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Cathy Birker-Hake tripped over a hose in her Los Angeles backyard not long ago, dislocated her shoulder and made a beeline for the emergency room.

Birker-Hake, 63, said her shoulder was treated at Providence St. Joseph Medical Center in Burbank, Calif., and she was given a sling to keep her arm immobile while it healed.

The hospital charged $6,223 for two ER visits. Her insurer, Oscar Health, paid nearly $4,400 of that.

Then, a few weeks ago, a bill arrived from a Carlsbad, Calif., company called Breg. Birker-Hake may have settled with Providence, but Breg wanted an additional $200 for the cloth sling she had been given.

Her experience is another example of in-your-face medical pricing that often reflects not what things really cost but what health care businesses think they can get away with.

The average American faces more than $10,000 a year in medical costs, according to the Organization for Economic Development and Cooperation. Out-of-pocket costs are often lower because of insurance. Per-person health care spending in this country is about twice the average amount for all comparable countries, the organization found.

I'm not laying this disparity at the feet of a single maker of orthopedic gear. But what Birker-Hake is going through helps underline how goofy our system is.

"In general, we pay higher prices for everything — drugs, supplies, hospital services, physician services," said Lawrence Casalino, a professor of health care policy and research at Weill Cornell Medical College.

He told me the higher prices "often result from market power" — that is, a lack of competition and transparency — and "the ability to surprise bill."

Surprise billing is exactly what it sounds like: hitting patients with unexpected charges after treatment has been administered.

Most other businesses disclose their prices up front, which is only fair and is crucial to a competitive market. Health care is one of the few industries that tells you what things cost after the fact, when you have little recourse but to pay.

Birker-Hake was surprised, to say the least, that the sling she had been given at the hospital would carry a $200 price tag, when comparable slings sell on Amazon for $15 or so.

And she had already paid $1,800 of her own money for the visit, not to mention the nearly $1,500 she pays in annual insurance premiums.

Birker-Hake complained to her insurance company, which looked into the matter. In a letter dated Aug. 15, the insurer admitted that the Breg charge "qualifies as a surprise bill."

As such, Oscar Health agreed to cover $5.86 of the $200 cost.

Hillary Schuler-Jones, a Breg spokeswoman, declined to answer questions about the price of the sling, called a Deluxe Shoulder Immobilizer. In most cases, she said, "we don't sell our products directly to patients, and we therefore don't have a patient price list."

My advice to Birker-Hake is that she pay the bill. She doesn't want to add insult to injury by having debt collectors come after her.

But this is yet another illustration of a health care system that's focused more on profit than on patients.

David Lazarus writes for the Los Angeles Times.