I understand that brown eggs come from red-colored hens, but why would these hens be better candidates to be cage-free? It doesn’t make sense to me that cage-free eggs tend to be brown.
Wild ass guess… I personally perceive brown eggs to be more “natural”, even though I’m almost certain that’s not actually the case. Perhaps other people have the same impression and thus brown cage free eggs sell better.
Yep, they sell for around 25% more locally, but there’s no difference, other then the color of the shell.
Brown eggs of all kinds, cage-free or battery-hen, tend to cost somewhat more than their white counterparts because they cost more to produce:
I imagine that canny poultry farmers are aware of the widespread impression that brown eggs are somehow “better” or more “natural” than white ones (by analogy with brown vs. white rice, brown vs. white bread, etc.). So they realize that we tree-hugging eco-foodies are likely to prefer brown free-range eggs and will probably be willing to pay premium prices for them.
Breeds of chickens vary in the amount they ‘wander’ when free-ranged, and whether they return to the coop to nest or create their own nests elsewhere on the farm. Farmers, of course, prefer that they return to the coop to nest & lay. (Foxes, weasels, etc. prefer that they nest out in the open.)
As I recall from neighbors who raised free-range chickens, some of the breeds that were best at ‘home-coming’ at night happen to lay brown eggs. They choose the breed for it’s home-nesting behavior; the color of the eggs was irrelevant.
But, as people have noted, the customers (especially those customers who seek out free-range chicken eggs) have associated the color of the eggs with something more ‘natural’, so they prefer brown eggs. So chicken farmers happily accommodate that.
I’d take the statement “Brown-egg layers are slightly larger birds and require more food, thus brown eggs are usually more expensive than white” with quite a few grains of salt. The difference is pretty small, and free-ranged chickens get that extra feed themselves, from bugs & seeds & such that they find on their own. So it doesn’t cost the farmer any more to raise them. The chicken farmers I knew didn’t provide any more feed to their brown-egg flocks than when they had white-egg flocks.
Some time in the last 10 years or so the brown eggs are what consumers seem to expect organic eggs to look like. In the 60’s or 70’s with all the farmers that had hens, most people were used to brown or white eggs. The standard white egg is larger on average than many of the other breeds that are raised. Farmers raised other breeds because of the feathers on other breeds being nicer for stuffing pillows. The flesh and eggs can taste slightly different also. Some breeds are also nicer in temperment. Farmers like other hobbiest liked to raise a few fancy birds to show off. The brown eggs were always cheaper than the larger whites, because they were smaller. White only was a big deal for Easter, because brown eggs don’t dye pretty. I think the brown eggs became the color expected for organic eggs, because some person when organic farming got going, liked the breed that layed them. Cage free will likely be organic, and I think research into when organic eggs first went into markets, would be the area to research. Look into the 70’s as a starting point. News letters and publications for organic folks, would have ads for people selling things, and the exchange of how something worked for other people in the past.
I’ve always wanted to get one of those blue eggs one breed lays. I’d tell everybody to look at the size of the eggs my robins are laying.
I honestly thought the color had more to do with the feed than the breed. You learn something new all the time! 
Don’t feel bad. Lots of people believe that brown eggs come from “free range” chickens. i.e: they aren’t fed “refind” food, so therefor the eggs aren’t white.
It’s a whole misconseption, that poultry ranchers aren’t about tom dispell.
Don’t they have to bleach eggs to make them white? Just asking you know, because it seems pretty logical they do. 
We had chickens when I was a kid, and the fancy South American breed (we had a white hen and a black hen of this type) laid blue and green eggs, which I always found to be pretty cool. The other ones were all red/white and black/white chickens, and they laid brown or white eggs. I was glad when we didn’t have any roosters around because then one didn’t have to worry about the eggs being fertilized and partially developed chicks coming out when one wanted to make french toast.
We pay the same to raise Rhode Island Reds as it costs us to raise any other hen we have had. White eggs, brown eggs - no difference although the reds we have had tended to be more dependable layers [quantity, and the number of double yolk eggs compared to regular eggs]