United States.