In his book The Science Of Wealth his analysis of customs statistics reveals that US cotton exports in 1850 yielded $71MM in revenue and US cotton exports in 1860 yielded $191MM in revenue.
During the same period, bale production rose from 2.1M to 4.7M.
So prices of cotton increased more than 30% even while production increased by 170% - a pretty incredible growth in value.
Your math, and your earlier statements are wrong. I will site numerous sources, with links to refute it.
Source:Slavery in America