I actually know a few guys who have tried to model this in real life.
According to them, in anything even remotely resembling our current economy, what would happen is that "printing" companies would rapidly and quickly get out of the business of producing and selling ink, much in the same way that publishing companies have basically 100% outsourced the actual ink-and-page production of books. (Almost no publisher today actually owns presses.)
The price of ink cartridges would drop extremely rapidly, and they'd become commodified, in the same way that printer paper is, with almost no brand loyalty except for a few specialist companies making special inks for special purposes. However, they'd also become creatively tamper-proof unless accompanying regulations prohibiting making said cartridges non-refillable were also implemented.
In the latter case, there'd be a market segment; you'd have very cheap disposable inkjet printer carts for those that don't give a shit or are lazy, and you'd have much more expensive, but cheap to refill, printer carts for those who care to go to that effort. Think "normal batteries and rechargable ones," kind of.
The price of the printers themselves would rise somewhat-to-significantly to offset the fact that the companies designing and producing them would no longer have ink as a profit center. A number of said companies would likely seek to be acquired by larger conglomerates in order to achieve financial security and stability, and would massively shed staff as they became much more specialized, focused entities. There'd be a refocusing on enterprise-level solutions, where you CAN lock people into your ecosystem and then milk them as a profit center, unless regulations made that impossible as well.
Economists are weird, but assuming they're not Chicago School nutjobs they can be pretty interesting when they talk about minutiae like this.