That's just creating a poverty trap. Sure you can use math and do a phased in/out credit based on income but that just replaces a welfare cliff with a welfare "steep grade". Unless the credit is so generously applied as to defeat the point of the price hike you're still making the metaphorical gravity well of poverty deeper.
Edit: Did I say something mathematically incorrect or is it just inconvenient?
Take more money from poor people and then give it back at the end of the year - after paying the salary of all the new bureaucrats you had to hire. Great idea.
With the key added piece that you're trying to disincentivize carbon emissions in the process. I'm much more worried about the risks of the climate crisis than I am whether a few extra bureaucrats are hired.
Gas tax already exists, as does the earned income tax credit. Doesn’t take any new bureaucrats to change the numbers, although it will perhaps force some of them to get off their ass and modify some forms.
