On average I would expect that if my chicken consumption goes down by 1/year, the production of chickens for eating will go down by about 1/year, for the sorts of reasons that erratim gives.
My issue is that there's a fair amount of waste built in. The chicken you don't buy is probably just going straight to the rubbish heap. A large supermarket is already throwing away hundreds of pounds of meat each year. For example, British chain Tesco said that in the first six months of 2012, some 28,500 metric tons of their food was wasted. With just under 6,800 stores, that's over 8 metric tons per store, per year.
To get the retailer to buy less chicken, you'd have to cut consumption enough to exceed their threshold for allowable waste.
I think that "practically zero" means "practically zero as a fraction of the whole, which is true but not directly relevant. (In the same way, donating to a charity that feeds starving people has "practically zero" effect on the problem of starvation, curing someone of cancer has "practically zero" effect on the problem of cancer, etc.)
I meant in absolute terms. If you donate to a charity, that money's going to help someone. Curing someone of cancer drops the cancer population by one. With chickens, there's the aforementioned waste problem where you may have to meet certain thresholds before you see any change.
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Yes you are. And I think this is wrong. And here is why (stated differently from my original reply which also thought it was wrong).
Consider a world in which the entire demand for chickens is one guy who lives on the island of Kauai. In Kauai, chickens run wild through the streets and yards and fields. Since there is this one guy who buys a chicken every week, the shopkeeper scoops up a chicken in his yard on his way to work whenever he knows his chicken customer is coming. Cost of production, close to zero.
Consider an alternative world in which everybody is eating a chicken every day. The chicken producers certainly buy up lots of land in low cost places where it is cheap to build chicken production. This doesn't fill the need, i.e. price is way above the marginal cost to produce the last chicken. So they build chicken production closer to centers of demand, where real estate and labor are more expensive. This doesn't meet demand, i.e. price is still higher than the marginal cost to produce the most expensive chicken. Finally, someone builds 10 level chicken coops with HVAC systems, water desalinators to provide drinking water to the chickens, and pays a fortune to process the chicken poop into a benign fertilizer product which they essentially have to give away in order to keep it from stacking up around their chicken coops. Finally demand is met.
The point is, demand is filled by suppliers that pay different costs to create the chickens they sell. The cheapest producer makes the most profit, he is lucky. The most expensive producer makes just enough profit to keep producing, the slightest drop in price will put him out of business.
Even within a given production facility, the marginal cost to produce an extra chicken rises as the "capacity" of the production facility is filled. So for the christmas rush, 10% more chickens are grown, but it raises the costs of the facility 15% because they are paying night-workers instead of day workers, they are having to build dormitories to house their extra workers, they need a higher quality of automation in order to get 10 chickens per cubic foot instead of 8 chickens per cubic foot which their cheaper robots manage, etc.
So in a world where everybody wants chickens a lot, people will spend more to consume chickens because they will spend more to produce chickens, because the cheapest production sites and methods will be saturated before the market is.
Looking at the extremes doesn't tell you that chicken production is an increasing-cost industry at the margin. Sure input costs are important (the OP agrees - see last section), but there are also economies of scale, R&D investment, and so on pushing the other way, so it's ultimately an empirical matter whether chicken production is increasing- or decreasing-cost at current levels of production (again I'm just repeating what the OP says).
IMO this issue is actually less relevant than the OP seems to think, because we're only talking about very small marginal changes to chicken demand, and there's no way the long-run supply curve is steep enough for that to matter. But one could try to estimate the long-run supply curve at least "locally", which might settle this issue.