Reitman is the Man
As a producer and director, Ivan Reitman put a big Stay Puft Marshmallow Man-sized footprint on the movie. We mention this in our Screenwriters section too, but it's worth repeating here that he was the guy who helped shape Aykroyd's original un-filmable script into something that could actually get green-lighted. (Green-lit?)
Where Aykroyd originally had the boys hopping dimensions to bust ghosts, Reitman suggested that our heroes start a ghostbusting business in NYC. This made the script more commercially viable by grounding it in reality and also by massively cutting the amount of moolah needed to make it.
Price is Right
Even with Reitman's budget-cutting influence, a big studio needed to sign on to make the thing happen. Luckily for the world, Columbia Pictures Chairman Frank Price had faith in a project written by Aykroyd and Ramis, with Reitman directing and Bill Murray starring.
Sure, all these guys were hot stuff in Hollywood at the time, but they'd made their names in comedies that had way smaller budgets than what Ghostbusters would need: a whopping $25 million dollars.
Despite the huge financial risk, Price rolled the dice and green lighted the project. Needless to say it wasn't a popular decision with the powers-that-be at Columbia. Columbia CEO Francis Vincent actually sent a lawyer to talk Price out of it.
Thankfully, Price trusted his gut. As we know, Price didn't pull out of the picture and was probably worshipped as a god around Columbia when Ghostbusters was a gigantic success, spawning a huge moneymaking franchise with a sequel, two cartoon series, toys, video games—the works. So take that Francis Vincent: in the end, the Price was right.