Yes, cities should put price caps on parking. I understand that parking is very limited in big cities. However, people working in and visiting these cities need a place to park, and it can't be exorbitant. In the long run it will discourage visitors if it costs a small fortune to park. Prices should be capped.
Parking my is a luxury in large cities and the price is going to reflect that. The city should work on better public transportation over subsidized parking and making sure that people are able to get around without taking up the valuable real estate that is parking spaces in a large city.
Most public parking is already regulated by cities anyway as a way to raise funds so it wouldn't really matter if they were allowed to do so anyways. For private parking, the price is usually associated with the areas location so it would make sense that people would have to pay to park at place that the owners payed good money for.
No, cities should not put a price cap on parking. Parking space is a product like any other provided for sale or rent. Individuals and companies should be able to charge in price they are able to get. However, cities should provide public parking at free or reduced prices in order to allow for more patrons at business and governmental facilities.