Is it right to buy eggs from caged chickens?

You are correct. Because of the size of commercial flocks they feed their birds huge numbers of antibiotics and all sorts of things to keep them from getting sick. All that goes into the eggs they lay. Small producers let their chickens roam and they are much healthier. The eggs are also better for you and taste much better. Since a chicken only lay 1 egg a day and often only 1 every 2 days, to keep them in a cage is cruel. They need to be able to move and scratch etc. They can also catch mice. I saw one of my chickens catch a mouse once. They don't manage it very often but they eat vermin like that and help to keep the place clean.

Having eaten both kinds of eggs I know that I prefer free range as they are much tastier. I keep my own chickens and the difference in taste compared with the caged birds is amazing. If I could not keep my own then I would buy free range or barn laid as both tend to be tastier. From the chickens point of view the barn or free range is a much better life. The cages turn the poor creatures in to nothing but egg laying machines and they go nuts not being able to scratch and move around. As to where they lay their eggs they do so in their nest. I keep my chickens free range but they have a shed with nesting boxes in it and a roost for sleeping. I let them out at 11.30 am to roam free because most of the eggs are laid by them. Sometimes a chicken lays one in the afternoon but they go back to the nesting box to lay it. They rarely lay just anywhere. As to which gives the most eggs the method makes no difference. All chickens lay the same number of eggs per day no matter how they are kept. In their first year they tend to start laying one a day then it drops off to 1 every 2 days by their second year, the time between eggs increases every year until they run out of eggs. They have a finite number of eggs determined at birth and if they do not eat the right food then they lay eggs without shells. I have seen that in my older birds. The shells are strong in the young and the eggs are small. As the chicken gets older the eggs get bigger and the shells get thinner. They can lay for a few years but commercial producers do not keep them past their second year, some get rig of them after their first year. I had one chicken who laid into her fifth year but only rarely.