Your math, and your earlier statements are wrong. I will site numerous sources, with links to refute it.
But the more striking and noticeable fact is, that, while the production had increased at this enormous rate, the prices also had advanced twenty-five per cent. According to the financial report of 1861, the average price of cotton from 1840 to 1850 was but 8.2 cents per pound; while, from 1850 to 1860, the average price was 10.5 cents per pound, — a difference, it will be seen, of a little over twenty-five per cent.
Taxation of Cotton - Amasa Walker
However, even with this "25%" increase cotton prices were no where close to what they were 20-30 years earlier.
Oh, I cannot wait.
I'm sure that you will be able to find at least one source who arrives at a different average price during the period.
Walker comes up with a conservative estimate of a 28% increase (8.2 cents per pound to 10.5 cents per pound).
One thing is certain: no reliable source will claim with a straight face that cotton was worth less in 1860 than it was in 1850.
Your comment about cotton prices in 1820 are immaterial: cotton production in 1820 was 9% of what it was in 1860 because factory ginning of cotton had only begun in the 1820s.
In 1820 cotton was much, much scarcer than in 1850-1860 and was a high-priced luxury item.
By 1850 cotton had become a standard everyday household item in every American and Western European home. Normally when a good is mass-produced on a grand scale, the economies of scale cause the price to drop.
But between 1850-1860 the South enjoyed a situation in which the price of the good continued to increase even though enormously higher quantities were being produced.
It was an economic windfall of historic proportions.