Aside from the fact that spinning takes a lot of time, would one save money by spinning and dying their own yarn? If so, how big is the cost difference?
Is it cheaper to spin your own yarn?
yes. and no.
Ok, if you figure that you can get a lb of decent fiber for not too much, maybe under $30. Dye costs are incremental (though take a bit of money at the beginning)
Then you get the enjoyment of dyeing
then you get the enjoyment of spinning
It can save you money. Sort of. But often it doesn't, because you want to try this artists fiber, or that artists fiber. And often, you can get higher quality fleece or fiber then what ends up in a lot of millspun. So what seems like a little more expensive fiber is actually getting MUCH nicer materials.
I ramble, kid whining at me right now. Basically, I don't spin to save money. I dye and spin and get a ton more time on happy hobbies for the financial investment. No matter how much I spent.
It can be in terms of money flow if you don't account for your time. A drop spindle is a great tool and not too expensive but spinning wheels are an investment. I love to dye and the dyes didn't actually cost that much but it does take a good chunk of time to set up, do the dyeing, clean up and so on.
I love spinning and dyeing but I do it because I love it, not because it saves me any money. If anything it means that there are that many more yarn related purchases I can make!
You could technically buy a fleece, process it, spin it, dye it, and knit it. And in the end you're final product would cost less to get there, but I've found with any new fun hobby I spend a lot more feeding it that I would have if I'd have just bought the final product. I still do it though, that's the fun part, is creating all of it.
I have been spinning for years, and have sold a lot of spinning fiber myself.
The answer is that yes, it can save you $, but it can also cost you a pretty penny. The yes & no answer is a good one actually lol.
There are tricks to it. If you want to save $, you need to find a cheap way to spin. That means you need inexpensive tools to start out with, unless you don't mind investing a lot of $ into a nice wheel. I wound up trading a service (photography) for a used spinning wheel - an Ashford Traditional, that worked great. It was a perfect trade for me. I've also made my own spindles very easily using a dowel, a hook, and a CD. There are tutorials all over the web for how to do that. Spindle spinning takes longer, but it is a lot of fun too, and you can make a spindle almost free.
Next, you need to find affordable (yet quality) fiber. I say quality because if it is cheaper but you are getting crap yarn you don't want to ever touch because it is so rough, are you really getting anything out of it? Probably not.
I buy my fiber in BULK at R.H. Lindsay. I buy them by the bump (which is usually 20 lbs or so), which gets me free shipping. If you want, order it with a group, and split the cost of the full bump. I started out that way. they have REALLY nice fiber already processed and ready to dye. There is NO vm in it and every single thing I have gotten from them has been the best quality I have seen, for the cheapest price per lb/oz out there. My favorites are the merino top and the bamboo top. Both are crazy soft, but if you are new to spinning, I would avoid the bamboo - it can be tricky. Merino is PERFECT to learn on and makes a soft yarn that is good even against baby skin.
If you want cheaper, slightly less quailty fiber, check out Sheep Shed Studio. You can get seconds there, and buy in small portions or in bulk for a bit cheaper. Their prices are pretty good, and I've been happy with my shipments from there. They always throw in a little goody as a thank you for an order too - usually a little clump of fiber or a bit of roving to try out.
You can dye anything, using very inexpensive ingredients. If you buy true "dyes" it can get expensive fast. I use frosting dyes from Wiltons and vinegar. There are lots of tutorials online for how to do that too. Kool-Aid dyeing is another fun way to go about it, and is VERY simple. You get great solid colors from kool-aid (frosting dyes will usually give you a variegated tone). Either way, you can do it very inexpensively, and it is FUN to see it come together.
If you are careful about where you get your fiber, and how much you spend on tools, you can save a LOT of money. I probably spent about $3 per 4 oz of merino wool, that was hand-dyed and hand-spun into a gorgeous yarn customized for my projects. On ETSY if you want to buy a handspun, hand-dyed merino yarn you're looking at upwards of $20/skein. Even in the LYS you're looking at $10-20 per skein for a nice merino yarn. It can be a nice savings if you're careful about what you spend, and where. :) Plus - spinning is FUN, so I don't add in the time to do it as "cost." It is just another fun hobby.