I have lived in many cities across different countries with dramatically varying economies, and the price of chicken has always been a good proxy for the cost of living. And maintains the same ratio to the price of a bus ticket (and similar things).

Does this phenomenon have a name?

In the rural UK area where I live farmers will often be happy to have you shoot them with an airgun, if you seek permission. Nice (if stewed) cheap meat.

Rabbit used to be the meat of the poor where I grew up. If you could not afford meat (beef/pork), you could always raise 5 to 10 rabbits in boxes in your garden and feed them with the grass from the road sides.

Price of chicken dropped steeply (and consumption exploded) in the second half of the 20th century after the introduction of broiler breeds and what’s essentially muscle tissue factories. Before that chicken was neither particularly cheap nor eaten that much.

Rabbit is comparatively cheap to produce, and available at low price wherever it is produced in larger quantities. Apparently no significant economies of scale where you live.