WASHINGTON — Medicare enrollees who take expensive medicines could save thousands of dollars a year under the Democrats’ sweeping social agenda bill, but those dividends won’t come overnight. Instead, they’ll build gradually over the decade.

Unveiled late last week, the bill’s Medicare prescription drug compromise barely survived a pharmaceutical industry lobbying blitz. Experts who’ve analyzed the complex plan say it would also offer people with private insurance some protection from the escalating cost of their medicines.

“The gist is that this is going to create substantial savings for seniors and taxpayers,” said Leigh Purvis, director of health care costs research at AARP’s Public Policy Institute. “This is going to reduce the price of expensive and widely-used prescription drugs, and that has an impact for everyone.” The institute is the policy arm of AARP. The group’s advocacy operation played a leading role lobbying in favor of restraining drug prices.

If the legislation passes, savings would be concentrated among patients with serious chronic illnesses such as cancer, diabetes, multiple sclerosis and rheumatoid arthritis, along with those who take combinations of costly medicines to try to control accumulating health problems.

The first tangible benefits would take about a year to show up. In 2023, the bill would impose a check on annual price increases for established drugs, as well as cost limits meant to keep insulin affordable. A huge development would follow in 2024: the first-ever cap on out-of-pocket costs for nearly 50 million seniors in Medicare’s Part D pharmacy drug program.

A year later, the health policy centerpiece of the legislation would go live. Seniors would see the first fruits of Medicare’s negotiations with drug companies, for no more than 10 medications to start with, but no numerical limit on negotiated prices for insulins.