You basically can’t or it won't have the same effects because medicine doesn’t really follow the same dynamics as most other markets: the supplier (doctor) has an information asymmetry and thus makes most of the decisions, while the buyer (patient) is not usually the payer (insurance) so aren’t really incentivized to save.
Kenneth Arrow famously analyzed the healthcare market and made the above insight: https://assets.aeaweb.org/asset-server/files/9442.pdf
I know he was a Nobel Laureate but not sure if this is the work that won him the Nobel.
Updated: I should qualify my statement by pointing out this is for the US healthcare system.
Fixing a severe shortage is actually likely to have some impact.
For instance, if there's a lot more doctors, the payer may be able to negotiate lower prices. We already have insurance mechanisms that drive patients to the providers that the insurer has negotiated with...
It's even worse. This isn't a simply supply-demand curve. Supply here often increases demand (patients live more and longer; They need more care).
> the supplier (doctor) has an information asymmetry and thus makes most of the decisions, while the buyer (patient) is not usually the payer (insurance) so aren’t really incentivized to save
Counterfactual: patients in India routinely shop around for second opinions and negotiate fees.