Here are two examples of higher prices:
1800 - 37¢
1801 - 44¢
By 1850 the price had plummeted to about $.10 dollars per pound. In 1857, it rose to $.15, a fifty per cent increase, but still significantly below earlier years.
As a result, cotton was extremely costly to produce and the price reflected that.
By 1850, cotton was extremely cheap to produce thanks to mass ginning that eliminated millions and millions of man hours of labor - yet demand was still so high that - as your source claims - it's price went up 50% in seven years.