"Relative surplus value is produced through the reduction of the value of labor power (variable capital) by means of improvements in the production of goods (effectively the appropriation of productivity gains by the capitalist class)." -Marxist definition

In other words, they will no longer need a wage that also represents the value of eggs, so: -the wage will ultimately be reduced -the portion of their unwaged labor (raising chickens) will increase

People who raise their own chickens can work for less than those who don't.

tldr: A service they could once afford will become unaffordable.