Do price subsidies raise prices?

Economics Economics Questions
1

Since public health care in Finland is a disaster zone, I try to use private health care when I can. But private health care receives hefty price subsidies here. For example, my recent visit to a private dentist for a basic check up cost me 125 € ($160). Out of this, the government automatically paid 58,80 € ($76) and I had to pay 66,20 € ($86). The whole thing took approx. 20 minutes.

I know everything costs an arm and a leg here, that taxes rob you blind and employment costs will bankrupt you, but I just don’t see how the 125 € price could be a market price. So does the price subsidy have a role to play?

2

my instinct is that the price subsidy was probably a government intervention that was thought up to address unintended consequences of prior interventions, those original interventions are responsible for increasing the private clinic’s cost up higher and higher. the government then decides to intervene on the behalf of medical customers at the expense of the general tax base.

make sense?