Yes, this is the reason that cotton production had shot up.
Step-by-step explanation:
The invention of the cotton gin made it very easy for the workers to use a machine to separate the cotton from its seed instead of doing it manually by hand which takes a lot of time.
This increased productivity in the cotton fields.
Effectively, this meant that more cotton can be worked from raw to the industrial one.
Thus Britain imported raw cotton from the colonies and used cotton gin to make the finished products often.