I posit a small household with a few chooks.
Assuming they are good layers is the cost of feed per egg more or less than the cost of commerical eggs throught the retail chain.
I won’t enter into organic or ‘free-range’ whatever that means. Just the cost of eggs.
(Disclosure: I have three layers and also buy eggs from the supermarket. I don’t keep accounts)
My mom has chickens. The cost of feed is tiny compared to the value of the eggs. There are other costs as well, mostly up-front, like the cost of building a coop… but even those are small stuff. Mom sells her surplus eggs to her neighbors for $3 a dozen, and IIRC, it took about three months for that to pay back the cost of the coop.
There is some labor involved, too, but that’s not very much, either. Mostly, you just have to make sure to give them plenty of water each day, and never miss a day.
We have seven hens. If they are just egg-producing animals, the price of feed, oyster-shell, etc is cheap. Our hens are “pets” however and that can make their delicious eggs costly. When one of our hens was mauled by a dog we spent over three hundred dollars on veterinary care to save her. Our hens are now peri-menopausal so there are few eggs. Realistically they should have been soup a couple years ago, but they are pets.
And therein lies the problem. My father-in-law kept chickens and he was a countryman so quite ruthless about wringing the neck of any that showed signs of impending failure.
My MIL turned them into soup and the ‘pullet eggs’ were pickled.
If you or your children start to give them names, common sense goes out of the window and your yard becomes a home for retired chickens.
As in all money-saving schemes, it depends upon how you value your own time. If the 30-45 minutes per day could be better spent, then it’s not worth it. If going out to water/feed/exercise the chickens is a welcome respite in the fresh air, then it’s worth it.
It also depends upon how many eggs you use/get. If you are single parent who uses two eggs per day, then it’s probably not worth it. (see also “time” above.) If you are the Duggar family, and your chooks are making a substantial contribution to the protein requirements of your family, then it’s a great idea.
My friends who do it in a suburban setting, are learning more than they wanted to know about the presence of predators in our environment. I’ve only done it in a farm setting, and when I complained to Grandpa Ed about the walk to the chicken coop, he pointed out that it was closer than the store.
It’s a lot to balance out, but yes, feed is slightly cheaper than eggs, if you don’t count effort.
In my experience, it is far, far cheaper to buys eggs at the store. They are under $2/dozen and feed is much more. You have to feed chickens even when they don’t lay.
Eggs don’t crow. Eggs don’t shit.
Hens don’t crow* and a rooster is not needed nor advised. Composted chicken manure is an incredibly nitrogen rich fertilizer. And fresh eggs from free range hens taste way better than store bought. It’s all in how you look at it.
*Post menopausal hens will sometimes show male behavior, including crowing, when estrogen levels fall low enough for background testosterone levels to manifest.
If you’re buying the cheapest eggs, it’s hard to compete. Even if you’re good about culling the less productive hens. And if you are, don’t forget to include the occasional chicken dinner in the equation.
If you have a lot of food scrap, or if they can find significant forage (e.g. we’ll fence off parts of the alfalfa field, where they go to town on grasshoppers and eventually the alfalfa), that can offset feed costs.
Note that feed is 65 to 70 percent of the total cost of egg production and the big producer is going to get feed at a lower price than you can. The big producer is going to be more ruthless in culling unproductive birds than you so in terms so in terms of dollar cost per egg you will be probably be paying more in feed costs than for total egg costs purchased from the store.
Of course, in that case, you’re not just getting eggs, either: You’re getting eggs plus companionship, or whatever it is you call what you get from a pet. Personally, I’d rate that as poor value: Chickens aren’t nearly as interesting companions as dogs or cats are. But of course, opinions will vary, there.
And predators aren’t a problem, as long as your coop is well-built. Just remember that you need chicken wire, or something solider, on all six faces, including underground.
I think that cost per egg is a minor factor in deciding to keep chickens. You can buy quality eggs for a pretty reasonable price, year round, with zero other issues or hassles. Unless you go through a hell of a lot of eggs, you aren’t talking about all that much money for the overhead of keeping a flock alive, healthy, productive and from stinking you out of your back yard.
Put another way, doing it solely on the cost per egg basis is foolish. You want to keep chickens? Good idea. You’ll get free eggs.
But if you’re buying the cheapest eggs, you probably aren’t going to value the improvement provided by eggs fresh from the chicken coop. A better comparison would be to the fancy organic, free-range eggs. Where I am, those can cost five or six bucks a dozen.
You are only going to get top-quality eggs from top-quality production - birds, feed, living conditions, care etc. I am not sure that the “oh, it’s super cheap to maintain a flock” and “you get unto godlike eggs” quite mesh.
Even at $5 a dozen, that makes eggs a pretty cheap food. $5 for a dozen to eat, $2 for a dozen to cook and bake with, and you’ve got a good part of a week’s meals for a small family. Unless you already have the space, conditions and experience to maintain a flock, I think that’s hard to beat on a cost-per-egg basis.
Especially considering that your egg factory is always one disaster away from infinitely higher costs - a rogue dog or fox, any of several diseases, flash weather conditions…
Could you say the cost is, essentially, chicken feed? 
Helpful info: Is Raising Chickens Worth It? - Flannel Guy ROI
After years of having chickens in our backyard, we finally, um, got rid of them this last year. There were lots of positives to owning them, but here are some of the negatives:
Feed was cheap. However the nearest feed store is 15 minutes away so add the time to drive and get feed.
We had Buff Orpingtons (among others). Sure, they don’t exactly crow, but they are not quiet birds. I hated when they’d start their chatter at dawn on a summer morning. Say 5:00 am. Noisy. Very noisy clucking.
Having to pay a neighbor kid to come over twice a day to feed/collect eggs every time we went on vacation. I paid about $100 per week. We couldn’t leave food out for them, as the neighborhood birds would eat it all. So the chickens had to have fresh feed scattered for them twice a day. The pigeons still learned when it was feeding time and would converge and try to steal it all. Then the pigeons decided hanging around our house was bomb-diggity. Lots of pigeons.
The feed is made of all kinds of grains/grasses. The chickens poop. We now have a huge crop of weird weeds in our backyard.
Versus $2-4 per week to just buy the eggs at the store… Hmm…
Having just enough chickens for just enough eggs for your family is probably the hardest way to be cost-effective. If you have more, people will pay stupid money for those eggs, thus subsidizing your own consumption.
Just to say that the best eggs I’ve had were on my auntie’s farm. She kept bantams and didn’t use chicken feed specifically but rather let them scrat around the surrounding fields and supplemented this with whatever vegetable scraps came from the kitchen.
They particularly liked pecking at the insects attracted by the cow pats. Not an appealing thought but bloody hell, those eggs were stunningly good.
When we are flooded with eggs they get used. Quiches for lunch or dinner, frittatas for breakfast, eggs Sardou, etc. Plus the dogs occasionally share.
I have a co-worker/friend down the road who started raising chicken this year. Apparently, she sells a dozen to friends/neighbors. She also trades them for favors - when her car crapped out she traded me several dozen eggs for me giving her a ride to work until her car got fixed. She trades them for the over-production from other peoples’ gardens (and kitchen scraps help feed the birds).
She thinks it’s a good trade-off, not just for feeding her family but for the few extra bucks, the traded favors, the vegetables… Given most of us around here are struggling financially it’s a win for several of us, basically trading surpluses around.
I think a lot depends on you, and on your situation. Her household has two adults and several kids old enough to contribute towards chores like feeding the chickens and collecting eggs, the area is bordering on semi-rural so no one minds the livestock (she’s not the only one with chickens, at least one family has a goat, and she lives next to a falconer/raptor rehabber with a half dozen very large, predatory birds on his property).