Is there any known estimate of the total mass of fur shed by a cat over a year? I can find some anecdotal estimates that full regrowth can be achieved over 8 to 12 weeks, but that does not give me any answer with regards to the actual mass.
The answer certainly depends on the cat size but also type of hair, and environment. Cat owners easily observe that shed amounts vary depending on, for instance, current temperature (the animal gets a lighter fur in summer, and denser in winter). It is possible that the growth rate varies with temperature. As such, there cannot be a simple answer valid for all cats, but that does not mean that the question is unanswerable, only that the answer will consist in multiple data points. It's like a question about the height of a human: not all humans have the same height, but it is not totally meaningless to talk of averages.
Cats are neither photosynthetic nor nuclear-powered. As such, the carbon atoms found in the fur keratin can only come from their food intake (excluding water). Basically, if a cat east 200g of food per day, then it cannot shed more than 200g of fur per day on average, or 73 kg over a year. But I really expect the figure to be a lot lower than that.
I find unsubstantiated claims that an average cat may have 20 to 40 millions of hair, with an average thickness of about 20µm, and can grow back a complete coat in "8 to 12 weeks" (if shaved). Assuming an average length of 4 cm per hair, and that hair density is close to that of water, then the total fur weight (under these assumptions) would be 250 to 500g and the beast could produce such an amount 5 times per year, leading to a total of up to 2.5 kg over a year.
This estimate is based on totally unscientific figures that could be off by a large amount. Moreover, if the growth rate varies depending on conditions, then chances are that a fully-shaved cat will have a higher growth rate, and a non-shaved cat will settle for a lower growth rate and thus shedding amount.
Thus, I am trying to find some better sources for data so as to get at least ballpark numbers. Basically, are we talking about 100g, 1kg, 10kg per year or so?