I'm not saying the GPO uses inkjet printers . . .
The "government" in "teen to government" was the GPO, yeah? So the price of printer cartages would only be relevant if the GPO used them.
Except you added "home printing", so you're not talking about the proposal the article is about. In which case you can probably find instructions for refilling your printer's cartridges. There are probably kits for your printer, but you usually just need some syringes and process inks. Or Office Max will do it for you, which will be more expensive but much less expensive than buying new ones.
It seems that Madeleine Stix (the writer of the article) brings printer ink up to contextualize costs for people who are more familiar with the price of HP ink cartridges (and I guess Chanel perfume?) than the kind of ink the GPO uses. Also, if you take a look at the video (@ 1:59-2:06), the teen in question states that his goal is not necessarily to get the GPO to change its practices, but "to get a few individuals to change." I have seen the process you're talking about and I've also read that home printers are very wasteful, perhaps even by design. To me, a better solution entails cheaper ink, but also very efficient machines that minimize waste. Of course, where's the profit in that?"Ink is two times more expensive than French perfume by volume," Suvir says with a chuckle.
He's right: Chanel No. 5 perfume costs $38 per ounce, while the equivalent amount of Hewlett-Packard printer ink can cost up to $75.