This rule was deduced by the American health services researcher Milton Roemer, working at the UCLA School of Public Health. Roemer and colleagues found a positive correlation between the number of short-term general hospital beds available per 1,000 population and the number of hospital days used per 1,000 population.
The law is thought to be a consequence of induced demand i.e. physicians encouraging patients to consume services that the patients would not have chosen had they been fully informed. Health planning and certificate of need laws aim to prevent the waste that would otherwise occur due to Roemer's Law.
"One problem in this finding is that it could be the case that hospital stays are shorter in lower hospital bed per capita regions because of a deficit in supply (reverse causation). An increased number of beds may be due to patient preference for in-patient (rather than outpatient) care in a region."
- Obituary of Milton I. Roemer
- Shain M, Roemer MI. Hospital costs relate to the supply of beds. Modern Hospital. 1959 Apr;92(4):71-3
- Problems and Prospects for Health Planning: The Importance of Incentives, Standards, and Procedures in Certificate of Need 
- "Roemer’s law." Healthcare Economist. 2006. http://healthcare-economist.com/2006/10/12/roemers-law/