Dec. 4 (Bloomberg) — Americans can save money by shopping for new health insurance plans through Obamacare, U.S. officials said, in a push to keep people from getting surprised by bigger bills when the coverage they have now through the program renews automatically.

Of the 765,135 people who applied for insurance during the two weeks starting Nov. 15, about half were customers who had coverage this year through the marketplaces created under the Patient Protection and Affordable Care Act. As a result, millions of people will be renewed in their current plans. The deadline to change plans or pick a new one is Dec. 15 for coverage that starts in January.

Not switching could be costly. More than 7 in 10 people who have insurance through the marketplaces can get the same level of coverage for less if they shop around, the U.S. Department of Health and Human Services said today in a report. If all returning customers bargain-shopped for a new plan, they could save more than $2 billion on premiums, according to the report.