Discouraging cars usage and promoting public transport

I propose offering free public transport for people in high income group as these are the people with higher probability of having a car/multiple cars in the household.

Possible outcomes:
1) They would still continue to use their cars without utilizing the public transport. There is no notional revenue loss to HSL.
2) They would gradually shift towards using the public transport option when they start to realize that, that option is always available without any additional cost. These are high tax paying individuals to which the cost of free transport is very nominal (EUR 54 pm) considering the environmental benefit.