You pose a great question; a common one when you think about two very specific and diverse areas of study competing against one another.
To really answer this question, though, I must ask that you a question or two. What would you ultimately like to do? On a scale from 1-10, how certain are you that that's what you want to do?
In the very act of posing this question, I would guess that you're not 100% tied to one or the other. The relative specificity of these institutions lend themselves to those that know with certainty of their initial paths. By no means is that a bad thing! I often tell my students that they don't need to know 100% what they are going to do for the rest of their lives when leaving high school and that's the very thing that the undergraduate experience is for!
I would encourage you to take a step back and look at potential schools that can offer both - a quality education in business as well as the arts - while you're exploring the coursework in your initial years at university and can then make a better, more educated decision about what you want to do. The possibilities are endless and many of those are unknown to you at this time. They will show themselves and come into better focus as you pursue your interests in the first and second years of the undergraduate experience. You may even discover another option that you hadn't known was there!
To address your question about four year degree plans, there are the options of double majoring or majoring and minoring. A school with some breadth of coursework would benefit you here as well. Typically double majors are not the equivalent as two complete degrees (4+ years in succession), but share the general education requirements and utilize electives. With a little research, however, I believe that you can find an institution like NYU which is strong in both the performing arts as well as business. Additional research into the undergraduate catalogs could provide degree plans and courses which could help steer you in the right direction.
College majors and careers often go hand in hand, but aren't mutually exclusive. For example, you may choose to pursue economics and marketing as majors and continue to work on a career in the arts. Conversely, you could pursue a degree in the performing arts and create your own business around your craft. Try not to get too focused at the onset. There are wonderful opportunities that await you, if you keep your eyes and mind open!
Good luck to you! It sounds like you've got an interesting path ahead of you --