Your friend is working on a paper for a medical sociology class

Market power is measured by 4-firm concentration ratio (C4), 8-firm concentration ratio (C8), or Herfindahl-Hirschman Index (HHI). C4 and C8 measures the market share (in terms of total revenue) of top 4 or 8 market players respectively, while HHI is the sum of squared market shares of all market players in the industry.

The higher the value of C4 or C8, the greater the market power of the hospitals and the less fragmented (more concentrated) the hospital industry is. Similarly the higher the HHI, the higher the market power of typical hospitals. HHI ranges from 1 to 10,000 where a value of 1 indicates a near-perfect competition (market share is near-zero) and a value of 10,000 indicates complete monopoly (market share = 100%).

By comparing total revenue of all hospitals in US and by computing above three indices, typical hospital's market power can be assessed.