In a medical system notorious for opaque finances and inflated bills, nothing is more convoluted than hospital pricing, economists say. Hospital charges represent about a third of the $2.7 trillion annual United States health care bill, the biggest single segment, according to government statistics, and are the largest driver of medical inflation, a new study in The Journal of the American Medical Association found. A day spent as an inpatient at an American hospital costs on average more than $4,000, five times the charge in many other developed countries, according to the International Federation of Health Plans, a global network of health insurance industries.