Two years prior to the invention of the cotton gin the US (as it was at the time) as a whole produced only 900 tons of cotton a year. With the invention of the cotton gin production increased greatly as one of the major limiting factors had been removed by the invention of the gin. This lead to a land rush for cotton cultivation; the Alabama Fever. Now the limiting factor was farm hands; this lead to a big increase in the slave trade.
Obviously there was a slave trade prior to the invention of the cotton gin (1793, well after the Declaration of Independence (US)), but the significant growth of the slave trade in the US occurred after the invention of the cotton gin (which lead to the massive growth of the cotton trade; especially in the US southern states as they had a better climate for cotton growth).
It's just depressing reading this that the solution to a labor shortage was to buy bonded slaves.
I know it's something certainly not unique to the american south and it's still going on today. I guess the contrast to the declaration of independence and slavery is so telling. Most other slavery occurs under the watch of despots.
The problem with the labor shortage was less that there was insufficient free labor available, but rather that the wages that would be demanded by free labor under these circumstances would be much higher than the subsistence level required by slaves, which would reduce the profitability for the upper-class plantation owners.
Evsey Domar wrote a famous paper in 1970, arguing that slavery/serfdom may be instituted when there is a lot of available land and few available workers, citing episodes in Europe in the Middle Ages, Russia's eastward expansion, and the US South.
Obviously there was a slave trade prior to the invention of the cotton gin (1793, well after the Declaration of Independence (US)), but the significant growth of the slave trade in the US occurred after the invention of the cotton gin (which lead to the massive growth of the cotton trade; especially in the US southern states as they had a better climate for cotton growth).