Fuzzy Math?
Most people in the Cleveland area live *outside* of Cleveland. Hence the creation of RITA (Regional Income Tax) for Cuyahoga County where Cleveland is... [Just a boot note 'cause I'm a skinny little boy from Cleveland Ohio come to chase your women and drink your beer!]
If the RFID tag is missing from the bin, they would know about it and probably fine the household to pay for the replacement of the tags... so not a good idea.
The point is that you want to recycle because it does eventually save you money.
As to everyone's math... the payoff is a bit faster...
Assuming that the average household produces X tonnes of garbage a year.
If people started to recycle... say y% of their garbage is recycled.. then its $26.00 * (y%)*X in revenue against $30.00*(1-y%)*X in terms of cost.
So if you can recycle ~54% of your garbage, you will actually start to save the taxpayers money on an annual basis. Of course this only talks about the annual cost of waste removal and not the sunk cost of the technology.
The point is that once you get past 54% in recycled waste, you can start to pay off your sunk costs and your annual maintenance costs so eventually you'll make money. Not all of your waste will be recyclable so your calculations on ROI and tROI will vary.
The other issue is that we're assuming that the cost of waste removal is a constant. Once the landfills start to fill up, it gets more expensive to create new ones or to move the trash further away from the city.