There is little science to how hospitals determine the prices they print on hospital bills.

Orla Roche with her mother, Emer Duffy. Orla, 2, fell and cut her forehead during a family vacation. The visit to the emergency room, where her cut was treated with skin glue, cost $1,696.Fred R. Conrad for The New York Times

“Chargemaster prices are basically arbitrary, not connected to underlying costs or market prices,” said Professor Melnick, the economist. Hospitals “can set them at any level they want. There are no market constraints.”

Prices for any item or service are set by each hospital and move up and down yearly, and show extraordinary variability, health economists say. The codeine that costs $20 and the bag of IV fluid that costs $137 at California Pacific are charged at $1 and $16 at the University of California San Francisco Medical Center, across town. But U.C.S.F. Medical Center charges $1,600 for an amniocentesis, which costs $687 at California Pacific.