The average beneficiary who falls into the coverage gap would have spent $1,504 this year on prescriptions. But thanks to discounts and other provisions in President Barack Obama’s health care overhaul law, that cost fell to $901, according to Medicare’s Office of the Actuary, which handles economic estimates.

A 50 percent discount that the law secured from pharmaceutical companies on brand name drugs yielded an average savings of $581. Medicare also picked up more of the cost of generic drugs, saving an additional $22.

The estimates are averages, so some Medicare recipients may do worse and others better. Also, it is still unclear if the discounts will start to overcome seniors’ deep unease about the law.

Concern over cutting Medicare to expand coverage for the uninsured helped push older voters toward Republicans in the 2010 congressional elections. Obama and the Democrats have been trying to woo them back ever since.

“For people with high drug expenditures, the 50 percent discount offers real savings,” said Tricia Neuman, director of Medicare policy for the nonpartisan Kaiser Family Foundation. “It’s certainly more helpful than no coverage at all, which is what they had previously.”

More than two million beneficiaries already have gotten some help, discounts that have gone largely to middle-class seniors, because the poor are covered in the gap at taxpayer expense.

Medicare covers about 47 million older and disabled people, and about nine in ten have some kind of prescription plan. Most rely on the drug benefit, also known as Part D, which is delivered through private insurance plans.

Beneficiaries have until December 7 to change their drug plans for 2012. Consumer advocates recommend that seniors check their coverage during open enrollment to see if their current choice remains the best for next year. Many families start the process around the Thanksgiving holiday.

The coverage gap, a money-saving idea from a previous Congress, never has been popular.

It starts after an individual beneficiary and his or her drug plan have spent a total of $2,840 on medications for the year. Seniors are then on their own for the next $3,600.

Once total spending reaches about $6,440, Medicare’s catastrophic coverage kicks in and beneficiaries pay only a token amount. Most people do not spend enough in the doughnut hole to qualify for catastrophic coverage.

Although few private insurance plans still cap the amount they spend on medications, Medicare’s hole-in-the-middle approach is highly unusual.

The Republican-led Congress that passed the drug benefit under President George W. Bush was trying to balance coverage and costs, as many conservatives fretted about creating a new unfunded entitlement.

Supporters wanted all beneficiaries to get some initial benefit from the program, and they wanted to protect those with overwhelmingly high costs. The resulting compromise led to the doughnut hole.

Under Obama’s health care law, the gap will be gradually phased down by 2020.

This year, the law provides a 50 percent discount on brand name drugs and 7 percent break on generics. Next year the discount on generics rises to 14 percent. When the changes are fully phased in, beneficiaries will still be responsible for their annual deductible and 25 percent of the cost of their medications until they reach catastrophic coverage.

If Republicans succeed in repealing what they dismiss as “Obamacare,” the discounts would be wiped out as well.