Such a result has interesting implications. Since we know the demand for medicine is not perfectly inelastic (various experiments with copays prove this), it would suggest that some external force (insurance companies?) is keeping prices down and the constraining factor is supply.
If you'd like some data to play with, however:
https://www.cms.gov/NationalHealthExpendData/05_NationalHeal... http://www.census.gov/compendia/statab/2010/ranks/rank18.htm...
The former contains Medicare spending per enrollee on a per-state basis, and the latter has the number of doctors per capita.
Of the top ten states in Medicare spending per enrollee, six are in the top ten in doctors per capita.
This is all just a back of the envelope calculation, of course, but it does argue against the thesis that more doctors equals cheaper health care.
Cheaper health care != less money spent on health care. Consumers might purchase more health care even as prices come down (resulting in more money spent).
This data doesn't show the direction of causality. It could just as easily reflect doctors chasing money as it could reflect prices increasing as a result of doctors becoming available.
(Similarly, states with more illegal immigrants tend to spend more money on farm labor. Do illegal immigrants raise the prices of farm labor?)
Still, it's interesting data to see.
http://www.newyorker.com/reporting/2009/06/01/090601fa_fact_...
Obviously it covers more than just this particular topic, but the odd behavior of markets for health care is a central concern he addresses.
I'm pretty sure that you could skim the article and find some numbers if you wanted to.
Actually, an increase in the number of doctors (or, presumably doctor-hours) seems to lead to an increase in medical care costs. Adding more doctors increases the amount of medical service provided rather than providing the same amount of service at a reduced cost.