West Palm Beach, FL. $4 a dozen for chicken eggs, $6 a dozen for duck eggs. I deliver in "town" once a week, when we're on our way downtown to the library anyway.
I think the only way to really make a living selling eggs is to do it in large quantities. But it's possible to cover your feed bill by selling the limited quantity from your backyard flock. No matter where you live, do NOT try to match the store prices, especially not for the commercially-produced factory-farmed white eggs. Even the high-end organic/cage-free eggs are produced in bulk, and thus able to be sold for the prices they ask and still make a profit.
What has helped my sales is finding the niche market for truly FRESH eggs produced by hens enjoying a pampered backyard existence. And being willing to travel once a week to deliver to the doors. Most of my customers are more or less on my way to the library so I'm not going crazy driving all over town. Many of them will arrange to leave a cooler on their porch with the $$$ inside, so we don't have to try & coordinate our schedules for delivery. I'll call or email them, or they me, by Friday each week.
Some folks live in areas, usually more rural, where backyard flocks are more common and many homes have signs on their gates advertising "Fresh eggs, $1 a dozen" or something like that. If that describes your neighborhood then I wouldn't even try to compete and try to find some other way to earn extra $$$ besides selling eggs.
Has anyone ever tried forming a co-op with other chicken owners in your area to sell your eggs together?