What guarantee is there that building apt buildings without parking will result in more affordable housing now and in the future?

Can city hall demonstrate through the use of valid comparison data from other cities which have tried this for awhile, that market forces insure that apts  without parking spaces  will rent at a lower rate than apts with parking?

Or will ordinances allowing no parking apts include language which mandates that said apts will always and only be rented for 30% less than market rate on similar sized apts with parking?