A different rational response could be to raise parking ticket prices.
I live in NYC. Parking here is so expensive that paying for a parking ticket (if you happen to get caught parking illegally) is cheaper than paying for the parking garage!
A monthly parking garage in my neighborhood (west village, manhattan) can cost $700-800. Parking on the street is not a perfect substitute, but I can get 10-12 parking tickets a month before the cost of parking illegally exceeds the cost of paying for garage space!