I live in a very poor area, and most people won't pay so much as $3 a dozen for eggs, but I deal with this in a few different ways.
First, I scout out potential customers among my coworkers, acquaintances, and neighbors. Because they know me, they are able to trust me more readily than a stranger would, and that warms them up to the idea of buying from me. They know that when I say "Free range" and "organic", it's not just a meaningless label on a box... Especially my neighbors, who have had occasional visits from my flock >.>
Second, I point out that $3 a dozen is actually cheaper than what Wal-Mart sells their free range organic eggs for, that our eggs are fresher (often no more than a few days old), and our hens the most spoiled birds on the planet. When put into perspective, $3 suddenly doesn't seem like so much.
And finally, when all else fails, I give them a dozen eggs for free. By the time they finish off the carton, they're addicted, and HAVE to come back for more! People just don't realize how dreadful storebought eggs really are until they've had real, homegrown cackleberries.
My dad also takes eggs up to the city with him when he goes to work during the week, and he fetches as much as $4 or $5 a dozen for them there without anyone batting an eyelash at the price.
Next year, we will be raising our price to $3.50 a dozen locally because of the increased cost of feed. For now, $3 is still enough to cover our feed and other expenses, especially with the eggs my dad sells in the city.