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you're arguing that demand actually increased by an amount proportional to the price increase, which seems highly unlikely to me.
What on earth makes you think that demand and price are proportional? That is simply not the case. When demand is at or near the limits of supply of an essential commodity, price swings are anything but proportional.
Let's put it this way...
You and eleven other people are marooned on a barren island. Twelve total. One of you has in their possession a bucket of KFC that has twelve pieces of chicken, enough for one piece for each person, willing to sell to the highest bidder. The first piece goes for 10 bucks. The second piece goes for 10 bucks. The third piece goes for 10 bucks. And then a flock of seagulls swoop in and steal three of the remaining nine pieces. What do you think the six pieces that are left will bring among the nine people (some carrying thousands of dollars) left bidding?
Look, I don't mean to be rude. But if you think that a finite resource that is in demand where even a tiny disruption in supply doesn't lead to wild swings in price, then you don't remember Tickle-Me Elmo circa 1996. In other words, again not meaning to be rude, you're simply incorrect.