No, in fact not.
Your MVP should focus on validating that you CAN and that it creates value for people. Anyone.
You don’t yet know the business model. Or rather, you shouldn’t presume to; it’s Minimally Viable – we’re validating that WE can do this and that people want it.
Remove the notion of a business model, if you can, as it will limit that validation. What if no one wants that model? What if they won’t pay that way? What if your presumption of the “customer” is incorrect, and you find that someone else, through some other model, would pay.
MVP isn’t testing the model, it’s validating that you can solve a problem and deliver value. THEN you figure out how to monetize that value. Avoid an MVP that limits your potential by stifling the ways in which your market COULD benefit from what you’re doing.
Notionally, you should already have live what many refer to as a Minimum Non-Viable Product… a landing page that does nothing more than validate that people want what you’re proposing – you start collecting that interest and data about the demand; that serves to design your MVP AND seeds for you a set of initial users of the MVP.