Jaime Rosenthal, a senior at Washington University in St. Louis, called more than 100 hospitals in every state last summer, seeking prices for a hip replacement for a 62-year-old grandmother who was uninsured but had the means to pay herself.

The quotes she received might surprise even hardened health care economists: only about half of the hospitals, including top-ranked orthopedic centers and community hospitals, could provide any sort of price estimate, despite repeated calls. Those that could gave quotes that varied by a factor of more than 10, from $11,100 to $125,798.

Ms. Rosenthal’s grandmother was fictitious, created for a summer research project on health care costs. But the findings, which form the basis of a paper released on Monday by JAMA Internal Medicine, are likely to fan the debate on the unsustainable growth of American health care costs and an opaque medical system in which prices are often hidden from consumers.

“Transparency is all the rage these days in government and business, but there has been little push for pricing transparency in health care, and there’s virtually no information,” said Dr. Peter Cram, an associate professor of internal medicine at the University of Iowa, who wrote the paper with Ms. Rosenthal. He added: “I can get the price for a car, for a can of oil, for a gallon of milk. But health care? That’s not so easy.”

President Obama’s Affordable Care Act focused primarily on providing insurance to Americans who did not have it. But the high price of care remains an elephant in the room. Although many experts have said that Americans must become more discerning consumers to help rein in costs, the study illustrates how hard that can be.

“We’ve been trying to help patients get good value, but it is really hard to get price commitments from hospitals — we see this all the time,” said Jeff Rice, the chief executive of Healthcare Blue Book, a company that collects data on medical procedures, doctors visits and tests. “And even if they say $20,000, it often turns out $40,000 or 60,000.”

There are many caveats to the study. Most patients — or insurers — never pay the full sticker price of surgery, because insurance companies bargain with hospitals and doctors for discounted rates. When Ms. Rosenthal balked at initial high estimates, some hospitals produced lower rates for a person without insurance.

But in other ways the telephone quotations underestimated prices, because they did not include the fees for outpatient rehabilitation, for example.

In an accompanying commentary, Andrew Steinmetz and Ezekiel J. Emanuel of the University of Pennsylvania acknowledged that there was “no justification” for the inability to provide estimates or for the wide range of prices. But they said that more rigorous data on quality — like infection rates and unexpected deaths — were required to know when high prices were worth it.

“Without quality data to accompany price data, physicians, consumers and other health care decision makers have no idea if a lower price represents shoddy quality of if it constitutes good value,” they wrote.

But, broadly, researchers emphasized that studies had found little consistent correlation between higher prices and better quality in American health care. Dr. Cram said there was no data that “Mercedes” hip implants were better than cheaper options, for example.

Jamie Court, the president of the California-based Consumer Watchdog, said: “If one hospital can put in a hip for $12,000, then every hospital should be able to do it. When there’s 100 percent variation in sticker price, then there is no real price. It’s about profit.”

Dr. Cram said the study did contain some good news: some of the country’s top-ranked hospitals came up with “bargain basement prices” in response to repeated calls. “If you’re a good consumer and shop around, you can get a good price — you don’t have to pay $120,000 for a Honda,” he said.

But that shopping can be arduous in a market not set up to respond to consumers. To get a total price, Ms. Rosenthal often had to call the hospital to get its estimate for on-site care, and a separate quote from doctors. And many were simply perplexed when she asked for a price upfront, Ms. Rosenthal said, adding, “The people who answered didn’t know what to do with the question.”