[theGeatZhopa]

not expanding capacity:

because less eggs == expensier eggs == more money. If everyone wants a restricted good, then the prices goes up and the one willing to pay more gets the good. And eggs are needed in a lot of areas starting with mayonaise for the quarter pounder and ending with the breakfast in rural restaurants known from the movies :)

wielding their market power to prevent others from:

while its not meant, that they prevent the small guy's small company or your neighbours from keeping chicken from laying eggs, its an economical question. If you're a big player, one possible way is to buy amounts of chicken food for even lower prices making it expensier for small quantity buyers to produce eggs. The eggs from competition are not competative in their price, so big mayonaise producers won't buy. ... And so on..

the bigger, the cheaper, the less competition is possible for the small ones.

[jacknews]

well explained, and there's also the issue of chicks - farmers don't generally hatch their own eggs but buy chicks, and it's easy the big companies to manipulate that supply chain, indeed I believe there are ownership and licensing deals in place that favor the big producers.

[theGeatZhopa]

Good point. There may be deals like x percent of your stock will be buyed by us. If I'm the stock owner, i would gladly agree and reduce the price, if x is bigger for one buyer than y+z+w percentages of three buyers. I would have a guarantee to sell more of my chickens for sure at once and would reduce the uncertainty of even finding three different buyers.. but this reduces the stake holders (different sellers) in the market and the big one can dictate the prices and produce amounts at will.

Bigger is always winning.