Given the price of battery cage eggs at the store (other than when they killed huge flocks in the midwest due to Avian Flu a year or so back) you'll never save money raising a few chickens for eggs.
By my calculation, my eggs cost me ~ $2.20/dozen and that does NOT include any costs to convert the barn stall to a coop. They do get Black Oil Sunflower Seed (BOSS) in the morning and scratch grains before roost time, those are "unnecessary" expenses if I were to have chickens for purely commercial purposes. And that cost could be lower if I stuck to the really good layers like sexlinks, Leghorns, Rhode Island Reds and Black Australorps. I do have 2 BAs and 2 White Rocks that are very good layers, but I also have other breeds for variety and they aren't the 5-6 a week breeds but they still eat every day

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When they become non productive, they go on "social security" and live for free, I have two 5 year old Faverolles that have never been very good layers and barely laid this year at all. And a 5 Y/O Ancona whose eggs were so soft shelled this year they were generally broken and unusable. Also, I do NOT force them in the winter with light as I am hoping they will lay more years if they aren't worn out early. As such, other than pullets in their first winter, none of my girls lay after their fall moult until usually mid to late February.
But the quality of egg you get from your chickens should be far superior to anything you get in the store if your hens get outside and eat whatever they want and get kitchen scraps (including meat and fat, they LOVE that, even bacon grease). My girls free range all day and eat whatever plants and bugs they like. They also still eat layer feed in the summer so they are eating whatever they think is best for them, not just what someone decided they "needed" in pellet form.
I sell 1/2 dozen a week to the people who live next door to my old house. There is a group in the neighborhood that have some chickens that are overcrowded and their outside space is so small it is just dirt. The neighbor took care of them for a few days when the "member in charge" that week was gone. She said the eggs, even the day they were laid were runny. Not a healthy chicken environment. And she keeps telling me how much better my girls' eggs are than even the "pasture raised" eggs she buys when she needs more than I can sell her.
Have your chickens for Spring through Fall eggs, enjoy their antics year round and don't think too much about what each egg costs
